THE
ENGINEER'S VALUING ASSISTANT.
LONDON : PRINTED BY
SPOTTISWOODE AND CO., NEW-STREET SQUARE
AND PARLIAMENT STREET
THE
ENGINEER'S VALUING ASSISTANT:
BEING
A PRACTICAL TREATISE
ON THE
VALUATION OF COLLIERIES AND OTHER MIN'fcS
INCLUDING
KOYALTIES, LEASEHOLDS AND FREEHOLDS, AND
ANNUITIES FROM OTHER SOURCES,
JJHtf) &ule& jparmul*, anfc
ALSO
NEW SETS OF VALUATION TABLES
CALCULATED ON THE PRINCIPLE OF ALLOWING INTEREST TO THE PURCHASER
OF ANNUITIES AT ONE RATE, AND REDEEMING THE CAPITAL INVESTED
AT ANOTHER, AND PRACTICABLE RATE PER CENT. ;
AND
TABLES OF VALUES
SHOWING THE DISCREPANCIES EXISTING IN THE ORDINARY TABLES OF PRESENT
VALUES, AND THE ERRORS CREATED BY THEIR USE ;
SOURCES FOR THE REDEMPTION OF CAPITAL
AT DIFFERENT RATES PER CENT. J
REMARKS UPON HOME AND FOREIGN MINES
AS INVESTMENTS; ETC.
BY
H. D. HOSKOLD, F.R.GKS., F.GKS., M.Soc.A. & INST.M.E., &c.
CIVIL AND MINING ENGINEER I
Late Mining Engineer to the Dean Forest Iron Co. for 16 years;
Author of 'A Practical Treatise on Mining, Land, and Railway Surveying and Engineering*
LONDON :
LONGMANS, GEEEN, AND CO.
1877.
All rights reserved.
THIS WORK
IS RESPECTFULLY DEDICATED
TO
J. PEASE, ESQ., M.P.
BUTTON HALL, GISBOROTJGH,
v and
> 5 " t?
H. HUSSEY VIVIAN, ESQ., M.P.
PARK WERN, SWANSEA,
BY THE AUTHOR.
PREFACE.
THE EFFORTS put forth in the literary world at the present time,
and the facility of production and means of distributing the
results of such labours, are truly astonishing, and without a
parallel in past times, and for the multiplication of Books of
all classes there seems to be a growing necessity, but although
various subjects connected with Arts, Sciences and Manufactures
have been largely treated upon, that of the Valuation of Mines
has been entirely neglected.
This circumstance is the more surprising in as much as the
subject is one of great national importance, affecting, as it does,
at least in some degree the interest of all those who are con-
nected with Mining and other branches of industry.
In these times, commercial prosperity in general seems to
depend more or less upon its relations to honest and successful
Mining adventure ; and although Mining and other branches of
trade have received and will still receive healthy stimulus,
nevertheless there are periods of reaction, causing depression,
the origin of which it is not always easy to trace and explain.
However, in very many cases it may be referred to inflated
notions of speculation, creating undue excitement, error in judg-
ment, and an unwarrantable lavish expenditure of capital
upon properties not capable of yielding profits compatible with
the outlay.
Immense sums of money are frequently spent in the pur-
chase of mineral properties, and it is a common occurrence that
much more is paid in order to secure them than they are really
viii PKEFACE.
worth, and cases coming within experience are by no means few
where the estimated value has exceeded the true value by 40 or
50 per cent., due in many cases to the employment of an
erroneous years' purchase. Table XII exhibits the source of
such discrepancies.
True value, and the economic expenditure of money upon
the purchase and development of any property, are therefore
matters of such paramount importance, that it has been consi-
dered necessary for the general interests of the public to point
out in this work, and illustrate by ample practical examples, how
such discrepancies as those referred to have arisen, and the
means necessary to be adopted in guarding against such an
enormous waste of Capital.
Taking a rational view of the matter, it is desirable that
any mode of deducing Values, having for its basis nothing better
than an approximate rule, or a mere guess, should yield to more
accurate treatment ; and as the interest at stake is so great, and
almost universal, it seems to be most essential that the public
should possess some standard work of reference embodying
information and easy rules of a reliable and practicable character,
so that by mere consultation, the comparative merits and value
of Mineral and other kinds of property that may come under
consideration may be readily determined. Hitherto, however,
no work of this description and specially devoted to this subject
has appeared.
The present work is therefore an attempt to supply this
need ; and it has been written chiefly with a view to facilitate
such calculations as are required generally, and especially by
those of the Profession on whom more particularly devolve the
important and onerous duties connected with Valuation, to in-
troduce a general system based upon equitable and scientific
principles, and to assist in obtaining more uniformity and
accuracy in general practice.
PREFACE. ix
In past years when I was extensively engaged in valuing
coal and other mines, the labour connected with the necessary
and frequent calculations involving the use of rules derived from
first principles became so tedious, that I determined once for
all to prepare full and complete sets of Tables required, to
be employed in Valuation as labour savers.
After much thought and labour this task has been completed,
and the result supplied by the publication of this work, in which
I have endeavoured throughout to render the treatment of the
subject as simple and intelligible as its nature seemed to admit
of, and, as I believe, free from all unnecessary mathematical sur-
roundings.
Throughout the work will be found numerous examples of
all the more important cases that can occur in practice, both in
Simple and Compound Interest as applied to Valuation generally,
including Annuities derived from Collieries or other Mines,
Koyalties, Leaseholds, Freeholds, and other sources.
These examples are derived from practice, and the utility
and advantage of the Tables in expediting work are fully
exemplified, and where, for the sake of illustration it has been
found proper, or convenient, Logarithmic computations have
been resorted to.
At the termination of the Third Part of the work a few pages
have been specially devoted to Logarithmic calculations of a par-
ticular order, and the accuracy of the numbers selected from the
tables has been rigidly tested, and in no instance has any error
been discovered in them. In these calculations the great supe-
riority of Mr. Gray's 12-figure Logarithms is made apparent ; and
the readiness with which any Logarithm or Anti-logarithm can
be found to 12 places of decimals is the great feature and
recommendation of his Tables.
Plain rules and formulae of a special character have been
xii PEEFACE.
author is of itself a sufficient guarantee of the accuracy of the
principles involved in a work with which he may in any way be
connected.
I have much pleasure in stating that I have received very
great assistance from Mr. William Hewlett, M.E., one of my
former Articled Pupils, and late Engineering Assistant. He
re-computed and corrected nearly the whole of the Tables and
Examples in this work, and for a period extending over a year
and a half took a considerable interest in its progress.
I am also indebted to Mr. William A. Taylor, who has ex-
hibited great kindness in assisting me, by reading, comparing
and correcting the proofs a labour of no small importance.
I now leave the work in the hands of an enlightened public,
venturing to express a hope that it may prove as much a be-
nefit to them as it has been a pleasure to me in writing it, and
I take this opportunity of expressing my grateful acknowledg-
ments for the liberal support and encouragement accorded to my
former publications.
H. D. HOSKOLD.
LONDON: May 1877.
INTRODUCTORY NOTE
BY
PETER ORAY, F.R.A.S.
Honorary Member of the Institute of Actuaries, and Author of ' Tables and
Formulae for the Computation of Life Contingencies' &c.
IA.
INTEODUCTOEY NOTE
THE PRESENT WORK, on the subject of the Valuation of Mineral
Property, contains matter of very great interest for both the Pro-
fessional Valuer, and the Actuary : for the former in its ample
discussion of the principles which should guide him in the
discharge of his duties ; and for the latter in its treatment of the
problems (of a somewhat unusual character) which arise in the
practical application of those principles, as well as in the mass
of original Tables it contains, specially adapted for the easy and
exact solution of any case that may present itself. The Tables
occupy no fewer than 225 pages, and of themselves form a stand-
ing monument to the perspicacity and industry of the author.
There is found to exist among professional valuators some
diversity of opinion and practice in regard to certain points in
the purely actuarial portion of their work; and upon these points
I have been requested to give my opinion. I will do so as
briefly and plainly as I can, supporting my views with the
requisite amount of demonstration, occasionally diverging,
perhaps, into cognate matters that may press themselves on
the attention.
The course of proceeding in the Valuation of a Mine appears
to be as follows : The valuator, in the exercise of his pro-
fessional skill and knowledge, names a sum and a term of years,
the former to be considered as the annual income to be derived
from the mine, and the latter as the number of years that this
income is to last. It is further arranged between the parties,
that the purchaser is to be allowed a specified rate of interest
on his outlay, during the entire term. The required value is
thus presented in the form of an annuity certain, the elements
of which the sum, the term, and the rate are known ; and
there remains only the conversion of that value into a present
sum.
xvi INTRODUCTORY NOTE.
One of the points on which I am requested to give iny
Opinion is as to the correct method of valuing the annuity
which forms the subject of the valuator's first determination.
Ordinarily the valuation of an annuity for a term of years,
when the rate of interest to be allowed to the purchaser has been
arranged, is a sufficiently simple matter. The well-known
tables of Smart (reproduced by Jones in his Treatise on Annui-
ties)^ and others, furnish, in the cases that usually arise, all the
aid that can be required, even by the most inexperienced
computer. But the cases with which we have here to do are
somewhat complicated by the entrance of a consideration that
does not present itself in so pressing a way, at least in gene-
ral practice.
It cannot be doubted that the purchaser of an annuity for a
term, on which he is to be allowed interest at a specified rate,
ought, as regards this transaction, to be in the same position,
pecuniarily, at the end of the term, as if he had lent his money
during the term at the same rate. The lender receives his
interest annually, and has the sum lent returned at the end of the
term. But the purchaser of an annuity must recoup himself by
investing the excess of his annuity over the annual interest on his
outlay, at such a rate that at the end of the term his capital
will be reproduced. The lowest rate at which this reproduction
can be assumed by the vendor or purchaser to be effected,
is the rate allowed in the purchase of the annuity, as will
presently be shown. In the case of annuities purchased at
current rates, but little inconvenience and loss will occur to the
purchaser from this restriction as to the rate of re-investment,
since practicable rates in respect of such will usually differ but
little from the stipulated rates. In the cases with which we
are here concerned, however, the state of matters is far other-
wise. In the purchase of mining property the purchaser, for
reasons with which we have nothing here to do they are fully
discussed in the following work^- is usually, perhaps always,
allowed a rate of interest on his outlay far exceeding that at
which he can invest the surplus of his annuity, which is called
with propriety the Redemption Fund ; and hence, if the ordi-
nary tables are used in the valuation of the annuity determined
and assigned by the valuator, the result must be a loss to the
purchaser, more or less heavy according to circumstances, since
INTRODUCTORY NOTE. xvii
in them the difference between the two rates is ignored. In
the present connexion, therefore, special methods must be em-
ployed.
I will show here, first, that to reproduce the capital at the
end of the term, when the tabular value of the annuity is used,
the redemption fund must be invested at the stipulated rate,
that is, the rate allowed to the purchaser ; and I will then show
how, when the practicable rate is taken account of, the value of
the annuity may be correctly determined.
Denote by a the annuity for n years, and by P n the purchase
money, which is to yield the purchaser r per on his invest-
ment.
The tabular value of the annuity is, we know,
whence
P n r r
a = ** .
I v n
Now, a year's interest on P n , the purchase money, is P n r', and
therefore, in accordance with what is above stated,
is the redemption fund ; and it has to be shown that this, if
invested as it accrues, at the rate /, will amount to P n in
n years.
p
_ P ^ _
lV n lV
Multiplying numerator and denominator by (i -f/) 71 , this ex-
pression becomes.
p
and this we know is the annuity which, at the rate /, will
amount to P n in n years. And it is thus shown that when the
value of an annuity is determined by the common tables (for
T _ fl*fl>
those tables consist of series of values of - ), it is neces-
sarv, in order that the capital shall be reproduced at the end
of the term, that the redemption fund should be invested at
the rate allowed to the purchaser.
XViii INTRODUCTORY NOTE.
I am now to show how, when the stipulated rate that
allowed to the purchaser is r', and the practicable rate that
at which the redemption fund can be invested is r, the correct
value of the annuity may be determined.
Let, as before, a be the annuity for n years to be purchased,
and P n the purchase money.
The redemption fund is aP n r' ; and if we denote by M n
the amount of an annuity of i, for n years, at the rate r, (the
practicable rate,) the amount of the redemption fund at the
end of the term will be (a P n r')M n . Hence, since this, by
condition, is to equal the purchase money, we have the following
equation :
and from this we get,
aM r
+ SJ*
This is the value required ; and it is in a form very convenient
for calculation, either by logarithms or otherwise. The form,
however, may be varied. Thus, dividing numerator and deno-
minator by M n9 we have,
a
Mj
and being the annuity which will amount to i in n years
in other words, the redemption fund necessary to produce i
in that time at the rate r, if for- we write s /t , the expression
lu n
assumes the more compact form,
and this is the most convenient for use when, as in the present
volume, we are furnished in Table V, with the values of s n for
all terms and rates that can present themselves in practice.
The form chiefly, for special reasons, used by Mr. -Hoskold
in the body of the work, is the basis of (3), by substituting
/y*
in it for 8 its value --
INTRODUCTORY NOTE. xix
We thus have,
a a
- , (4)
writing R for I + r.
I give now a numerical example, in further illustration of
what precedes.
Let the annuity be 100 for 20 years, on which the pur-
chaser is to be allowed 5 per' cent., while the redemption fund
can be invested only at 3 per cent. The present value the
purchase money is required.
I shall solve this first by the formula (J.), which ignores the
difference between the stipulated and the practicable rates.
The formula is, for this case,
p . 1 00(1 -Q
~^r
This might be worked by Table IV, which gives the value of
v n for all required rates and terms. But it is easier to take at
once the value of the annuity of i for 20 years, from Table
XII, p. clxxvi. We thus have P 20 = 1246-221.
This value fulfils the condition of replacing the capital at
the end of the term, if the redemption fund can be invested at
5 per cent.
Thus, a year's interest on the capital is 62-311, and hence
the redemption fund is 100-62-311 = 37-689. Now, the
amount of i per annum in 20 years, at 5 per cent., being
(Table III, p. xxxvi) 33-0660, that of 37*689 will be 33-066
x 37-689 = 1246*223, establishing the theorem.
On the other hand, if the redemption fund can only be in-
vested at 3 per cent., its amount at the end of the term will be
no more than, (p. xxxiv,)
26-8704 x 37-689 = 1012-718,
showing a deficiency of 233-503.
I now give a correct solution by (3).
The formula is,
s 20 +'05
a2
XX INTRODUCTORY NOTE.
s, (p. liv) -03721571 at 3 per cent.
05 ^5__
08721571 log 2-9405948
colog 1-0594052
100 log 2-
P 20 1146-582 log 3-0594052
Hence, 1146-582 is the value sought, and it fulfils the pre-
scribed condition as follows :
A year's interest on P 20 , at 5 per cent., is 57*329, and the
redemption fund, therefore, is 100 57*329 = 42*671. And
26*8704 x 42-671 = i 146-582, as it ought to do.
It is needless to enter on an inquiry as to the comparative
advantages of the expressions that have been given for the solu-
tion of the problem under consideration, for in truth almost
every case under the problem that can present itself has been
already solved, and the solution is recorded in the following work ;
so that it is very rarely indeed that there will be occasion to
have recourse to any formula. Tables VI to IX, occupying pages
Ixv to cxi, give the years' purchase, that is, the value of P n on
the supposition that the annuity to be purchased is 1, for
every practical combination of the stipulated and the practicable
rates, with the element ti, the duration of the annuity ; so that
to complete the valuation there only remains the multiplication
of the proper tabular value by the annuity whose value is
required. The process, in fact, is entirely assimilated to that
requisite in the use of the common tables, with the important
distinction in the results that, in Mr. Hoskold's tables, due
account is taken of the disparity between the stipulated and the
practicable rates, while in the common tables this disparity is
altogether ignored.
Table XII is very instructive. It shows, for various com-
binations of the stipulated and the practicable rates, the excess
of value assigned by the old (the common) tables over the true
value for every pound of annuity purchased. I leave this table
to make its own impression.
I have now indicated with sufficient distinctness that the
method of valuation which I have sought to illustrate, and which
is that advocated and employed by Mr. Hoskold, is the correct
one. But before leaving the subject I would call attention to
INTRODUCTORY NOTE.
a variety of the problem which presents itself to be dealt with
when, as is sometimes the case, the annuity to be purchased is
deferred ; that is, which, while making the same number, n,
does not commence its payments till after the lapse of, say, t
years. The symbol for the value of the annuity, when subject to
this condition, might with propriety be P,,,,. 1
The value here, in accordance with a well-known principle, is,
equivalent forms, since v l and (i + r')* (in which r' is the stipu-
lated rate), are reciprocal, each to the other; and hence, when
the value of an immediate annuity is found (or known), that of
the same annuity, when deferred, can be readily deduced.
A demonstration is given also, by Mr. Hoskold, on p. 34,
founded on elementary principles. And I may remark that it
is, as I believe, only now, that, for the first time, the value of
the deferred annuity is correctly assigned.
Here, too, as in the case of the immediate annuity, the wants
of the computer have been anticipated and supplied by Mr.
Hoskold. Tables X and XI, occupying pages cxiii to clxxii,
contain the values, for most practical rates, of a deferred annuity
of i (the number of years' purchase), the periods of deferment
ranging from i to 10 years. In consequence, the necessity for
having recourse to a formula will very rarely occur, the value
required in any particular instance being usually obtainable
from the tables named by the merest inspection.
It is only such as have had some experience in the construc-
tion of tables who will be able to realise the great amount of
labour involved in the formation of those that have been specially
referred to I mean Tables VI to XI ; but it is very certain that
everyone who may have occasion to use them for practical pur-
poses will bear willing testimony to their great utility,
1 Mr. Hoskold uses P t+n . The form above suggested seems on the whole
preferable : the suffix t + n, being the sum of the periods of deferment and dura-
tion together, is the entire term over which the transaction extends. [I w r ill add
that, having instinctively here written deferment, while Mr. Hoskold writes
deferrence, I have been accustomed to do ?o on the authority of the late
Prof. De Morgan (Compan. to the Almk., 1840, p. 16). I find neither of the
words in the dictionaries to which I have present access ; probably therefore
both may be equally legitimate or illegitimate.]
XXli INTRODUCTORY NOTE.
On pages 30 to 32 Mr. Hoskold points out, demonstrates,
and freely uses a relation that may be thus enunciated :
The annuity for n years that i will buy, exceeds the
annuity that will amount to i inn years, by r, the interest of
i for a year.
This relation I find is not unknown to some actuaries ;
nevertheless, as it has not yet, so far as I know, found its way
into the books, it may be worth while here to place it on record.
The proof is very simple. The annuity for n years that I
will buy is,
i-v n '
which we may write thus,
r(i+r) r
and the annuity that will amount to 1 in n years is
Subtract now the second from the first, and we get
and so the theorem is established.
The foregoing relation can be shewn to hold from ether
considerations than those adduced above. The formula (3), p.
xiv, ante, when a = I , becomes
and denotes the value of an annuity of i for n years, at the
rate /, when the redemption fund is invested at the rate r ; and
if / = r, the value indicated is that of the ordinary annuity.
In this case then s n + r will be the annuity for n years that i
will buy, since this annuity and its present value are mutually
reciprocal. And hence, since s n is the annuity that in n years
will amount to i, we again see the relation to subsist.
INTRODUCTORY NOTE. xxiii
I will just add by way of corollary, that, the value of the
annuity which i will buy being of course i 9 and that of the
annuity which in n years will amount to i being v n (since
this is the value of i to be realised in n years), the difference
of these values is I v n . Now this must be the value of an
annuity of r, (the quantity by which the annuities themselves
differ,) for n years. And this is seen to be the case as follows :
i v n
xr= i v n .
There is another point in the valuation of Mining Property
in regard to which diversity of opinion and practice exists among
valuators ; and on which also I have been requested to give
my opinion. The point here referred to arises as follows :
A mine is to be sold having a specified term to run. The va-
luator, in the exercise of his best judgment and technical skill,
assigns the annuity on which the purchaser may probably reckon
during the term of duration, with the rate of interest to be allowed
him on the purchase-money. Here a new consideration some-
times perhaps I should say frequently arises. The sum named
by the valuator as the probable annual return to the purchaser is
that which he considers ought to be the return if the mine is fully
developed. At the same time he may be of opinion that to
bring the mine into this condition an expenditure of greater or
less amount in the early years of the mine is necessary. In
these circumstances he does not abate from his estimated annual
return, but names a sum, as cost of development, to be expended
by the purchaser in equal portions during the first few years of
the mine, to bring the mine into the required condition ; and
which sum consequently, when valued subject to the conditions
of its disbursement, will constitute a deduction to be made from
the gross value of the mine, so as to determine the amount of
the portion of this value payable to the vendor. And it is as to
the manner in which this deduction is usually made that I am
requested to give my opinion.
For illustration I quote a case given by Mr. Hoskold, p. 119.
The term of a colliery for the next 21 years is to be sold.
It at present yields a net return of 8,000 per annum ; and the
valuator estimates that to maintain the return at this rate.
INTRODUCTORY NOTE.
during the term, it will be necessary for the purchaser to
expend in works, &c., 12,000, in equal portions of 4,000
during each of the next 3 years. Also, the purchaser is to be
allowed 20 per cent, per annum on his outlay, redeeming
his capital at 3 per cent. Eequired the net amount now
payable.
I will determine the required amount first in the customary
way. .
By Table VII, p. xcii., the gross value of the mine is
4-25764225 x 8,000= 34.061-138
And the abatement is :
Cost of works, &c. . . . 12,000
Interest on the same, 3 years at
5 per cent 1,800 13,800-000
Net amount now payable, . . . 20,261-138
Now this cannot be correct. The abatement here is the
amount in 3 years, at 5 per cent, simple interest, of the dis-
bursements to be made by the purchaser ; and it could be legiti-
mate only if the entire 12,000 had been disbursed three years
ago. The purchaser in fact receives a bonus for delaying pay-
ment of a portion of the purchase-money a bonus, moreover,
which increases as the delay increases.
Surely nothing further needs be said to establish the inad-
missibility, in accordance with any rational or recognised prin-
ciple, of the method just exemplified for determining the net
amount now payable.
The following shews the manner in which 1 consider the
required determination ought to be made :
Gross value as before, . . . 34,061-138
Abatement for cost of works :
Value of an annuity of \
4,000 for 3 years, at 3
percent. (Table XIII)
2-82861 xOoo =
Net amount now payable, . . 22,746-698
INTKODUCTOKY NOTE. XXV
The annual payments to be made by the purchaser consti-
tute an annuity, and there exists no conceivable reason why
they should not be valued as such.
The only point in regard to which there may be thought
to be room for question as to the validity of the method here
employed, is the rate at which the annuity of 4,000 ought to
be valued ; and somewhat plausible reasons might be adduced
for making the valuation at the rate of 20 per cent. I am
quite satisfied, however, after full consideration, that any
arguments in this sense that could be assigned are groundless.
The purchaser is entitled to 20 per cent, on his outlay, which
is the gross value of the mine. It is true that a portion only of
this in the present case the larger portion goes at once into
the pocket of the vendor ; but the rest is expended in the ame-
lioration of the property, whereby the purchaser is proportio-
nally benefited.
I am pleased to find myself in regard to this second method
of solution in entire accordance with Mr. Hoskold, who has
largely attended to the subject; and whose remarks on pp. 120,
121, I commend to careful consideration.
P. GRAY.
LONDON :
June 11,1877.
CONTENTS.
PAG It
PREFACE, ....... . . . . vii
INTRODUCTORY NOTE, ...... . xiii
PART I.
REMARKS UPON THE VALUATION OF MINERAL PRO-
PERTY AND MATTERS CONNECTED THEREWITH.
Definition of ' Value ' Labour the mainspring of creative wealth Ex-
tent of mining operations Importance of legitimate home mining
Worthless schemes Skill, judgment, and a knowledge of the appli-
cation of scientific principles, necessary for successful mining Legiti-
mate mining a lucrative undertaking Mining legislation Supposed
early exhaustion of our minerals erroneous Other discoveries to be
made No insuperable difficulty in winning deep mines Status of
mining report writers, and persons acting as engineers Necessity
for firms of bond fide mining engineers in large commercial centres
An engineer should be a financier Operations on virgin tracts not
mere speculation An engineer should be a geologist Extension of
Staffordshire, Leicester, and Somerset coalfields Extension of Staf-
fordshire field due to Mr. Johnson Trials by boring Mismanage-
ment Quantity of water in known fields can be computed before
pits are sunk Ample machinery should be provided Interference
by boards of directors Engineer who reports on property should
bring out every point in favour of or against it Estimating value of
opened mines Quantity and proportion of coal in seams ; mode of
estimation Yield of haematite iron mines Estimation of quantity
from unopened mines Estimate of cost of winning Conditions that
affect the cost of winning Ample percentage should be allowed on
purchase-money to cover risk Mining engineer best qualified to
estimate risk Redemption of capital Estimation of annuity from
general accounts Difference of opinion as to amount of percentage
to be allowed to a purchaser Mr. Buddies opinion in 1829 Dunn's
reference to Mr. Buddie Discordance in the statements Rating of
xxviii CONTENTS.
PAGE
m j nes Inquiry by House of Commons in 1857 Opinions of Messrs.
Pease, Dobson, Cotterell, Taylor, and Schneider, taken in evidence
Mr. Scott's opinion Example of value in Dunn's work on the coal
t^de Fallacy of his mode of valuation Bisk cannot be determined
by rule Circumstances should vary the percentage allowed on
purchase-money Value is a question of compound interest Esti-
mated annuity from an undeveloped mine should be treated as de-
ferred during period of development, . , , , . 1-20
PART II.
CONSTRUCTION OF TABLES OF VALUES, WITH
RULES AND FORMULAE.
Nature and value of annuities Increase of principal ; formula, rule and
example Present value of a perpetuity of i payable once every
nth year, the first payment due n years hence ; formula, rule and
example Present value of a perpetuity of i deferred n years; for-
mula, rule and example Theory and mode of ascertaining the ad-
vantage of payment of annuity at varied intervals ; values by yearly,
half-yearly, and quarterly payments Amount of I per annum in n
years ; formula, rule and example Present value of i due n years
hence ; formula, rule and example The annuity which i will pur-
chase, found by adding together the redemption fund and interest
Redemption fund to reproduce i in n years; formula, rule and ex-
ample Present value of 1 per annum for n years, allowing one
rate of interest on purchase-money, and another rate of interest for
redemption ; formula, rule and example Recapitulation of formulae
Examples illustrative of, and demonstrating the accuracy of, the
formulae Deferred annuities, with two rates of interest ; formulse,
rule and example Discussion of subject, with further examples;
formulae and rules Difference of opinion ; analysis of ditto Rule
established and confirmed by further practical examples Redemption
of capital ; examples Conditions considered in forming the tables
of values The tables calculated from first principles Inaccurate
tables worse than useless Tables great labour-savers, as values may
be found by mere inspection The amounts proved by logarithmic
process Tables have been frequently published, but have not been
calculated above 10 per cent. Other writers, rules, formulae, and
papers written on two rates of interest Problem ; solution of pro-
blem by other writers Mr. Peter Grays solution Rates of interest
allowed on mining property 10 to 25 per cent. Errors in the con-
CONTENTS. xxix
struction of ImvoocTs table ; how such errors have arisen Errors in
Mr. Taylor's and Mr. Dunn's years' purchase ImcoocFs years' pur-
chase compared with the true value, showing discrepancy of fr.s
tables Loss of capital by use of such tables ; examples Deferred
annuities with two rates of interest ; rules in use only give approxi-
mations Thoman's rule, with example Correct formula and rule,
with example, showing difference in value between it and Thoman's
Difference of value between correct rule and Inwood's rule, show-
ing loss to a purchaser by valuing with old tables Securities for ob-
taining redemption of capital Surplus annuity from mines cannot
be re-invested in the same mines to reproduce original capital Mr.
House's view of the old tables of values, . .... . . 21-62
PART III.
PRACTICAL EXAMPLES IN VALUING COLLIERIES,
IRON AND OTHER MINES, ROYALTIES, LEASE-
HOLDS, FREEHOLDS, LIFE INTERESTS, $c.
SIMPLE INTEREST. Use of tables for facilitating calculations Logarith-
mic calculations To find the amount of a certain sum at a fixed
rate per cent, and number of years To find the principal when the
amount, rate per cent., and number of years are given To find in
what time a principal will amount to a given sum at a fixed rate per
cent. To find at what rate per cent, a principal will amount to
a given sum in a certain time To find the discount to be allowed
on a certain sum at a given rate per cent, and time To find the
amount of an annuity within a given time and rate per cent. To
find the time in which an annuity will amount to a given sum at a
certain rate per cent. To find the rate per cent, when an annuity
amounts to a given sum within a certain time, . . . 63-67
COMPOUND INTEREST. To find the amount of a certain sum within a
given time and rate per cent. ; proof by logs To find the principal
that will amount to a certain sum within a given time and rate per
cent. ; proof by logs ; Gray's 1 2-figure logs To find the rate per
cent., when the principal amounts to a certain sum within a given
time ; proof by evolution and logs. To find the time in which a
principal will amount to a certain sum at a given rate per cent. ;
proof by the tables and by logs, ...... 67-69
ANNUITIES. To find the amount of an annuity within a given time and
rate per cent. ; proof by logs. To find the annuity that will amount
XXX CONTENTS.
PAGE
to a given sum within a certain time and rate per cent.; proof by
logs and by the tables To find the annuity that will amount to a
given sum within a given time and rate per cent., when payments
are made half-yearly and quarterly ; proof by the tables To find the
time in which an annuity will amount to a certain sum at a given rate
per cent. ; proof by logs To find the rate per cent., when an annuity
amounts to a certain sum within a given time To find the present
value of a certain sum within a given period, at a fixed rate per
cent. ; proof by logs To find the sum that may be secured at the
end of a certain period by a present payment at a fixed rate per
cent. ; proof by logs To find the time at the end of which a certain
sum may be disbursed, by a present payment at a fixed rate per cent.;
logarithmic process To find the rate per cent., when a certain sum
due in the future may bs discharged by a present payment within a
given period ; log process, 69-73
PRESENT VALUE OF ANNUITIES. To find the value of the lease of an
estate having a certain time to run, at a given rate per cent., when
the annual value is in excess of the annual rent To find the annuity,
to continue a certain number' of years, that may be purchased for a
given sum, at a fixed rate per cent. To find the duration, when an
annuity is purchased for a given sum, at a fixed rate per cent. ; log.
process, . . . . . -.. . . . . . 74,75
PERPETUITIES. To find the present value of a perpetuity at a given rate
per cent. To find the perpetuity which may be purchased for a given
sum and rate per cent. To find the rate per cent, when a certain sum
will purchase a given perpetuity, 75
REVERSIONS. To find the present value of a deferred annuity, to con-
tinue a given time at a fixed rate per cent. To find the annuity de-
ferred, to continue for a certain period at a given rate per cent., that
may be purchased for an immediate given sum To find the duration
after a period of deference, when a certain sum will purchase a given
annuity, at a fixed rate per cent. ; Calleffs 2ofigure log table To
find the present value of the reversion of a perpetuity of a certain sum
at a given rate per cent. To find the annuity that should be pro-
duced by an estate in fee-simple, which may be purchased for a given
sum and rate per cent., deferred a certain period To find the time a
perpetual annuity may be deferred before being entered upon, when
it is purchased for a given sum and rate per cent. To find the sum
to be paid for renewing the lease of an estate when a certain
period has expired, at a given rate per cent, and annual rental
Interest available to a purchaser for the redemption of his capital
High rates of interest involve extra attendant risk Monetary trans-
actions to be governed by average rate of interest over a series of
years Normal rate of interest 3 per cent, . . 76-79
VALUATION OF MINES. To find the present value of a freehold colliery
when interest on capital is at one rate, and interest for redemption at
Vr.
CONTENTS. xxxi
PAGE
another rate, the duration and annuity being given To find the re-
demption fund necessary to produce i within a given time ; formula,
rule and example To find the present value of the unexpired term
of the lease of a colliery subject to a lessor's royalty ; the annuity,
rate per cent, on purchase-money and for redemption, royalty, and
value of the plant being given To find the present value of a colliery
with a certain annuity and duration, subject to a lessor's royalty to
be paid quarterly ; interest on purchase-money, royalty, and for re-
demption, being given Difference in present value due to yearly and
quarterly payments ; rate of interest gained by quarterly payments
To find the present value of the lease of a colliery having a certain
annuity and time to run, subject to a variation in the lessor's dues at
fixed periods, and the expenditure of an additional sum of money to
sustain the annuity during the period ; interest on the purchase-
money and for redemption being given, together with the estimated
value of the plant Detailed values 'Customary' interest Valua-
tion of the lease of a colliery under varying circumstances Practical
example ; detailed values ; redemption fund, &c. Remarks on last
preceding case To find the present value of an unopened colliery
with the overlying estate ; time and cost of development, prospective
annuity, rate per cent, upon purchase-money, for redemption, royalty,
wayleave, &c., being given Value under similar conditions as in pre-
ceding case, payments to be made half-yearly Difference in value
between yearly and half-yearly payments Value under similar con-
ditions, payments being made quarterly Differences in value between
yearly, half-yearly, and quarterly payments To find the value of
the lease of a mineral property with several seams of coal and iron
ore ; annuity, time of duration after opening the seams, interest on
purchase-money and for redemption, wayleaves, royalties, &c., being
given Details of the whole of the valuations in preceding case Re-
duction from gross to net values Summary of preceding cases
Remarks on last preceding case Lease of 2 1 years' duration Com-
parison of values in preceding case, time of lease being shorter Sum-
mary of values under shorter duration of lease Deduction arrived at
from comparison of values To find the present value of the life in-
terest of a person A, aged .r, in the royalty of an iron mine ; the
annuity, interest on purchase-money and for redemption, being given;
formulae, rule and example Correct method of valuing compared
with ( customary ' mode ; detailed example, .... 80-121
DEDUCING VALUES FROM TABLES OF MULTIPLES OF YEARS' PURCHASE,
&c. Nature and use of tables To find the annuity, the present
value being given Deferred values Mode of determining deferred
values from Tables (IV) and (VII) Multiples of the annuity which
i immediate will purchase; examples Multiples of the annuity i
deferred will purchase ; examples Multiples of redemption funds ;
examples Various methods of arranging Tables of Multiples exhi-
bited as a precaution against those who pirate Tables, . . 121-140
xxxii CONTENTS.
PAGE
REMARKS ON LOGARITHMIC CALCULATIONS. Very accurate results to
be obtained Properties of logarithms available for arithmetical ope-
rations 7-figure logs Mr. Gray's 12-figure logs Determining
amounts by logs Results by Mr. Gray's 12-figure logs Present
value by logs ; Value by Table (VII) and by 1 2-figure logs Present
value deferred by logs : Value by 1 2-figure logs and by Table (X)
Difference in value deferred between Table (X) and 1 2-figure logs
Redemption fund by logs Difference in value between 7 and 1 2-
figure logs, and between 1 2-figure logs and Table (V) Present
value due n years hence, by logs Difference in value between 7
and 12-figure logs, and between 1 2-figure logs and Table (IV)
The annuity deferred which i will purchase, by logs Difference
in value between 7 and 1 2-figure logs, 140-144
PART IV.
SOURCES FOR REDEMPTION or CAPITAL. Redemption of capital at rates
of 2, 3, 3^, and 4 per cent. Difference in value of years' purchase,
redemption being at different rates Consols as a source of redemp-
tion Maximum and minimum rates of interest by sale of stock
Causes operating to influence stock Stockbrokers, agents, and job-
bers Money market influenced by the press Rates of interest pro-
duced by British railways Railway preference stock Debenture
stock Indian, Colonial, American, and other foreign railways, obli-
gations and bonds Colonial Government investments Insurance,
dock, shipping, telegraph, trust, and other industrial companies
Foreign stock, loans, bonds, &c. Care and judgment required in
selecting stock Indian railway debenture bonds Government in-
vestments Limited banks How to redeem the capital from sur-
plus annuity derived from mines, . , . . . . 145-151
REMARKS ON FOREIGN AND HOME MINING. Mistake to invest in foreign
mines indiscriminately Much depends on surrounding circumstances
Minerals of the United States The far West Argentine Repub-
lic Great percentage of silver in the Oero-de-Pasco district Draw-
backs to general working English colonies should be established
Mining in the Brazils, Australia, India, and New Zealand Legiti-
mate fields for enterprise Spain ; her minerals English companies
in Spain, and fortunes to be made there Legitimate home mining
most certain Valuable mines in the United Kingdom ; when to pur-
chase Commercial excitement ; its results Bubble companies, &c.
CONTENTS.
PAGE
Good mines must be secured to escape risk of capital Quantity
of minerals necessary to be raised from mines Ample machinery
should be provided for extracting large quantities of minerals Mode
of working suggested Those who should speculate in mining
Drawbacks to the success of a mine Purchasing foreign mines ;
extra risk incurred ; higher rate of interest should be allowed Gold
and silver mines Examples of deferred values ; Tables (A, B, 0,
and D) of Immediate and Deferred Values, for use in purchasing
foreign mines at high rates of interest, . . . ^ . .152-164
RECAPITULATION OP FORMULAE. System of notation, . . .165-167
TABLES.
TABLE
I. Amount of i in any number of years to 100, at , f, I, i,
i, if, 2, 2|, 2$, 2}, 3, 3i, 3i, 4t 4i 5, Si, 6 > 7, 8, 9, ">, u,
12, 13, 14, 15, 16, 17, 1 8, 19, 20, 21, 22, 23, 24, and 25 per
cent. Calculated to 10 places of decimals to 9 per cent., 6
places to 15 per cent., and to 5 places to 25 per cent., , i
II. Amount of i in any number of years to 100, at the rate of 3
per cent. Half-yearly and quarterly payments. Calculated
to i o places of decimals, . . , ^ . ' . xxi
III. Amount of i per annum in any number of years to 100, at
the rates of , f, i, i, i, if, 2, 2$, 2$, 2f, 3, 3$, 4, 4$, 5,
5, 6, 7, 8, 9, and 10 per cent. Calculated to 10 places of
decimals, ......... xxvii
IV. Present value of i due n years hence, at 3, 3^, 4, 4^, 5, 6, 7,
8, 9, and 10 per cent, to 100 years, and at 1 1, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, and 25, per cent, to 50 years.
Calculated to 8 places of decimals, . . xli
V. Eedemption funds necessary to produce 1 in n years, up to
100, at the rates of i, 2, 2$, 3, 3^, 3^, 4, 4i, 4i, and 5 per
cent., calculated to 10 places of decimals ; and for rates of 10,
12, 15, 1 8, and 20 per cent., calculated to 10 places of deci-
mals, and for 50 years. Also, for rates of 3, 3^, 3^, 3f , 4> 4i,
4, 4f , and 5 per cent., payments being made half-yearly and
quarterly ; calculated to 6 places ef decimals and to 100 years, li
VI. Present value of i per annum, redemption of capital being at
2\ per cent., and interest at the rates of 3^, 4, 4^, 5, 5, 6,
7, 8, 9, 10, 11, 12, 13, 14, 15, 1 6, 17, 18, 19, 20, 21, 22, 23,
24, and 25 per cent.; calculated to 8 places of decimals and
to 100 years, . . . V . 't > l*v
b
xxxiv CONTENTS.
TABLE PAGB
VII. Present value of 1 per annum, redemption of capital being at
3 per cent., and interest at the rates of 3^, 4, 4^, 5, 5^, 6, 7,
8,9, 10, n, 12, 13, 14, 15, 1 6, 17, 1 8, 19,20,21,22,23,24,
and 25 per cent. ; calculated to 8 places of decimals and to
100 years, . .. . . . * Ixxxi
VIII. Present value of i per annum, redemption of capital being at
3^ per cent., and interest at the rates of 4, 5, 6, 8, 10, 12, 15,
1 8, 20, and 25 per cent. ; calculated to 8 places of decimals
and to loo years, ....... xcvii
IX. Present value of i per annum, redemption of capital being at
4 per cent., and interest at the rates of 5, 6, 8, 10, 12, 15,
1 6, 1 8, 20, and 25 per cent. ; calculated to 8 places of decimals
and to loo years, . . . . . . . cv
X. Present value of i per annum, deferred I, 2, 3, 4, 5, 6, 7, 8,
9, and 10 years, redemption of capital being at 3 per cent.,
and interest at the rates of 4, 5, 6, 8, 10, 12, 15, 18, and 20
per cent. ; calculated to 6 places of decimals and to 100 years, cxiii
XI. Present value of i per annum, deferred i, 2, 3, 4, 5, 6, 7, 8,
9, and 10 years, redemption of capital being at 3^ and 4 per
cent., and interest at the rate of 20 per cent, j calculated to
6 places of decimals and to 100 years, .... clxi
XII. Comparison of the difference in value between the old or ordi-
nary tables of present values, and a portion of the new tables
calculated for this work, which allow one rate of interest on
capital and another rate for its redemption, for rates of interest
at 4, 5, 8, 10, 12, 15, 1 8, and 20 per cent., showing the
amount and rate per cent, lost on the purchase of every i
annuity, by the use of the old tables ; calculated to 5 places
of decimals and to 50 years, + , -i. . . clxxiii
XIII. Present value of i per annum in n years, redemption of capital
being at 2 and 2^ per cent, with interest at the same rates per
cent. ; calculated to 5 places of decimals and to 100 years, clxxxiii
XIV. Multiples of the present value of i per annum in n years;
interest at 2 1 per cent., and for redemption 3 per cent. ; cal-
culated to 9 places of decimals and to 100 years, . clxxxvii
XV. Multiples of redemption funds at the rate of 3 per cent,
per annum, necessary to produce i, 2, 3, 4, 5, 6,
7, 8, 9, and 10; or from i to 100,000,000, 2
to 200.000,000, 3 to 300,000,000, &c., up to 10, or
1,000,000,000; and by employing the decimal system of
notation, for any intermediate sum. Calculated to 10 places
of decimals and to 100 years, . . .-. .' ' . cxcv
CONTENTS.
XXXV
TABLE
XVI.
XVII.
Present value of a perpetuity of i } receivable once in every
nth year, the first payment due n years hence ; also of a per-
petuity of i deferred n years, at the rates of 3, 3^, 4, 4^, 5,
6, 7, and 8 per cent. ; calculated to 4 places of decimals and
to 100 years, . cciii
Single life annuities (Carlisle) ; interest at the rates of 4, 5, 6,
8, and 10 per cent, per annum, redemption being at the rate
of 3 per cent. ; calculated to 3 places of decimals, , ccxiii
XVIII. Decimal equivalents for every farthing in the pound ; also the
rate per cent. ; calculated to 8 places of decimals, . ccxix
INDEX,
[1-2,]
ERRATA.
Page 12, line 1C from bottom, reads, ' il possible ; ' should read, ' if possible.' Page 18, line C from
top, reads, 'Royal Forrester ; ' should read, ' Royal Forester.'
TABLE I.
| per cent., 91 years, reads 1-9937856536
should read
4-8950437169
104-987432
87-562068
71750-979401
2194245-22623
803-44413
421687917-92926
1-9737856536
3-8950437169
103-987432
87-565068
71750-879401
2194245-12623
863-44413
421687917-72926
TABLE III.
If per cent., 11 years, reads 12-0418439241 should read 12-0148439241
3 28 43-9309225246 42-9309225246
5 80 971-2288123372 971-2288213372
5 97 2251-9416156374 2251-9146156374
8 7 8-992803 8*922803
Corrections to be made by the Pen
Page Ixxii, for 63 years at 11 % reads 6'56986861 should read 8'56986861
Ixxiii,
Ixxxix,
xcni,
ccxix,
21
14 %
4.65651405
43
14 %
7-59203993
44
14 %
7-61245131
45
14%
7-63195168
46
14%
7-65059272
47
14%
7-66842240
97
22 %
7-5083922.6
lOfd.
ii
0.4479167
5-65651405
6-59203993
6-61245131
6-63195168
6-65059272
6-66842240.
4-50839226
04479167
Engineer's Valuing Assistant
PART L
PRELIMINARY REMARKS
UPON THE
VALUATION OF MINERAL PROPERTY
AND
OTHER, IMPORTANT MATTERS
CONNECTED THEREWITH.
)
^C4
PART I.
VALUE has been defined as < the quality in anything which fits
it to be given and received in exchange ; ' the meaning of the
term, however, has been much discussed and controverted. It
frequently occurs in the writings of political economists, and
has by them been employed in a modified sense, as ' value in
use ' and ' value in exchange.' Considered therefore relatively,
the former may be defined as representing the intrinsic, and
the latter as the estimated or market worth of an article.
The value of all exchangeable articles of utility must, how-
ever, be determined by the money worth set upon each com-
modity when brought into the market. The deduction then to
be arrived at from the general order of things is that a pound
sterling will command the purchase of a larger quantity of
articles of commerce of one kind than it will of another, and the
amount of each as compared with a pound sterling as a standard
will also vary with the fluctuations of trade, which are dependent
upon and regulated by the law of demand and supply. When,
therefore, materials intended for commercial purposes are pro-
duced and brought into a proper marketable condition, they
are said to possess a certain relative worth.
Value is as comprehensive as it is significant, constituting
as it does a general standard of the comparative excellence or
worth of all commodities necessary for the use, comfort, and
maintenance of life.
Such articles as are of daily consumption cannot, however,
be produced, distributed, and applied, without the expenditure of
a considerable amount of labour, which in itself is the mainspring
of creative wealth. The science of values, therefore, is one of
immense public importance, and underlies political economy in
all its branches.
I do not propose entering into this very important though
B 2
4 THE ENGINEER'S VALUING ASSISTANT.
intricate subject further at present, except so far as relates to
one of its leading branches, viz. Valuation of Mineral Properties.
Mining operations are now conducted over wide-spread fields,
in which the most highly educated, the profoundest thinkers, as
well as those in the possession of more moderate intellectual
capacities, may enter and work, each in his own way and order
contributing his mite of knowledge to the forwarding of the
general interest, welfare, and intelligence of the age.
The great importance of legitimate home mining to the
general support of the State, and the advancement of the in-
terest and creation of wealth of the English nation, can hardly be
over estimated ; but that there are other than honourable specu-
lations in mining matters, tending to produce opposite effects,
is also true, and it is this latter class that should be avoided,
discouraged, and exposed.
Millions of pounds sterling are annually sunk in worthless
mining schemes, many of which never were or could be capable
of yielding any good results, and some of them probably
never had any real existence at all, except perhaps in men's
imagination and on paper. It is therefore in this and many
other ways of a similar nature that an honourable, generous, and
unwary public are beguiled by the plausible representations of
designing men, and led on to contribute year after year to the
highly coloured but rotten plans and schemes for making money
so frequently presented to their view, until a crisis is produced,
resulting in the utter ruin of thousands.
In no branch of industry is there required so much real prac-
tical skill, sound judgment, indomitable perseverance, combined
with undeviating integrity of purpose, and the knowledge of
the application of scientific principles, as there is in Mining ;
indeed upon the possession of such qualities, exertion of abili-
ties, and timely application of these elements to the various
operations involved, the success of every mining enterprise
mainly depends ; but whether the general conduct of such un-
dertakings is always entrusted to persons of this description,
possessing abilities of the higher order, is quite another ques-
tion, and the general experience of the mining world would
probably go far to negative such an assumption. *
Mining, when honestly conducted, is undoubtedly one of the
most legitimate and lucrative undertakings that can possibly be
VALUATION OF MINERAL PROPERTY. 5
entered into, as is evinced by the large fortunes realized by
those who have entered into and carried on bond fide concerns
for lengthened periods.
Of late years Mining has become a leading branch of in-
dustry, and upon the general success of such adventures depends
very much that of nearly every other trade.
It is a subject of paramount importance, and has received
and is still receiving great attention both from legislators and
capitalists ; but whether the Acts of Parliament recently pro-
vided, regulating the working of mines, will prove of great
benefit, and justify public expectation, is a question time must
solve.
The amount of capital invested in mines during the past
three or four years was at least ten-fold, as compared to what
was expended in any similar period during the past half century.
During the former period the unprecedented stimulus given to
trade at home, on the Continent, in America, and the Colonies,
in articles of general commerce, has hurried on and produced
the present reaction.
As time goes on, however, producing a certain firm balance
in trade, and all illegitimate means of speculation have been
checked, avoided by the public, and crushed when dis-
covered, Mining will be placed upon a more solid foundation,
and will receive still greater attention from men of wealth,
and eventually become a strong arm of the nation.
The estimate of an exhaustion of minerals in our coal-fields
will, I trust, fall very short of the truth ; and as it is now
known by recent discoveries that some of the English mineral
fields extend much further than was formerly supposed, in time
new boundaries mil be assigned, giving to them a much larger
area, and, of course, a larger quantity of minerals. I believe
that other discoveries will also be made, upon further explora-
tions being conducted, leading to results not now anticipated.
Correct reasoning, therefore, should lead to the conviction that
Providence has placed and hidden from immediate view im-
mense wealth, at great depths in the earth's crust, which it is
to be hoped will be brought forth as necessity requires until the
end of time. Very little, if indeed anything definite, is known
as to the condition and thickness of the deeper coal-formations
below the Permian and the Trias ; but however deep coal-seams
6 THE ENGINEER'S VALUING ASSISTANT.
may have to be encountered in the future, I am convinced they
could not so exist without being of service to man, which
implies the possibility of extraction ; and that when their de-
velopment is found to be necessary, practical science will be
applied so as to overcome every difficulty which is now associated
with great depths. We are well aware that the area 'of circles
are to one another as the square of their diameters ; it is there-
fore reasonable to infer that by increasing the size and number
of down-cast shafts, also the in-take roads from them, and air-
ways to similar up-cast shafts, in proportion to the depth, with
the addition of more powerful ventilating machinery, a greater
quantity of air may be conveyed, reducing the temperature to
a fit condition for the support of life, and equal to that in
mines of comparatively shallow depth, with ordinary sized shafts
and air-ways. It therefore seems to me to simply resolve itself
into a question of time and cost in the development of the
deeper mines. With our present appliances for sinking shafts
by machinery, and with the great improvements they will
doubtless receive in the future, very great depths ought to
be attained at a moderate outlay, and in a shorter period, as
compared to the cost and time occupied by employing hand
labour.
The great drawback at the present time to the immediate
development of virgin properties, even of a good class, arises
chiefly from the fact that the minerals contained in them exist
at a considerable depth, and from opinions expressed by persons
who really have no experience or valuable knowledge with
regard thereto, but who nevertheless take occasion to insinuate
their advice with the view to damage the interests of some and
serve those of others. It is, no doubtj an undeniable fact
that capitalists are frequently misled as to the nature and
value of mineral properties.
Numerous mines of all kinds are constantly introduced to
the notice of capitalists, and each offer to sell is generally
accompanied with some statement of the merits of the property,
or a general report compiled by some local engineer. The
documents so produced are sometimes from men of great ability,
experience, and integrity, but in many other cases they are
concocted for a purpose, which in a general way may be seen
by men of judgment upon the face of them.
VALUATION OF MINERAL PKOPEKTY. 7
Unless, therefore, the writer of any such report is a man of
some status, it is customary for an intending purchaser to in-
struct some other engineer to proceed to the locus in quo,
examine into all matters connected with such property and
report thereon, the value and reliability of such report de-
pending entirely upon the ability and truthful purpose of the
engineer so engaged and trusted. Capitalists should therefore
use due caution in employing persons upon whose very word
so much depends.
I consider that gentlemen embarking their capital in exten-
sive mining undertakings should well understand the position
they are about to occupy, whether voluntarily entered into, or
by the introduction of others, and that persons entrusted with
their absolute confidence should make a sacrifice of their own
interests, if needs be, rather than deviate one iota from a
strictly honourable course.
The best advice should be given, whether each individual
proprietor is a business or financial man, or otherwise ; but that
parties are constantly let into worthless concerns is too obvious
a fact to admit of doubt or denial.
It appears to me there is great need in London and other
large cities for the establishment of firms of mining engineers,
comprising persons of practical ability from each mining
district, who would conduct their business in an honourable
way, and upon terms that would receive the countenance and
co-operation of bankers, brokers, financiers, and other gentlemen
seeking bonafide properties as investments.
All the mines of importance for sale in each district would
consequently be known, and in a short time would flow into the
offices of such establishments. Such a business, conducted
upon high class principles, must undoubtedly find support from
the general public, and would exert a healthy influence, and
produce results of incalculable benefit to the legitimate mining
community and public at large.
All advice upon mining business comes within the province
of the Mining Engineer, who should not only be a scientific
man, but a financier as well. It is, however, true that the
latter acquisition is not necessary to the actual conduct of
the mere operations of a mine, except so far as relates to its
cost, but it is an additional knowledge very necessary to be
8 THE ENGINEERS VALUING ASSISTANT.
possessed in order to be able to make any mine pay a divi-
dend upon the capital invested in it.
Mining operations conducted on virgin tracts, in compara-
tively old, well-known, and proved fields, are not so much
questions of speculation as of sufficient capital to develope the
minerals contained therein, as the number, thickness, depth,
quality, and condition of the several veins or seams of coal con-
tained in such fields are generally known. But when it is
intended to open up a colliery or other mine in a field wholly
unexplored, the case is different, and frequently becomes
very perplexing, and creates considerable toil and anxiety in
arriving at a just and reliable conclusion with regard thereto.
To the experienced mining engineer, who is, or at least
should be, a geologist, there are always certain distinctive
features in the strata protruding to the surface of the earth in
many places, in every district, or laid bare by quarries and
cuttings, pointing out the probable existence, and also the kind
of minerals likely to be discovered ; even in an entirely new
field the indications are sufficient generally to lead to the exact
site of the outcroppings of the minerals, unless covered by a
newer formation, as is the case of various seams of coal in the
Somersetshire, Leicestershire, some portions of Staffordshire,
and other coal-fields. This was notably the case at the Sand-
well Park Colliery in Staffordshire, a spot where no coal was
believed to exist by the generality, being outside the known
field, but a recent sinking there has however turned out an
immense success, through the knowledge, energy, and persever-
ing skill brought to bear upon it by Mr. Henry Johnson. To
him therefore alone is due the credit for the discovery of the
extension of this field.
In cases where the outcroppings of mineral veins or coal-
measures are overlaid by strata of a newer formation, explora-
tions become more difficult and expensive, and can only be
carried on successfully by resorting to boring operations, which
are in doubtful cases preferable to sinking a shaft ; but should
it be decided to sink a trial shaft in the first instance, and a
considerable sum is to be so expended, dependent upon the
recommendation and knowledge of any individual, it becomes
a question for mature deliberation for all parties concerned,
before entering upon it.
VALUATION OF MINEEAL PEOPEETY. 9
When the minerals are known to exist, and it is only a
question of development, the annual income likely to be derived,
and consequently the value of the mine, will be affected more or
less by the mode of operating, and by the amount of skill
brought to bear upon it, for if the plan proposed to be adopted
has been well thought out and laid down, failure in any one
important point in the execution, resulting from defective
knowledge of the district in general leading to a large expen-
diture upon inadequate machinery or other mischance, the
value may be considerably diminished, or indeed entirely lost.
I am aware of a similar case where a party came into a
certain mining district with which I am perfectly familiar, but
with which they had no acquaintance whatever, and after
purchasing a small colliery property, they erected plant and
commenced sinking two shafts, and carried them down I believe
about 150 yards, without making any provision for a pumping
engine or pumps, and although they were repeatedly informed
by persons conversant with the district that a considerable
though not excessive quantity of water existed, nevertheless
they entirely disregarded such advice, and upon continuing
their shafts down to the watery strata the pits were soon flooded.
The outcrop of the coal-seams and general measures were
elevated considerably above the top of the pits. They after-
wards erected a pumping engine, but the machinery was
cumbersome and inadequate, and to the present day the
water remains, although it is believed that over 100,000
has been wasted, Now here is a most glaring case, although
perhaps not an isolated one, for the site selected was to the dip
of the field of coal, and it might have been anticipated
that all the water in the rise area would flow downwards. The
outcroppings of this field were well defined and thoroughly
known ; several land works also existed, surrounding the site of
the new winning, but no attempt whatever was made to ascer-
tain the quantity of water pumped from each mine to the rise,
although it was susceptible of computation.
Putting a problematical case, and assuming that a valuation
had been made of this particular property which was small in
area and that it was 60,000, which without actually going
into figures I believe to be too much for it, by spending
100,000 in vain attempts, would leave a loss of the entire sum,
10 THE ENGINEER'S VALUING- ASSISTANT.
minus the present value of the plant and machinery ; but sup-
posing that all the coal had been extracted, and that the profit
per ton upon which the valuation was made had been realized,
there would be a clear loss of ^40,000, and the only set-off
against this would be, as before stated, the present value of the
machinery.
It is very probable that many such cases as this have
occurred, but it is high time that the expenditure of large sums
of money should be entrusted to men of better judgment.
Before commencing operations for the development of any
mine, it is very necessary to examine all the valley outcroppings,
or low levels, if such exist, natural or artificial outfalls or free
drainage, existing old adits and pits from which water is or
may have been pumped, surrounding the entire area to be
developed, also the probable effect produced from the average
rainfall due to the district, the quantity of water likely to be
delivered from the rise area may then be closely computed, and
the size of the pumps necessary to raise a similar quantity of
water from a given depth be determined. Of course in such a
case ample allowance should be made in the size to provide
against sudden inflow of water through porous strata, occasioned
by excessive wet seasons, and other contingencies. The allow-
ance to be made must depend upon the requirements of the
case, and the judgment and capabilities of the engineer in charge
of the execution of the works ; but it is not un frequently the
case that the hands of a good man are completely tied by the
control exercised by a board of directors, who perhaps for the
first time may have engaged in mining. Such interference is
most absurd, and occasionally proves very ruinous to the share-
holders, because a really good and efficient man could not work
under such restrictions.
I believe it will always be found, as a rule, that to err on
the side of excess of size for machinery and pumps is far better
than defect.
It is clearly the work of the Mining Engineeer in charge of
getting up a Report, Estimate, or Valuation, to ascertain every
fact, and to bring out every point bearing upon any property
under consideration, whether in favour of or against it ; and it
is only by such proceedings that a satisfactory conclusion can
be arrived at, but it is very important that all facts should be
VALUATION OF MINEKAL PKOPERTY. 11
ascertained by personal attention, not taking for granted or
using the information supplied by others, unless it were to
agree with independent investigation.
The characteristics of any adjoining property will generally
form a good guide as to the condition of the minerals in the
estate in question ; but as there are faults and denuded parts
existing in every coal-field, it would be very difficult to discover
if any such existed, and how far the seams of coal might be
affected thereby, if the property or estate is situate at a
long distance from any well-known underground workings.
The strike of any general disturbances may, however, be
determined pretty clearly if they have been found to exist in
any neighbouring colliery.
It is not possible, when property is so circumstanced, to de-
termine with absolute accuracy, the exact quantity of minerals
contained within any given area not explored, and when faults
and other disturbances are suspected, but not defined, it fre-
quently becomes a very complicated question, and then an
approximately correct estimate only can be expected.
A great many points involved and relating to each distinct
property, will present themselves to the engineer for considera-
tion and analysis, and there will always be found some special
and distinctive features and circumstances connected with each
property which will tend to affect the value, which can only be
determined by the persevering skill and judgment of the
engineer.
When a colliery or other mine is opened up and partially
exhausted, the mode of procedure is very different and more
direct, as all the seams are laid open, and everything in connec-
tion with them can be satisfactorily determined, and it only
becomes a question of accuracy in surveying the underground
workings of the colliery and those adjoining it, and the surface
boundaries, in order to determine the reserve area, and conse-
quently the quantity of coal, presuming, however, such area is
free from faults, and the seams of coal of uniform thickness.
In a general way, the quantity of coal per statute acre may
be accurately determined by taking the average specific gravity
of several samples from different parts of a seam, and then
deducting a certain proportion for waste. The quantity to be
allowed will vary with different seams, and under different cir-
12 THE ENGINEER'S VALUING ASSISTANT.
cumstances in each district, and sometimes in different collieries
in the same district.
The proportion of large and small, and the marketable
quantity of coal to be obtained from any seam, will depend
upon the uniform thickness and condition throughout, the
system of extraction employed, and the general management.
My practice has been to allow |-th upon the quantity as de-
termined by the specific gravity, when the seams are found, or
at least believed to exist, in a healthy condition, leaving about
1,200 tons per statute acre of one foot thick, to be realised by
extraction. I have, however, known the yield to differ from
this, both in excess and defect.
My experience of Hematite Iron Mines, taken throughout
a district, is that they are capable of yielding about from 5,000
tons to 10,000 tons per acre, and in a few instances as much as
20,000 tons per acre. This refers to general deposits, existing
in the Carboniferous Limestone, and not to surface or mere
accidental and isolated patches.
In making an estimate of the quantity of minerals to be
expected from any unopened mine, such a quantity should be
assigned per acre as would be justified by the experience of the
general yield of a whole district*
Of course barren, unhealthy, and denuded portions exist in
most stratified mines in every locality, and these should be dis-
covered, il possible, and due allowance made for them in the
final result.
Great attention should also be given to the nature of the
strata to be passed through in sinking, the cost of labour and
materials, and, in fact, to everything connected with a general
estimate of the cost of winning, including plant and machinery
of every description necessary to produce certain results. These
are points demanding very full investigation, involving con-
siderable experience and judgment in the execution of works
of a similar nature to those under consideration.
The cost of establishing an extensive winning, including
the conduct of all the present and future operations, affects the
value of a property to a present purchaser very considerably,
although it does not alter the original condition of the pro-
perty. It is therefore of the first importance to ascertain the
outlay likely to cover the cost of the whole of the development,
VALUATION OF MLNEKAL PKOPERTY. 13
not forgetting to make ample allowance for contingencies, or
any unforeseen difficulties which may be encountered.
The position of the property in relation to railways, mar-
kets, and to surrounding collieries, competition in trade, demand
for the produce, cost of labour and production, and the net
profit per ton, are among some of the principal points which
are of very great importance to be determined.
The cost of production will be very much affected by, and
depend upon, the state of the labour market, the nature and in-
clination of the measures immediately over and underlying the
coal involving a small, moderate, or large quantity of timber
quantity of noxious gases to be encountered, uniform thickness
and quality of the seams, existence of faults, or denuda-
tions, and whether any of the coal has to be left in order to
support any part of the estate or royalty, upon which any por-
tion of a town or other buildings may have been erected, as also
the amount of capital, if any in the case of a going concern
required to extend any present or future operations which may
be necessary to support a given yield of coal, or other minerals,
per annum, during the remainder of its duration.
The accessibility of any other seams of coal or minerals
in the royalty from existing winnings, and if the property is
extensive, and the lease of short duration, the probability as to
its renewal, amount of dead rent and royalty, and power to
assign the lease at any time, with its responsibilities, are all points
which must be duly weighed by the valuer on behalf of the ven-
dor, and the incoming tenant. There are also other points too
important to be lost sight of, viz. facilities for the extension of
surface arrangements, such as new erections, railway branches,
areas in reserve for tipping colliery refuse ; also any trespass
committed upon the royalty at remote points by the workings
of adjacent collieries, all tending to produce an effect upon the
cost per ton of the minerals raised, and all of which must enter
into the calculation, in order to arrive at a just and reliable
valuation.
Every purchaser of mining property, should have ample
allowance made upon his purchase, but the amount of such an
allowance, as a percentage, must depend upon a point difficult
to calculate, viz. the attendant risk to be incurred in mining
matters, in making a certain annuity or annual income during
14 THE ENGINEEK'S VALUING ASSISTANT.
the existence of the mine, and to be placed in a position to re-
coup the capital invested within the period of duration or time
of the lease./
All things being considered upon a fair basis, and assuming
the property to be a good one, no one would be in a better position
or qualified to ascertain the attendant risk, than an experienced
mining engineer, but whether from caprice, fear, or doubt as to
certain results, the question is too frequently left to the decision
of an intending purchaser ; it would therefore appear to re-
solve itself into a question of agreement between vendor and
purchaser, and no doubt it is a safe plan of throwing all
responsibility upon the shoulders of the purchaser, and would
save the reputation of the engineer, assuming the property in
question did not eventually come up to the expectations which
sanguine persons may have entertained with regard to it.
Hitherto, therefore, in very many cases, valuation has been con-
sidered more as arbitrary means, dependent upon mere opinion,
than that of a system based upon correct and scientific principles.
The income derived from the working of mines may be
ascertained from the general accounts, if they have been strictly
and truthfully kept, and the value deduced therefrom, coupled
with all existing circumstances connected with the mine, but it
would be necessary to employ in the process the average annuity
that may have resulted over a series of years in the past.
With regard to the amount of percentage to be allowed, or
years' purchase a mineral property is worth to a present pur-
chaser, much difference of opinion has existed and still exists,
as will appear from the following quotations :
In 1829 a Committee of the House of Lords examined Mr.
Buddie, a mining engineer in the county of Durham, upon the
valuation of mines, and he stated that, ' Having considered
what the risk is worth according to the nature of the colliery,
the profit is estimated as an annuity, and that annuity is pur-
chased at so much per cent., varying according to the probable
risk from 8 to 20. In some instances it would be a safer
purchase at 10 per cent., and redeem the capital, than in other
cases of great risk it would be at 20 per cent. ; but then, in
these valuations, if it is for a purchaser, I generally submit a
scale of purchase at such a rate as would be worth so much, and
at such a rate so much. You may take my advice as to the
VALUATION OF MINERAL PEOPERTY. 15
risk, but you must decide for yourself. One man may be satis-
fied with 10 per cent., while another less adventurous might
expect fully 15 ; therefore it altogether depends upon the
opinion of the person purchasing at what rate per cent, he would
purchase.'
Mr. Dunn states on page 82 of his work on the Coal Trade,
that Mr. Buddie in his evidence asserted that ' 5 per cent, was
the average profit of collieries, after returning the capital. The
highest rate of profit he knew of was 14 per cent., including
redemption of capital, viz., 5 per cent, profit, and 9 per cent,
redemption.' Some error must exist in this statement, and it
is most probable that 9 per cent, profit and 5 per cent, redemp-
tion was meant, but it is difficult to see how a mistake could
have been made, inasmuch as Mr. Buddie says 5 per cent, profit
in two cases.
The report of the Select Committee of the House of Com-
mons, published in 1857, on the Rating of Mines, presents the
opinions of several engineers and others called to give evidence
upon the mode of valuing mines, J. Pease, of Darlington, said
'he would calculate his purchase on about 10 years, as applied
to coal-mines.' Mr. S. Dobson, Glamorganshire, said that he
'thought coal-mines should be valued at an average of 8 to 10
years' purchase. Land is worth about 30 years' purchase, dwel-
ling-houses from 20 to 25 years', manufactories perhaps 15
years', and in respect to coal-mines, you may take the average
at from 6 to 8 years' purchase, and you may take ironstone
mines at much the same. He thought there was no more diffi-
culty in fixing the annual value of a colliery th'an there is in
fixing the annual value of a factory. You must always take
into account the quantity of minerals raised, because the annual
value of the property in all cases (or nearly so) depends on the
quantity raised.' J. H. Coterell, surveyor, Bath, ' had settled
the value of mines in arbitration, and fixed them at from 6 to
8 years' purchase ; they were very short of railway accommoda-
tion to their collieries ; when they got that, he thought the
mines in his district would be worth a little more.' T. J.
Taylor, of Earsdon, Northumberland, upon being asked ' How
many years' value do you calculate you ought to give if you
were going to open a mine ? ' said, ' There are two distinct
circumstances which arise for consideration in answer to this
16 THE ENGINEER'S VALUING ASSISTANT.
question. The first is that where the freehold of a mine is
purchased it is usual to allow 8 per cent, upon the perpetuity
that would be 12^ years' purchase. The duration of a mine is
less than a perpetuity say 10 or n years' purchase; the
allowance for that depends entirely upon the length of time the
mine has to last. The other case is the case of the purchase of
a lessee's interest in a mine ; the purchase of the interest of the
occupier of the mine in distinction from that of the lessor.
Then an annuity has to be purchased, subject not only to the
mining risk but also to the occasional risk ; it is calculated as
an annuity for the term of the lease. It varies from 12 to 1 8
per cent., and gives from 8 to 5 years' purchase.' H. W.
Schneider, M.P., said : ' From my knowledge of the subject
of the value of mines, taking iron- mines and coal-mines of
every description taking the whole of England from one
end to the other ; I would not give 10 years' purchase for all
the mines in the country including royalties. If anyone would
give me 10 years' purchase for my own best mine (Park Iron
Mine, in Dalton, Lancashire), I would very gladly take it;
indeed, in stating in general terms 10 years' purchase, I have
gone beyond the mark. Public opinion, which is the best
criterion in such cases, shows that from 7 to 8 years is about
the average with respect to mining property generally through-
out the country. If you look to the value of any great mine,
and see the dividend it is paying, and multiply that dividend
by 7, you will find that that is very nearly the value of that mine.
As regards the royalty supposing the amount of the royalty is
io,OOO a-year, the question would be, what would that 10,000
produce in land ? Taking it at 3 per cent., it would give you
300 a-year, and that would be somewhat equal to 10 years'
purchase for the royalty.' >
In Dunn's work on the Coal Trade, at pages 208-9, ne sa J s '
'If [the mine is] unopened or unproved, its value must be
necessarily dubious, especially if the prospective period of its
being brought into productiveness be uncertain. These various
data, therefore, must be calculated, and suitable allowance made
for time and uncertain value in the winding up of the moneyed
consideration. The rental, then, being once assumed, the value
will be the present worth of an annuity during the expected
term of its duration, minus the number of years' duration which
VALUATION OF MINERAL PROPERTY. 17
it is expected to lie dormant ; the rate of return being varied
by the valuator according to certain or uncertain data, and the
probable profit to be realised under all the circumstances of the
case. The customary course of valuing the lessor's interest in
mining property in Scotland has been 10 years' purchase upon
the ordinary rental, unless some prospective increase of value
present itself; but in the North of England it is constructed
after a more detailed principle. First, then, the prospective
annual value must be assumed, as also its duration, and if it
amount to a perpetuity it will be valued as a freehold ; but as
this description of property is liable to uncertain or suspended
return, a percentage of 8 to 10 per cent, rebate is taken to be
equitable. For instance, a landlord's interest in a coal property,
say 500 per annum for 30 years as a perpetuity, is worth, at
8 per cent, rebate, = ii'25 years' purchase, or 562,500. The
lessee's interest is treated in a similar manner, but is subject to
still greater uncertainty, inasmuch as it involves consideration
of stock and other expenditure, and even the duration of the
lease itself, which might be given up or brought to a termina-
tion by policy or by some catastrophe. The first and main
consideration is -the probable profit to be derived amongst all
the varying circumstances of the cost of working, the amount
of selling price, the probable yearly quantity to be produced,
and probable expenditure necessary from time to time to keep
up the said contemplated quantity.
' These, therefore, are data which must a priori be assumed,
after which the valuation resolves itself into the following prin-
ciple : Assuming the annual profit during the lease to be
1,000, and the un expired term to be 15 years, then it is an
annuity, the purchase value of which, under all the uncertainties
of the case, ought to repay a purchaser 14 per cent, per annum,
with a return of capital = 6*14 years' purchase, or 6,140;
then, taking the colliery stock as valued, in a working state, at
6,000. But, to be sold off by auction at the end of the term,
including expenses for 2,500. The value of the said 2,500
to be received by the purchaser, at the end of the term of 1 5
years, is worth, in ready money, at 5 per cent, discount, '48
purchase, or 1,200. Leaving net value 7,340. The rate of
purchase value differs from 12 to 18 per cent., according to the
18 THE ENGINEER'S VALUING ASSISTANT.
degree of risk and uncertainty of the profits, whether from mine
accidents or the fluctuations of trade.'
We shall test Mr. Dunn's statements in another portion of
the work.
In a published Report, made in 1872, on the Cannop Bridge
Level, parts of Royal Forrester, Speculation, and Rose-in-Hand
Colliery Gales, in the Forest of Dean, Mr. Marcus Scott states
that an annuity of ' 3,000 for 28 years, at 20 per cent, per
annum, is worth 14,909 in present money ; ' or in other words,
that the present value of i per annum at 20 per cent, for that
period is 4*96967 years' purchase. Also that the ' published (and
unpublished) tables by which the calculations are facilitated are
compiled on the assumption that a purchaser can re-invest
annually at compound interest (and at the same rate of interest)
the surplus money above the rate of interest he calculates on
making on his purchase money. As, for instance, suppose we
take, under Table 3 (of his Report), that a purchaser is going
to pay down 62,893 (f r an immediate annuity of 7,000 per
annum for 24 years), on which he calculates he will realise 10
per cent, (on his purchase money), and at the end of 24 years
he will have redeemed or recouped the sum of 62,893. Now,
10 per cent, on that amount is 6,289*3 ; the difference
between which and the annuity or profit of 7,000 is 710 7s.,
which amount, invested annually at 10 per cent, compound in-
terest, will, at the end of 24 years, amount to within a fraction of
the purchase money, 62,893 ; but, suppose a purchaser can only
invest for the purpose of redemption, at the rate of 3 per cent,
compound interest, then, instead of realising 10 percent, on his
purchase money, he would only realise 8*179, or && 3 s - 6<#.'
This is certainly a most unintelligible passage, and a mis-
take as well, for, if the 10 per cent, is allowed for, or added to,
the redemption fund at 3 per cent., and then unity divided by
it, we get the present value. Thus, if a purchase were made,
allowing interest on the purchase at 10 per cent., and redeeming
the capital at 3 per cent, at the expiration of 24 years, we have
7-74909 years' purchase, and the present value = 54,243.
Then, 10 per cent, upon this . . = 5424*363.
And the redemption fund, at 3 per cent. = 1575*637.
Annuity . = 7000*000.
SITYJ
VALUATION OF MINERAL PROPERTY. 19
Mr. Scott calculated the whole of his values upon the prin-
ciple if it may be so called of redeeming capital at the same
rate per cent, as that allowed upon the purchase money; but he
does not say anywhere in his Keport where money could be
placed in order to accumulate at 10 per cent, interest, but he
does value up to 20 per cent, upon the same assumption.
He, however, refers to the redemption of capital at 3 per
cent., and proceeds to remark : ' To calculate the whole of the
Tables I have given you' (i. e. in his Eeport) ' on the latter mode
of present value and investment, would entail an enormous
amount of figures, as there are no published Tables that I am
aware of which give the years' purchase on investment for
redemption at 3 per cent., except Willich's, which only go as
high as for the purchaser to realise 5, 6, and 7 per cent, with
investments at 3, 3^, 4, and 5 per cent.'
He also states that 'the calculations of annuities for any
number of years deferred, or any number of years with redemp-
tion at 3 per cent., are very intricate.'
The discrepancies that have arisen in valuations made by
the inaccurate mode practised by Mr. Scott and many others
will be fully treated of hereafter.
In the case of unopened mines it has been my practice, in
deducing the present value deferred, to allow 20 per cent, to a
present purchaser, and redeem the capital at 3 per cent, per
annum ; which I consider in a general way is a safe mode of
dealing with any mine with average prospects; although, in
special cases, where mines had a more certain character, I
have allowed a percentage as low as 14, and in some of less cer-
tainty as high as 25.
A rule cannot be laid down expressing the attendant risk of
mining adventure, as nearly all mines exist under circum-
stances differing widely from each other. It is a matter of
experiment: each mine must, therefore, stand upon its own
merits, and the amount of percentage to be allowed must also
be varied according to the circumstances of each particular case.
In working up a valuation, after the number of tons are
ascertained in the given area, a reasonable and practicable out-
put per annum must be assumed such as would be justified by
the probable state of the market, continuance of supply from
c 2
20 THE ENGINEER'S VALUING ASSISTANT.
the surrounding collieries, and other circumstances which,
multiplied into the profit per ton, will give the yearly income
or annuity expected.
The annuity so determined has to be purchased upon an
agreed or allowed percentage, and resolves itself into a question
of compound interest, or the present value of i per annum
at a certain rate on the purchase, and to redeem the capital
not in an imaginary way but at another practicable rate per
cent., and during a denned period, multiplied into the annuity
expected per annum for the present value.
If the mine is not opened, the annuity must be considered
as deferred during the period the mine is unproductive ; thus, if
the time necessary to win a mine, is 3 years, and its duration
afterwards 50 years, allowing 20 per cent, to a present pur-
chaser, and redeeming the capital at 3 per cent, per annum,
the present value deferred would be 2*77070 179 years' purchase,
which would accumulate during the time occupied in winning
the mine to 4-78777025, which, in point of fact, is the present
value of i per annum or years' purchase immediate, at the
rates of interest stated.
PART II.
CONSTRUCTION AND USE OF VALUATION TABLES,
RULES AND FORMULAE.
PAET II.
EVBHY beneficial interest or sum of money accruing, or to accrue,
and to be paid at the end of a year, or portion of a year, may
be considered as an annuity, and may be either terminable with
the life of an individual or perpetual. Any sum of money
left unpaid for a certain number of years is called an annuity
in arrear, and when not payable until after a fixed number of
years it is said to be a reversionary or deferred annuity.
In either case the annuity is transferable, and may be pur-
chased on certain agreed terms ; each class of annuities must,
however, receive a particular mode of treatment, adapted to,
and peculiar to the nature of the circumstances connected with
each particular case.
If money could not be employed, and a marketable rate of
interest obtained for its use, the value of any sum of money or
annuity would be equal to that to be paid at the end of one
year, multiplied by the whole period or number of years the
annuity has to run ; but as compound interest is involved in
all these cases, it is clear that if A desires to sell an annuity to
B, and which has to last a certain number of years, a certain
agreed interest or discount must be allowed to B upon the
whole sum. to be purchased, and received by him for the fixed
period.
The Increase of the Principal at compound interest may be
illustrated by the following mode of expression :
Putting r = interest on i for one year or other integral
period,
R = amount of i with one year's interest,
n = any integral number of years,
Then
(0 ., . ',, R n = (i+r).
24 THE ENGINEER'S VALUING ASSISTANT.
Supposing the rate of interest to be 3 per cent., then r =
03, and R i+'O3 = 1-03 = the principal of 1, and
simple interest on it at the above rate for one year. If im-
proved in a similar manner during the second year, it would
amount to (i -f *O3) 2 or = 1-0609, and so on until (i +'O3) 100
would amount to 19-2186319809.
In words, the rule may be thus expressed, Add to unity or
i the interest due upon it at the end of the first year ; in-
volve the sum, to the power ivhose index is the number repre-
senting each successive year, in the given period.
It is manifest that the present value of i, at 3 per cent.,
must be such a sum less than i as would, if improved by a
year's interest, amount to it. Thus the principal of i, and
interest, -03, thereon = 1-03, the amount ; and - - =
1-03
9708738, the present value of 1. For, -9708738 x 1*03 = i.
Similarly, the present value of i, due 6 years hence, at
3 per cent., would be = - . - = -837484. It therefore
1-194052
follows that if i is raised to any amount resulting as shown
from its improvement at compound interest, at a certain rate
per cent., during any number of years, and unity or I is divided
by it, the resulting number or quotient will represent the present
value of i, due at the end of the same periods the amounts
were raised for. The value or years' purchase of perpetuities
may be found by dividing the annuity by the rate of interest
on i for one year. Thus i = 33'3333> i = 25, = 20,
i = 14-2857, and ^ = 10 years' purchase respectively.
The Present Value of a Perpetuity of i payable once in
every Tith year, the first payment due n years hence, will be
denoted by V n ; thus we have,
And, for the value of such a perpetuity payable every 10
years, at 4 per cent, we have,
The present value of i to be paid annually in perpetuity,
at 4 per cent, is, as stated above, = 25 years' purchase ; but if,
CONSTKUCTION AND USE OF VALUATION TABLES. 25
instead of being annual, the payments are only made at intervals
of say 2, 3, or 4 years, or other periods, by taking the amount
of R n from the Tables for the variable periods, the formula
Y n = -- will of course continually represent the present
j\> ~~ I
value of the perpetuity. /
If the perpetuity is deferred for say 5 years, so that the
first payment is to be made 1 5 years hence, the value found as
above must be multiplied by i> 5 ; and if the perpetuity is
anticipated 5 years, the value found must be multiplied
by R 5 .
In the former case i> 5 being '82192711, we have
2-0823 x -8219271 1 1-71149882;
and in the latter case R* being 1-21665290, we also have
2-0823 x 1*21665290 = 2-53344909, the value of the perpetuity.
Again, putting s n = redemption fund, we also have
(3) - Vn= |||
Thus ' 83292 = 2-0823, as before.
04
Also, the Present Value of a Perpetuity of i, deferred
n years, may be deduced as follows :
Putting D = deferred value,
5 , v n = value of i due n years hence,
we have
Thus '_7__ _ r 5-889 1, value at 4 per cent, for 10 years.
04
Also 152. = 25,
04
and -6756 x 25 = 16-8891, the value deferred as before.
When large sums are invested at compound interest, a
certain advantage would accrue to an investor if interest on
capital were to be paid at several equal intervals during the year,
instead of one single payment at the end of the year.
It does not come within the scope of this work to enter into
a theoretical investigation of the subject, but the practical
26 THE ENGINEER'S VALUING ASSISTANT.
mode generally adopted in solving problems of this nature may
be exemplified as follows :
If interest were to be realised m times in a year, at the
rate , the expression becomes
m
Assuming the principal to be i, and r = -06 per 1 for
one year, for half-yearly payments we have
+ = 1-0609.
Payments being made quarterly, we also have
By the same rule, for monthly payments the amount would
be i -06 1 6778 1 , and for weekly payments it would be I -06 1 7998 1 .
On the same principle, if it were possible for payments to
be made momentarily, the amount of all the increments would
depend upon, and be expressed by, the well-known principle of the
4 Binomial Theorem,' and if the series are continued to a sufficient
extent, would = 2-718281828459, which is the base of the Na-
pierian logarithms. The log of this number is 0-43429448 1903,
and -06x0-434294481903 = -02605766891418, the natural
number of which is 1-061836546557, or the amount.
Thus, it is evident from the nature of the above formula,
that if payments were made on the assumption that a year could
be divided into an indefinite number of periods, the resulting
amount of all the increments, at the end of the year, would,
according to this hypothesis, be in excess of that derived from
the employment of periods of time having greater duration, as
a day, week, or month, &c. &c.
The Amount of 1 per Annum, if invested and improved at
compound interest, in n years, may be determined by the fol-
lowing expression :
Let r = interest on i per annum.
M n = amount of 1 per annum for n years.
R = (i -f r) , as in last case.
CONSTRUCTION AND USE OF VALUATION TABLES. 27
Then
(6) ... *-*=!.
Assuming the rate of interest to be 3 per cent.,
Then
M l = *l = i
03
for the first year's amount, and if improved for the second year,
R i __ i -0609 i
2*03 ;
03 -03
and so on, until
19-2 18631 9809-1 ^ 607 . 38773269>
the amount at the end of 100 years.
In words the rule is thus expressed : Deduct unity or i
from the amount of i in n years, and divide the remainder
by the rate per i.
The amounts may also be found thus : Multiply the first
year's amount, i.e. 1x1-03+1 = 2*03, the second year's
amount; then 2-03x1-03 + 1 = 3*0909, the third year's
amount. The same results will be obtained by adding the
amount of i in n years, i.e. R n , to the amount of i per
annum in n years, or M n \ thus 1 + 1-03 = 2 *3> then 2-03
+ I -0609 = 3 -0909, the third year's amount.
When interest can be realised m times in a year, the ex-
pression becomes
771
Therefore, for half-yearly payments, the interest being at
the rate of 4 per cent, per annum, for 10 years, we have
jf lc = - 4 - = 12-1486848994.
04
28 THE ENGINEER'S VALUING ASSISTANT.
And for quarterly payments we also have
- = I2-22I593339.
The Present Value of 1, due n years hence, may be deter-
mined from the following data :
Putting v n = present value of i due n years hence,
R n =z (i + r) n as before,
(7) - * then v n = ~.
Supposing 5 per cent, to be the rate of interest, we have
*=i = r^ = -9523809523,
the first year's present value, and the 6th year's present value
would be equal to
= 7462153964.
1*340095641
In words the rule may be thus expressed :
Divide unity or i by the amount of 1 in n years ; the
quotient will then represent the present value of 1 due at the
end of n years.
The same results may also be obtained by first dividing unity
or i by the amount of i in one year, and afterwards to
constantly divide the successive quotients by the same amount.
Thus -L, = -9523809523 ;
then '9523809523 = .9070294784,
the second year's present value.
If it were possible to realise interest m times in a year, the
expression becomes
(7) . . . v n = I
i
m
CONSTRUCTION AND USE OF VALUATION TABLES. 29
Therefore, for half-yearly payments, at 4 per cent., and for
5 years, we have
And for quarterly payments we also have
The Redemption Fund that will amount to i inn years
may be computed from the following expression :
Putting s n = redemption fund,
R n and r = the elements as previously assigned.
Then
(8)- -.
Allowing the rate of interest to be 3 per cent, and to
redeem i at the end of 3 years, we have
**= W^ = 1-092727-. = ^35303633,
or the redemption fund ; and for redemption in 20 years, we
also have
s 20 = o ^ -^ - = -0372157076.
1-80611123471
The rule for finding the redemption fund may be written in
words thus :
Divide the rate of interest per i by i less than the amount
of i in the time.
Assuming interest to be convertible m times in a year, the
expression becomes
Therefore, for half-yearly payments, at 4 per cent., and for
IO years, we have
04 -04
I-48594739 6 - 1
= -08231343;
30 THE ENGINEER'S VALUING ASSISTANT.
And for quarterly payments we also have
4
4
the redemption fund.
We may also deduce similar results from
(9) . -^i*
Thus
s n = = -08182239, the redemption fund, as before.
12-221593
It may be remarked here, that for very nice work, i.e. to
make the simple interest at a certain rate per cent, on the
deduced value and redemption fund balance the annuity exactly,
it is necessary to employ a table computed to eight or ten
places of decimals.
Putting A = the Immediate Annuity which i will purchase,
we have
(9 a) . . . A = s n + r f .
The annuity is therefore readily obtained by adding to the
redemption fund necessary to produce i at the end of any
given period, the interest allowed upon the investment.
Thus, the redemption fund necessary to produce i at the
end of 3 years, at 3 per cent. = "3235303633; then, the interest
allowed on the investment being 3 per cent, we have,
3235303633 + '03 = -3535303633,
or the annuity. This rule applies to all percentages ; for,
assuming the interest to be allowed on the outlay to be -20 per
instead of -03 per , for a period of 40 years' duration, we have
the redemption fund necessary to produce i at the end of the
assigned period = -01326238 ; then
OI326238 + -20 = -21326238,
or the annuity which i will purchase.
Table V. is therefore well adapted for determining the
annuity, without having a special Table for that purpose.
CONSTRUCTION AND USE OF VALUATION TABLES. 31
The Present Value of 1 per Annum, deduced by the old rule
for n years, may be computed as follows :
(10) . . Present value p n = 5LJ or LzU*
-it T V
Assuming the rate of interest to be 3 per cent, per annum
for 5 years, we have
18626087846 = 4 . 579707 , 9; the present value .
The value deduced by either of the last preceding rules is
erroneous, when it is necessary to employ rates of interest above
those which can be realised in the money market for the
redemption of capital. See Table XII. for discrepancies in the
old table of present values.
The Present Value of 1 per Annum for n years, allowing to
a purchaser of annuities one rate of interest on his purchase
money, and to redeem his capital at the expiration of the time
by annually investing the overplus at another practicable rate,
may be deduced as follows :
Putting P n present value,
R, 8 n9 and r = the elements as previously assigned,
and tf the interest allowed on capital.
We have
(II). . . P n = 1 or
R n -i
Assuming the rate of interest on capital to be 5 per cent.,
and to redeem it at 3 per cent., at the expiration of 3 years, we
*have
1 2-677158534.
3235303633 + *05 "" '3735303633
Assuming interest to be convertible m times in a year, the
expression becomes
j N ~W~\
32 THE ENGINEER'S VALUING ASSISTANT.
Therefore, for half-yearly payment?, interest on capital being 1
10 per cent., and redemption 4 per cent., and for 10 years, we
have
=5-484859137,
L-4Y-i i -485947396- 1 +
2)
And for quarterly payments, we also have
" '
=5-499842456,
1-4888637336-
4
the present value.
It will be observed that the purchase money being P n , it is
evident from = P n , that the interest / allowed or ex-
pected to be realised for investing a sum P n , would be equal to
P n -/, and s n , invested at another rate per cent., r, which being
accumulated at compound interest, will reproduce the original
capital P n at the expiration of a certain denned period.
The annuity being unity or i 9 is consequently made up of
two distinct parts, that is, r' per cent., a years' interest on P n ,
and s n , which being invested at another rate of interest per cent.,
r per annum, will produce P n .
The annuity of i is therefore equal to r'-f s. M , which may
probably be more clearly seen by the following mode of work-
ing:
Putting the period of duration, n, of the annuity . =55
years
the rate of interest, r, to reproduce P n within \
the period of 55 years . . . . j
the rate of interest r f to be realised on the
purchase money P n
Then from (i i) we have
lt"-i
CONSTRUCTION AND USE OF VALUATION TABLES. 33
Also R H = R = 5-082148592,
I I
and P., =
03 '03
5 -082148592- i
= 4-82278505, or
00734907104 + '20 -2073497104
present value.
To insure, therefore, the purchase of an immediate annuity
of i under these conditions, the purchaser must pay down a
sum of 4-82278505 = P 55 , the present value, or years' pur-
chase.
Again, 855 at r per cent. = 8 K at -03 = -00734907104, which
is the redemption fund necessary to reproduce i in the given
time
ThenP 55 r' = 4-82278505 x -20 :*i . = -9645570100
And P 55 s 5 5= 4*82278505 x -00734907 104 = -035442989^
Also r' -f s 55 = the annuity receivable, or i -ooooooooo
.If, therefore, -0354429899 is annually invested at the rate
of -03 per cent, compound interest, it will reproduce P 55 , the
original purchase money, or capital, at the expiration of the
term of 55 years.
Thus the amount of i per annum for 55 years =
136-0716197, which, multiplied by -0354429899 =
4-82278505, the original capital, or P 55 .
What has been hitherto advanced relates more particularly
to formulae, and rules, employed in the construction of the Tables
necessary for determining the present value of immediate and
deferred annuities, realised under certain conditions ; but when
annuities are deferred, and the present value required to be
tabulated, special treatment must be adopted ; and the construc-
tion of Tables of this nature becomes very tedious.
In calculating the Tables in this work of the present value
of I per annum for n years after t years, allowing a purchaser
interest on his purchase money at a certain agreed rate per
cent., also such a surplus as, invested at another practicable
rate per cent., would reinstate the capital at the end of the
term, the following conditions were necessary to be considered.
D
34 THE ENGINEER'S VALUING ASSISTANT.
If instead of an annuity of p pounds being entered upon
immediately, it can only be realised at the end of the -th year>
and to continue n years thereafter, the purchaser will expect to
realise '/ per cent, on his outlay P t+n , during the whole term of
t -f n years ; and here, as was shown in the last preceding case,
he can invest the surplus annuity only at the rate of T per
cent.
It is necessary, therefore, to determine the relation existing
between P t+n and p 9 and, as it may be seen that no annuity can
be paid during the deferred term of t years, P t+n would accumu-
late or amount at the end of the t-th year to P t+n ( i -f /)*.
When, however, the annuity is entered upon, which as a
matter of course it would be at the end of the t-th year, it is,
as previously shown, separable into two parts, that is to say,
first, a year's interest on the amount which the purchase money
P t+w has now attained, namely, P t+n r^(i +/)*; and, secondly
p P t+n r^(i +/)*, the sum which must be invested at the rate
of r per cent., and which will reproduce P t+n (i +r / )* at the
end of t + n years. Then, by condition, we have,
{p-P^ (i -f /)'} M. = P ttn (i +/)'.
Solution of this equation gives
in both of which M n denotes the amount of an annuity of i
in n years.
If in (12) p be put = i, we have for the value (the years'
purchase,) when the annuity is i 9
(I 4 ) . . P< + n = (
and if the value, i.e., the sum invested, be i 9 we have from
(13) by making P t+n = I, the annuity which i will purchase,
viz. :
(is). . P = ( -
CONSTRUCTION AND USE OF VALUATION TABLES. 35
The value of an annuity to continue 5 5 years after 3 years
deferrence, ? / being = *2O, and r '03, may be deduced
from (14).
Thus,
JT<* , CK ~ , ~~ i~Z;
(l+*20) 3 (l + '20M &5 )
Table (III.) gives M^ 136*07161972, at 3 per cent.
Therefore,
p _ 136*07161972 __ 136*07161972
3+55 "" 1*728(1 +*20 X 136*07161972) 48*75435056
2*7909633636, value of deferment required. Again, if the
purchase money P t+n is made = i for the same continuance
and period of deferment, and at the same rates, the annuity i
will purchase may be deduced from (13) :
Thus,
p = (l+*20) 3 (l+-2Q3/ 55 >) ^
and by substituting the numerical quantities we have
_ 1*728(1 +*20x 136*07161972) _ 48*75435056 _
r ' 136*07161972 " 136*07161972 ~
3582991858, or the annuity deferred which i will purchase ;
and it is, as it ought to be, the reciprocal of the value, when
the annuity is i.
thus :
- -^ -3582991858,
2*790963636
the deferred annuity which i will purchase, as before.
The value of the annuity when deferred, may be readily
derived from the value when immediate, by virtue of the
following relation.
i- t
where n is the term of continuance, and t the term of deferment.
Applying this to the last example, we have,
P - P
*
D 2
36 THE ENGINEER'S VALUING ASSISTANT.
P 55 is = 4-82278505, and v 3 (at -20 per i) is = -57870370
(See Table IV.) Hence,
Fs+ss = 4*82278505 x '57870370 = 2-790963636, the same as
before.
In order to illustrate the power of the Tables, and to give
an additional method of obtaining the deferred value, we have,
^(16). r:3v-7 '
Then, by substitution, we also have,
p
*+w /T~
+ -20 + -00734907
4-82278505
2-790963578, or value of deferrence, practically the same as
above.
There is nothing in the amount of work involved in this
method to frighten a student on the contrary, I consider it
simpler than when employing M n . But for practical purposes,
and in order to get over a larger amount of calculation in a
given time, no doubt P n -y* should be employed, which is the
simplest possible form the formula can be made to assume.
Tables X. and XI. were computed by this rule.
Again, for obtaining the deferred annuity which i will
purchase, we have the following expression :
Or,
It may be here remarked that it is not necessary in practice
to work up any of the elements involved in the solution of these
problems, as they are tabulated in this work, and may be im-
mediately obtained by reference.
It is to be observed that when working the numerical
quantities represented by the formulae, (14), (^15), the operation
should be taken from right to left, thus : -
i.e., 136-07161072 x -2O-f i x 1-728.
CONSTRUCTION AND USE OF VALUATION TABLES. 37
If t is made equal to o, that is to say, if the annuity can be
made available on present entry, then (1-f/y = I, and the
formula deduced, becomes for this case
Putting p therefore = i, we have from (18)
P - *
' i+SM.'
and by substituting the numerical quantities we also have
P - 136-0716197 _ _ 136-0716197 _ 4 . 82278 - oi;i
55 I +('20 X 136-0716197) 28-21432394"
which is the present value, or years' purchase immediate.
Again, putting P n = i 9 we also have from (19)*
. 1
p
and by substitution we also have
I +('20 X I 3 6-07l6l97),28-2I432394 _ .20734907104,
136-0716197 136-0716197
which is equal to the redemption fund necessary to produce
i in the given time, plus the interest allowed to a present
purchaser. See (90,.), page 30.
The results deduced from the last two preceding formulae
for immediate annuities, prove the accuracy of the plan upon
which the Tables of this class have been computed for this
work.
The subject of Deferred Annuities has been considered by
some to be very complicated, and by many avoided altogether
when two rates of interest are involved as something unap-
proachable. The great difference of opinion that exists in re-
lation to the proper mode of treating the question, as applied to
Mines, has led me to investigate it thoroughly, and I believe the
conclusions arrived at are such as are not to be controverted.
The resulting number deduced from (14) and (16), that
is to say 2-790963578, is the sum necessary to be paid down by
38 THE ENGINEER'S VALUING- ASSISTANT.
a present purchaser, in order to secure an annuity of i for 55
years (which is not to commence, however, until the expiration
of 3 years), which would yield him 20 per cent, during the
entire period of 58 years, and redeem the purchase money, that
is to say 2790963578, and its amount during the 3 years of
deferment, together equal to 4-82278505 1, by investing the
surplus annuity at 3 per cent, compound interest.
Again, under similar conditions, if, instead of 2*790963 578?
one pound only had been invested, then an annuity of
3582991858 would have been secured by the purchaser.
Generally, therefore, in cases of deferred annuities of this kind
that is, when two rates of interest are involved a certain sum,
P t + n , has to be paid down immediately ; but as no annuity is or
can be payable under the circumstances during the deferred
period, the purchase money, P i+w , accumulates at the rate al-
lowed to the purchaser on his capital, or r f per , to a certain
sum = P t+n ( I +/)* = P n ; but, at the expiration of t years, the
deferred period closes, and the annuity commences or is then
entered upon, and its payments have to yield interest at the
rate agreed upon between the parties to the business, or r' per
on the accumulated purchase money P n = P t+n (i +/)*, and
also a sum sufficient to reinstate the sum P w , to which the pur-
chase money has accumulated at the end of the assigned term
of t + n years, at another rate per , or r. In the present
case the deferred period t is equal to 3 years, and the term n to
run afterwards is equal to 5 5 years.
Then,
P, +n (i+r7 = P, +w (i-f 20) 3 = P, +n x 1728 = 2790963578
= 4-822785051 =P
n ,
the amount to which the purchase money has accumulated at
20 per cent, at the end of the deferred period.
The interest on P n = P n r' = 4-822715051 x -20
= -964557010, or that part of the annuity due to the agreed
percentage. P t+n being the present gross value to be paid
down = 2-790963578, and the redemption fund required to
produce i at the expiration of 55 years at 3 per cent, is
equal to -007349071.
CONSTRUCTION AND USE OF VALUATION TABLES. 39
Then,
P n s n at r per cent. = P n x '007349071 = 4-82278505 1
x -00734907 1 = -03544299,
the amount necessary to be annually set aside and to accumulate
at 3 per cent, for the assigned term of n years*
Also the interest on P w , or P n r^^plus that
on P n s n at r per cent., is equal to
P n x -26= to that portion of the an-
nuity enjoyed for present use . . = -964557010
And P n s n at r per cent. = the other part
set aside for redemption within the period = -03 5442990
And P H / + P n at T per . . . = i -ooooooooo
or the annuity to be received by the purchaser under the pro-
posed conditions.
If further proof of the accuracy of the foregoing mode of
working were required, it is only necessary to multiply the
amount of an annuity of I in 55 years at 3 per cent, by the
surplus annuity set aside to reproduce the capital at the expira-
tion of the given time.
Thus, the amount of i per annum for n or 55 years
= 1 36-0716 197 x -03 5442 99 = 4-822785051,
the original capital invested, with accumulated interest.
When the sum invested is i, the annuity purchased, as
previously shown, is equal to '3582991858, and if treated as
above, P t+n (i-f /)* = i (l+*2o) 3 = 1728 = P n , the accu-
mulated amount during the deferred period of 3 years ;
Then 1-728 x -20 = -3456000
And P n = 1-728 x -0073490 . = -0126991
-3582991
the annuity as previously determined.
Then, if we multiply the amount of an annuity of i as
before, we have 136-07161970 x -00734907104 = i, the
original capital, or purchase money paid down.
If further proof of the principle involved in the return of
the capital were required, we may select an example embracing
a short duration, and proceed in detail as follows :
40 THE ENGINEER'S VALUING ASSISTANT.
The present value of i per annum, allowing 20 per cent,
and to reproduce it at 3 per cent, within a period of 5 years
after 3 years = 1-490142634, which accumulates to
2-574966472 in 3 years.
The redemption fund to produce this
sum is . . . . = -485006705689
And 2-574966472 x *20 . . = -5 149932943 1 1
The annuity. . 1-000000000000
And in detail thus :
485006705689 = 1st year's redemption fund.
30-1 inverted.
485006705689
14550201170
-499556906859 = amount at end of 1st year.
485006705689 = 2nd year's redemption fund.
984563612548
30' I inverted.
984563612548
29536908376
I -0141005 20924 = amount at end of 2nd year.
485006705689 = 3rd year's redemption fund.
1-499107226613
30-1 inverted.
1-499107226613
44973216798
1-54408044341 1 = amount at end of 3rd year.
485006705698 = 4th year's" redemption fund.
2-029087149100
30-1 inverted.
2-029087149100
60872614473
2-089959763573 = amount at end of 4th year.
485006705689 = 5th and last year's redernp. fund,
2-574966469262 = the accumulated present value.
CONSTRUCTION AND USE OF VALUATION TABLES. 41
The first year's redemption fund to
be invested = -485006706689,
And at 3 per cent., at the end of
the year becomes . . = '499546906859.
The second instalment of the re-
demption fund . . . =-485006705689,
Is again invested, and at the end of
the second year the fund is = 1-014100520924,
To which, at the end of the third year, -485006705689 is
again added, and so on to the end of the fifth year, when the
original purchase money, 1*490142634, and its accumulation
during the deferred period, by multiplying it by
(I+/) 5 = 1-728 = 2-574966470.
Care must, however, be taken that no delay is occasioned in
investing the annual instalment at the proper time, otherwise
a discrepancy will exist in the account at the end of the period.
The Tables introduced into this work have been carefully
calculated from data deduced from first principles, and involved
in the doctrine of interest and annuities. The formulae and
rules which were employed in their construction, are laid down
in the most simple form, so as to be readily understood, and
applied by those who may not have either time or inclination to
investigate, and employ rules containing algebraical combina-
tions of a more complicated nature. I have strenuously endea-
voured to divest the subject of all intricate formulae and elaborate
mathematical reasoning, that would, in my opinion, tend in
any way to confuse it. I trust, therefore, that this has been
effected so far as it was considered to be convenient and benefi-
cial, and consistent with the nature of the enquiry. And it is
presumed that any person having occasion for calculations of
this nature may, by merely consulting the Tables, obtain at
sight any years' purchase for a given time and rate of interest,
and consequently arrive at a reliable conclusion as to the value
of any annuity in a much more satisfactory manner, in less
time, and with greater ease than could be expected to result
from a tedious process of direct calculation. The same remark
applies to all the other Tables.
Those who are sufficiently expert, and object to the use of
tables as labour savers, will find that the rules laid down are suffi-
42 THE ENGINEER'S VALUING ASSISTANT.
cient for the calculation of values in a specific and direct manner,
or for the production of tables similar to those I have referred to.
Inaccurate tables are worse than useless, and without
employing some special means for the correction of error, it
certainly could not be expected that tables involving so many
figures and direct computations could be entirely free. Consi-
dering this, therefore, and being aware from long experience of
the trouble and difficulties that are created by the employment
of incorrect tables of various kinds, I was led to adopt means to
the end in view. I have, therefore, every reason to believe that
the result is, Tables free from error, and which may absolutely
be relied upon.
Vv r ith regard to the Tables of Amounts, an additional test as
to the accuracy was applied to the final number in the column
of each rate per cent. The mode of calculating an extreme
number by a logarithmic process in a series having no ratio, will
be fully illustrated in another portion of the work.
Tables of the value of leases and annuities have frequently
been published : that of Mr. Ward was written as far back as
1710; but Mr. Smart's celebrated five Tables of Compound
Interest, which appeared in 1726, far excelled all that had been
done previously to that time: indeed, his tables have been
incorporated more or less into the works of many writers to the
present time.
The tables specially referred to are
1. The amount of i in any number of years.
2. The present value of 1 due at the end of any number
of years.
3. The amount of i per annum for any number of years.
4. The present value of i per annum for any number of
years.
5. The annuity which i will purchase for any number
of years.
None pf the tables of this class that I have seen (and I have
examined a large number of works upon the subject), are com-
puted to rates of interest higher than 10 per cent., and many of
them extend only to 5 per cent.
The fourth and fifth tables, previously described, must
CONSTRUCTION AND USE OF VALUATION TABLES. 43
necessarily be inaccurate for rates of interest higher than from
4i t 5 P er cent. This will be fully demonstrated further on.
Tables L, II., and III. of the Amounts in this work were
originally calculated to 1 5 decimal places, with a view to print
them to 10 places; but on account of the great expense of
publishing, I determined to reduce all the other Tables to
their present condition. The ordinary table of the present
value of i per annum is the same in the works of all
writers upon annuities ; and, as the basis upon which it has
been computed is in error, it follows that the annuity which i
will purchase is also in error, because the latter is dependent for
its formation upon the former. That is, p n being the present
value, and A = the annuity i will purchase, we have
A = . Thus for 60 years at 10 per cent., in the old table,
Pn
p = 9*967157; an d ^ = "1003295122, or the annuity.
For the same period of time, and rate per cent., but redeeming
capital at the rate of 3 per cent., P n 9-42214381. Also, we
have A = = - - = -1061329587, or the annuity.
Thus it is evident that the years' purchase upon the old basis, is
in excess of the truth, whilst the annuity which i will purchase,
derived from it, is in defect.
The reverse is the case in the Tables calculated for this work.
For 9-9671569-42214381 = -54504319, the difference in
excess jf a years' purchase; and -1061329587 -1003295122 =
0057034465, the difference in defect.
Mr. Peter Hardy states it as his belief that Mr. Griffith
Davies was the first to compute a table showing ' the value of
an annuity on a single life, which was to pay the purchaser 5 ,
6, or 7 per cent, on his outlay, and to replace the original
capital at 3 per cent., according to the Northampton rates.'
This table seems to have been published in 1825. Mr. Benwell
also appears to have written a small pamphlet on the subject,
containing a table of limited extent (similar to the one appended
to Mr. Hardy's paper), and published it in 1831. Between the
years 1837 and 1850, a rather cumbrous rule was introduced
into, the Appendix of In wood's Tables, relating to two rates of
44
THE ENGINE EK'S VALUING ASSISTANT.
interest. I give it here from my copy of that work published
in 1850:
'Let a = amount of clear improved rent.
f amount of i per annum at n per cent, com-
| pound interest for r years.
(rate of interest per cent, required on purchase
money.
x = amount of purchase money.
( sum to be annually laid by at n per cent, com-
y = \ pound interest, to replace capital at expiration
( of lease.
Then from this statement we shall have
for the amount of i per annum for the num-
ber of years of the lease at the given rate of
compound interest, multiplied by the number
of pounds annually laid by, must equal the
i, purchase money.
ex
for - = the annual interest on purchase
money, since the annual interest on any sum
= that sum multipled by the rate of interest,
and divided by 100, and the annual interest
on the purchase money added to the sum an-
nually laid by to replace capital, must = clear
improved rent.
x
From the first of these equations, y = T, which, substituted
in the second, gives
by x -
ex
100
-ry = a
ex x
+ T
100 b
X =
looab
and = =
-
100 + bc
This rule supposes that an annuity may be purchased,
securing interest on the purchase money at one rate, and rein-
stating it at another rate, per cent.
CONSTRUCTION AND USE OF VALUATION TABLES. 45
Mr. William Morgan gave a solution to this problem at page
321 in the Appendix to his work on Annuities and Assurances,
published in 1821, and I give it here verbatim :
' Problem IV. To determine the sum which should be paid
for any given annuity for n years, so as to secure to the pur-
chaser the return of his capital at the expiration of the term,
supposing him to have the means of reproducing that capital at
p per pound, and that the value of the annuity is computed at
r per pound.
' Solution. Let a be the given annuity, and x the capital to
be reproduced at the end of n years, or the sum which should
be paid for the annuity on the above conditions.
Since i ^' ~ is the amount of i per annum at p in-
P
terest in n years,
(a rx) x v ~T~P> """ _ will be equal to x ;
P
from which equation x is easily found
p-f (i f p) ra I XT'
c Example. A purchases an annuity of 65 for 10 years,
and is to be allowed 9 per cent, in the purchase, but being
unable to improve the difference between 65 and the interest
at g per cent, on the capital at a higher rate than 3 per cent. ;
it is proposed to make him such allowance in the purchase
money as shall enable him to replace his capital at the end of
the term by improving it at this reduced interest. In this case
p is '03, r = '09, n = 10, and a = 65 ; and x will therefore be
-344 =
03 + ( i -03) 10 - 1 x -09 -03 + -344 x -09
' In other words (and this is meant for a proof) ; 3667 10 x -09
= 33-004, and 6533-004 ( = 31-096) multiplied into 11-464.
the amount of i per annum in 10 years, gives 366-710.'
Taking the annuity at i instead of 65, the result comes
46 THE ENGINEER'S VALUING ASSISTANT.
out equal to the years' purchase. It is thus deduced from Mr.
Morgan's figures ;
= 5.64:692307, ' .....
but by taking the amount for 3 per cent to 8 places of deci-
mals, and working his problem, we get a little difference in the
result. Thus :
65x(i-03) 10 --i = 65 x -34391638 _ 22-3545647
03x(i-03) 10 i x-09 '03 + -3439 1638 "" -0609524742
= 366-7540160, and 366-7540160 = 5 . 642369476j
which is the present value of i per annum under the con-
ditions.
In the year 1850, Mr. Peter Hardy, a well-known writer on
annuities, wrote and introduced a paper on this subject to the
Institute of Actuaries, which created considerable interest at
that time. His mode of treating the question is here
given :
6 Problem. To determine the present value of an annuity
certain of i for n years, which is to pay during its continuance
a given rate of interest on the original purchase money, and to
replace that purchase money at the expiration of the term at a
different rate of interest.
6 Solution. The payments of the annuity being each = i,
let i' = the rate of interest which the purchaser intends to
make on each i of his investment, or, as it may be termed,
the remunerative rate.
'Let(r i) = the rate of interest at which the purchaser
expects to accumulate the surplus annuity, in order to replace
the original capital, or, as it may be termed, the accumulative
rpn _ j
rate. Let - = the amount of an annuity of i for n
ri
years forborne and accumulated at (r i ) rate of interest, and
put V = the required value.
* Now it is obvious that
Vi' = the purchaser's annual interest,
i Vi f = the surplus annuity to be accumulated,
so that in n years it may reproduce F.
CONSTRUCTION AND USE OF VALUATION TABLES. 47
If i per annum in n years will accumulate into
then
r i
and if, for the sake of simplicity, we represent
r-i '
by a single symbol, say A, we shall have
7= (i-Fi')4,
F= A-Vi'A,
V+ VVA = 4,
F==
6 Example. Eequired the present value of an annuity of
i per annum for 20 years, the purchaser to make 5 per cent.
per annum interest of his outlay, and to replace his capital by
the investment of his surplus annuity at 3 per cent.
'Here the annuity = i, i f = '05, (r i) = '03 'and
A = 26*8703 at 3 per cent., and
log 26-8703 = 1-4292677
i'3435i5
i
0*36086^0 i
log 2-343515 = -^ v = log 11-466 = value.'
1-0594027
The rule proposed by Mr. Hardy, was intended to effect the
same purpose as that of Mr. Morgan, but at the time of its
introduction it was considered by some to be very diffuse, and
that the subject admitted of simpler and more lucid treat-
ment.
Peter Gray, Esq., F.R.A.S. and F.E.M.S., an eminent
mathematician, and author of several valuable works, took the
48 THE ENGINEER'S VALUING ASSISTANT.
matter up in the Assurance Magazine, and, signing himself
' A Subscriber,' published a mode of solving the problem in a
much more simple, lucid, and satisfactory manner than that
adopted by his predecessors. In my opinion it is most elegantly
constructed, and admirably adapted to the purpose. I give it
here according to the author's own version, and for the original
letter see pages 101 and 102 of the Assurance Magazine,.
vol. i. 1851 :
6 Call the sum advanced, the present value, m
Annuity . . . p
The realised rate . . r per .
Investing rate . . r'
And we have to find the relation between m and p when r and
r' are given.
4 The annual interest on the sum advanced is mr, whence
the sum to be annually invested is p mr ; and if A denotes
the amount of an annuity of i at the investing rate during
the term, we have by condition
(p mr)A = m.
( From this we get
and
m (i -f rA) f i \ ( x
p= L^ >, or mQ + rJ ... (2)
c If the annuity is i we have from ( i)
A i
m = , or
J T
f Again, if the sum advanced or present value is i, we get,
from (2),
6 Once more, if the arrangement as to the annuity and
the sum to be advanced is made between the parties without
CONSTKUCTION AND USE OF VALUATION TABLES. 49
reference to rates, we find for the realised rate from the first
expression
(p mr)A = m,
m
^^U.orP '
m m A
The rule laid down in ( I ) is the same as that which I have
employed, wherein is what I have termed the redemption
_L
fund, and called by French writers the amortizing annuity.
Attached to Mr. Gray's letter, is a very important note by
the Editor of the Assurance Magazine, in which he states
that his correspondent ' did not seem to have anticipated that
Mr. Hardy's paper would appear in that magazine,' and that the
subject had been previously investigated by Mr. Morgan, and
further that it had not ' occurred to any of these writers that
by far the most simple way to treat the question would be to
construct tables showing the annual payments required at prac-
ticable rates to produce i at the end of n years. Calling these
results /, we shall have the relation between p and m (to use
our correspondent's notation) by inspection, and
m = ** , p = m (r-fr'Xand r == - rV
s
Although rules have thus been supplied by a few mathe-
maticians, nevertheless there is but little to be found upon the
subject in books, neither can I discover any table computed to
any extent by their means. Mr. Hardy calculated and attached
a small table to his paper previously referred to, extending to
one 8vo. page only, for rates of interest of 5, 6, and 7 per "cent.,
and to redeem capital at rates of interest of 3, 3 J, 4, and 5 per
cent, carried to 3 decimal places.
This table was introduced into Inwood's Tables, by the per-
mission of Mr. Hardy, in 1853, but it is cut down to 2 places of
decimals, and extends to two I2mo. pages only. This orio-inal
table by Mr. Hardy, was also cut down to two places of decimals,
and incorporated into Mr. C. M. Willich's book, as may be seen
in the edition published in 1871. It is less perfect than the
50 THE ENGINEER'S VALUING ASSISTANT.
original, as the years' purchase is only given for every loth year
after 50 years.
Mr. Downing Biden also published in 1 864, two 8vo. pages
of tables of this kind for rates of interest from 3^ to 8 per
cent, carried to 3 places of decimals.
There is also a table of the same class, in Hurst's * Architec-
tural Surveyors' Hand Book,' published in 1866, computed from
3|- to IO per cent., and to 4 places of decimals, and is the best
that has come under my notice. All these tables, however,
especially the last-named are very useful within the limits
assigned ; but I am not acquainted with any tables of this class
that are sufficiently extensive to be of any real practical use to
persons engaged in valuing Mineral properties, where high rates
of interest are expected to be realised on the purchase money,
or capital invested.
The rate of interest allowed to a purchaser of mineral pro-
perty, such as Collieries, Iron Mines, and others, frequently
ranges between 10 and 25 per cent., but more generally between
14 and 20 per cent., depending of course upon the character of
the property. It is evident, therefore, that tables calculated
for rates of interest no higher than 8 or 10 per cent.^ and to 2
or 3 places of decimals, could not be employed for ascertaining
the true value of annuities derived, or to be derived, from high
rates.
It is stated on page 2, in all the editions of 'Inwood's Tables
of Annuities' that I have seen that is to say, those published
from 1837 to 1866 that 'A lease or annuity for 14 years, to
make 3 per cent, and get back the principal, is worth 1 1 -296
years' purchase of the clear annual rent,' and this rule is repeated
as a foot-note as far as page 9, as being true for all the rates of
interest up to 10 per cent. The table goes no higher than 10
per cent., but it is identical with Mr. Smart's table and that
of all subsequent writers of the present value of 1 per annum,
for any number of years. This table, and others of its kind,
to be found in most works on Annuities, is constructed cor-
rectly according to the mode laid down ; but as that mode is
based on incorrect principles, its application to the valuation
of annuities, where interest is allowed at higher rates p-er cent,
than can possibly be found for reproducing capital, is entirely
fallacious, for the principle upon which it is based assumes that
CONSTRUCTION AND USE OF VALUATION TABLES. 51
we can reproduce capital which may have been invested, at the
same rate of interest as that allowed and expected to be realised
on the purchase money invested.
Tables of this class are, therefore, limited in their use to
cases where the rate of interest on the capital invested, is the
same as that which may be practically obtained in the funds
for redeeming the capital. I have, however, good reason for
concluding that many well-known Engineers, and others, still
employ tables of this kind in valuations connected with mineral
properties, even when the rate of interest ranges between 10
and 20 per cent. A clear proof of this assertion may undoubt-
edly be found on examining the evidence published as having
been given before a Committee of the House of Commons, on
the Eating of Mines in 1857, and fully quoted in the foregoing
pages of this work.
I desire it to be understood, however, that I am antagonistic
to none, but feel great respect for those gentlemen who gave
the evidence referred to, as I conceive they believed they were
right. I certainly cannot, however, consent to pass over a
matter so vastly important, and which is, in my opinion, at
variance with reasoning based on correct principles.
Eeferring therefore again to Mr. Taylor's statement, ' that a
perpetuity at 8 per cent, is worth \2\ years' purchase,' that is
to say, the present value, of i per annum according to the old
Tables is 12-4943 years' purchase, and it must be evident that
it is this class of table Mr. Taylor employs in arriving at the
value as stated.
The value by Mr. Taylor's statement = 12*4943
by correct tables . . = 12*24789
Difference . . = -24641
or 45. I id. too much, equal to 24*641 per cent, lost on every i
annuity purchased according to his rule. Mr. Dunn also states
(see his work on the Coal Trade) c that 30 years' duration at 8
per cent, is 11*25 years' purchase' that is, the present value of
i per annum at 8 per cent, for the period stated is 11*2578
years' purchase.
The value by Mr. Dunn's statement = 11*2578 years' purchase.
by correct tables . . = 9*8991
Difference . =s 1*3587
B 2
52 THE ENGINEER'S VALUING ASSISTANT.
or i 75. 2d. too much, equal to 135*868 per cent, lost on every
i annuity purchased. But to be clear that no mistake has
occurred in Mr. Dunn's statement, he further adds, ' that for a
duration of 15 years at 14 per cent.,
The years' purchase is . =6*14
The value by correct tables = 5-16084867
Difference . . = '9/915133
or 195. 6fd too much, equal to 97-915 per cent, lost on every
i annuity purchased by the use of the old tables. (See Table
XII.)
Now, as these gentlemen must have believed their method
of deducing the value to be true, it would be very much out of
place to pass any severe stricture on them ; but as correct rules
were in existence, by which the accurate value in years' purchase
at a given rate could have been ascertained, before they gave
their evidence, it is, to say the least, a great pity they did not
avail themselves of them.
Furthermore, I apprehend that such evidence was obtained for
the purpose of recommending the passing of some enactment as
to the Eating of Mines ; it was, therefore, placing the Committee
in a wrong position ; as all the evidence collected and published
by them tends to show that coal and other mines were of greater
value than could, in strictness and on just and equitable prin-
ciples, be assigned them.
The question is, as I have before said, of vital importance,
and may, I think, be so far demonstrated as to put it beyond a
doubt or mere matter of opinion ; and by employing the proper
rule previously referred to and laid down in this work, the truth
may possibly appear more clear and convincing by deductions
arrived at from numerical examples.
Taking 3 per cent, as interest to be realized on capital
invested, and redeeming that capital at the same rate within
14 years, we have, the redemption fund to reproduce the
capital at 3 per cent, within 14 years = '05 8 5 2634.
Then '05852634 + -03 = -08852634 and
-0885 2634
= 11*29607314 years' purchase, practically the same as in
vl
CONSTRUCTION AND USE OF VALUATION TABLES. 53
Inwood, and in all other writers on Annuities, but correct to
more places of decimals.
Now, assuming a purchase was effected by allowing 20 per
cent, instead of 3 per cent., and by the same rule also to recoup
at 20 per cent., we have, the redemption fund to recoup at
20 per cent, within 14 years = *o 1689305 5 2>
Then -oi6802 + -20 = *2i6802 and
= 4*610567171 years' purchase.
Suppose the annuity to be purchased equals 20,000, its
present value, immediate, would be 4*610567171x20,000
= 92211*34342.
Then 20 per cent, upon this sum = 18442*268684
And 9221 1*34342 x -0168930552= 1 55773*3 16
The annuity . . 20,000*000000
It is, therefore, evident that if a purchaser were to invest
92211*34342 in purchasing an annuity of 20,000, derived
from some mineral property, he could not invest annually in
any funds so small a sum as i 557*73 J 3 J 5 f r J 4 years, that
would yield him 20 per cent. It would, therefore, be impossible
to realise or reproduce the original capital invested, within the
time, under the circumstances.
Now, if we apply the proper rule, which is founded upon the
principle that an investor realises a certain rate on his capital,
and can reproduce that capital at another, but lower, and more
practicable rate, we shall find that a serious discrepancy exists
in the last preceding mode of ascertaining the value.
Taking 20 per cent, as interest to be realised on capital, and
to redeem that capital within 14 years at 3 per cent, compound
interest, we have the redemption fund necessary to replace i
within the time = -058526339.
Then -O58526339 + -2O = -258526339,
-258526339 = 3-868077828 years' purchase,
54 THE ENGINEER'S VALUING ASSISTANT.
which is the true sum that must be given, in order to secure i
annuity for 14 years, allowing 20 per cent, upon it, and to
replace it at 3 per cent, within the time.
To secure an annuity, therefore, of 20,000, there must be
invested a sum equal to 77361-55656; and to get it back
in 14 years at 3 per cent, an annual redemption fund of
4527-6887446 would be required to be set aside to accumulate
at compound interest.
For 20 per cent, on 77361-55656 = 15472-31131
And 77361-55656 x -058526339 = 4527-68869
The annuity as before = 20000*00000
The present value obtained by Inwood's rule,
and endorsed by many others (see pages
2 to 9 of his book) . . . .= 92211*34342
The present value found by correct method,
viz. to realise at one rate per cent., and to
redeem at another rate, say 3 per cent. . = 77361*55626
Difference * * . = 14849-78716
It is conclusive, therefore, that a present purchaser would
be paying too much by -742489358, in order to secure i
annuity, or a total of 14849-78716.
For the difference between the incorrect and the true years*
purchase
= 4-610567171-3-868077813 = 742489358,
and -742489358 x 20000 = 14849-; 871 6,
being the difference in error as before, or a loss of 74-2489 per
cent, on the annuity purchased. (See Table XII.)
The practice, therefore, of valuing upon tables constructed
on the assumption of reproducing capital at the same high rate
of interest, as that which may be realised on it, is opposed to the
truth, and calculated to mislead and injure a purchaser to a very
large extent.
CONSTRUCTION AND USE OF VALUATION TABLES. 55
The subject of Deferred Annuities, embracing two different
rates of interest per cent., has not, in my opinion, hitherto re-
ceived so much attention as some other of its branches, although
deferred annuities involving one rate of interest have been fre-
quently and ably discussed. Nevertheless, after diligent search
and enquiries that I have instituted, I cannot discover anything
which appears to me to bear directly upon the case when two
rates of interest are considered in any of the published works
devoted specially to Annuities.
The rules already in use may give approximations, but
I have deemed the question of sufficient importance to call for
further investigation ; and with a view to establish more uni-
formity in practice, appropriate formulae, and practical rules,
have been devised, peculiarly adapted to the construction of
tables of this nature. These rules have previously been laid down
in a former portion of this work, and a proof of their accuracy ,
demonstrated. They are, I believe, important ones, and the
Tables calculated by their aid are now introduced for the
first time.
When one rate of interest is considered, the general prin-
ciple applied to deferred annuities is, that when the value at a
specific rate of a benefit with reference to a specified epoch has
once been determined, the value at the same rate with reference
to any other epoch is assigned by multiplying that first deter-
mined, by the power of v whose index is the number of years
in the period of deferment, or the interval through which the
value is in a sense transferred.
Thoman's definition is ' that the present value of a deferred
annuity is equal to the difference between two immediate an-
nuities of the same yearly income, one for the whole term, the
other to continue until the time of entering on the deferred
annuity.
This rule, however, embraces but one rate of interest in the
present value of i per annum, but it has, I believe, been fol-
lowed by all writers on Annuities, and by many valuers since
Thoman's time. It is thus illustrated :
Assuming the annuity to be deferred t years, and to con-
tinue n years afterwards, that is, say 5 5 years after 3 years, we
have
56 THE ENGINEER'S VALUING ASSISTANT.
The present value of 3 + 55 = 58 years
at 3 per cent. = 27-33100549
The present value of 58 55 = 3 years
at 3 per cent. ... = 2-82861138
Present value deferred 3 years =24-50239411
Now if we suppose the interest allowed on an investment is
20 per cent., and also to reproduce the capital at the same rate,
employing the above rule, we have for a duration of 14 years
after 3 years :
The present value of 3 + 14 = 17 years at
20 per cent = 47746338
The present value of 17 14 = 3 years at
20 per cent. . . . . .= 2-1064815
Present value deferred 3 years . =2-6681523
But allowing a purchaser 20 per cent, upon his investment,
and to reproduce the capital at 3 per cent, for a similar period,
that is to say 14 years after 3 years, we have from (14),
Or,
17-08632416 _ _ 17-08632416 _ 2 . 2 ~ g47og6 -
1728 X(I+'20X 17-08632416) 7-63303363
years' purchase, or value deferred three years.
The deferred value by Thoman's or Inwood's rule = 2*668 1 52300
The deferred value by correct method . = 2-238470965
Difference =-429681335
A purchaser would, therefore, be paying too much for each
i annuity, by -429681335, or Ss. jd. ; and if an annuity of
20,000 were purchased, the gross overpaid sum would amount
to 8593-6267, or 8593 I2s. 6lcZ., or a total loss of 42-968
per cent, upon the annuity.
CONSTRUCTION" AND USE OF VALUATION TABLES. 57
For 2-668152300 X 20000 = 53363-0460
And 2-23 8470965 X20OOO = 44769-4193
Difference as before = 8593-6267
Again, taking another case under Thoman's and Inwood's
rule, as generally adopted, and allowing 20 per cent, to a pre-
sent purchaser, and to reproduce the capital at the same rate,
we have for a duration of 5 5 years after 3 years :
The present value of i per annum for
58 years at 20 per cent. . . .= 4-999872221
The present value of i per annum for
3 years at 20 per cent. . . = 2-106481481
Present value deferred 3 years =2-893390740
But, by allowing to the said purchaser 20 per cent, upon his
investment, and to reproduce the capital at 3 per cent, the period
of time being as in the last preceding case, or 55 years
after 3 years, and adopting the correct rule for such a case,
we have
_ 136*07161972 _!36-07i6i972_ 2 6 6
1728 X (l +-20 X 136-07161972) 4875435056
the correct value deferred.
The deferred value by Thoman's or Inwood's
rule ....... = 2-893390740
The deferred value by correct method . = 2-790963639
Difference = -102427101
The difference, therefore, is equivalent to 28. o^d. per i 9
and, if as before, an annuity of 20,000 were purchased, the
overpaid value or total loss would = -102427101x20000
= 2048-54202; that is to say, every i annuity purchased under
such conditions would cost too much by -102427101, or 10*243
per cent.
When one rate of interest only is considered in the purchase
of an annuity, and redemption of the capital invested is made
58 THE ENGINEER'S VALUING ASSISTANT.
at the same rate per cent, the rule as employed by Inwood,
which may be found from pages 2 to 9 of his Tables, and which
has been the subject of investigation in this work, would un-
doubtedly be correct, and the value derived, tolerably reliable
for percentages up to 4 or 4-| ; but it has been shown that when
two different rates of interest enter into the question, its appli-
cation to the valuation of mineral or any other property would
produce erroneous results.
In the purchase of mineral properties, the rate of interest
allowed on the investment that is to say, purchase money or
capital should not be fixed at the same rate as that proposed,
or which may be found practicable, for the redemption of the
capital, otherwise a difficulty would be created in obtaining a
return of the large sums annually laid out in gigantic
mining concerns ; and this applies to Collieries as well as other
mines.
It has been previously stated that in the purchase of Mines,
the rate of interest ranges from 14 to 20 per cent. ; but it is
evident that such rates could not be realised for the purpose of
redeeming capital invested in a mine by available means,
such, for instance, as in land, houses, Consols, or other, similar
well-known securities. What I mean by the redemption of
capital, is being put in a position to find the original sum
expended, in safe keeping, at the time the mine and annuity
ceases.
From a consideration of these circumstances, it is difficult
to conceive how those persons accustomed to make valuations
dependent upon tables which assume that the profit rate is
identical with the reproductive rate of interest, no matter how
high the former may be are justified in adopting and con-
tinuing such a system. It has, however, been strongly urged to
me, as a sort of defence of the system, that a proprietor having
an open colliery or other mine, equal in duration to a perpetuity,
or say 100 years, may profitably reinvest, so to speak, his sur-
plus annuity in the extension of his mining operations, and
thereby produce an annual increase in minerals, and conse-
quently in annuity, and so gain upon it the same rate of in-
terest as that realised on the original capital already brought
into productive action. The surplus annuity, which should
have been invested in some good security at either 2~ or 3 per
CONSTRUCTION AND USE OF VALUATION TABLES. 59
cent., thus becomes charged as original capital, simply written
off the ledger accounts, or paid to shareholders as dividends
year by year, until the mine is unproductive ; but, at the same
time, there has been no special means adopted on this hypothesis
in providing for the redemption of the accumulated capital.
Only upon this suggested, but really impracticable mode,
can an attempt ever be made of reinvesting the surplus annuity
at the same rate as that realised on the capital, unless, indeed,
a purchaser is willing to accept 3, 4, or 5 per cent, on his in-
vestment.
But to realise the idea fully, the mine operated upon in
such a way as that suggested, must be made to yield constant
results, and the state of the market must also be such, as to
produce uniform profits upon the minerals annually produced, in
the case of a going concern, but in the case of a deferred an-
nuity, expected to arise from an undeveloped property, the rate
per cent, upon which the mine was purchased and expected to
be obtained during its continuance, must not only be guaran-
teed by an engineer's report, but, to be actually realised, the
general state of trade must not fluctuate so as to depreciate the
value, as previously determined, when the mine is brought into
productive condition. Again, at the expiration of 20 years
from the present time, the result to be obtained from any mine
cannot be absolutely guaranteed; and, although the value may
have been arrived at with very great care and judgment, never-
theless unforeseen contingencies, arising from some particular
and unavoidable circumstance connected with a mine, coupled
with a downward tendency of trade, may depreciate the value
of that particular mine.
Then, if it be granted that from such causes the annuity
derived from any mine is not a constant amount, but that it
may suffer from the fluctuations of trade, it is also granted, or at
least it would follow, that as the annuity is a variable quantity,
although it had formerly been fixed, or guaranteed, by allowing
a certain rate per cent., as profit on the purchase, a valuation
made upon the assumption that the capital could be redeemed
at a uniform rate, as high as that fixed for profit, would be alto-
gether unreliable.
I have gone into this matter rather fully, because I am
aware that the kind of tables I have mentioned as being erro-
60 THE ENGINEEK'S VALUING ASSISTANT.
neous in principle, are much employed in Valuation, and that if
a rule becomes established as applicable to one mine, it would
be equally competent to apply it to all other mines. I should,
however, discard the principle involved, and reject any valuation
made upon it.
To such considerations as those enumerated, earnest atten-
tion must be given, and in order that large capital sums should
not be lost, it is undoubtedly the safest, as well as the wisest
plan to anticipate, as far as possible, every contingency, and
out of the general annuity derived from a certain realised rate
per cent, on the capital invested in any mine, set aside such a
sum as may be determined by calculation, and which, if in-
vested in Consols, or some other fund equally secure, will, at the
normal rate of 3 per cent, interest, reproduce the original
capital at the time when the annuity ceases.
I intended to have concluded this subject here, but having
communicated my views to a friend, he forwarded to me a
pamphlet, entitled c An Investigation of the Errors of all Writers
on Annuities,' by William Kouse, published by Lackington,
Allen, & Co., 1816. It extends to 40 small 8vo. pages, and, as
I conclude it is scarce, I take the liberty of making a quotation
from it. He says, commencing at page 36, 'As to the tables
published at rates of interest above 5 per cent, per annum,
when the principle on which they are formed is considered,
they will be found both impracticable and illusive to pur-
chasers.
' The principle on which all the tables hitherto published,
for the valuation of terminable incomes, whether for years or
lives, have been formed, is that the yearly income will not only
be equal to the interest per cent, named in the tables, but as
much more as will replace (at the end of the term of life) the
capital employed. For instance, if a person pay 802 for an
income or i oo per year for 1 7 years, he employs his money, or
capital, at 10 per cent, interest (according to the tables); that
is, he is supposed to receive 10 for every 100 advanced, and
as much more as will replace the 802 at the end of the 1 7
years. 10 per cent, on the capital employed is So 43. od., but
as he will receive 100 each year, the difference, or ig i6s. od,
per year, is the sum to replace the 802 at the end of the
term; this it will certainly do if a man can make 10 per cent.
CONSTRUCTION AND USE OF VALUATION TABLES. 61
interest on ig i6s. od. every time he receives it; but at 5
per cent, the same sum will only amount to 511 in 17 years.
Now I appeal to the common sense of every man, if it be prac-
ticable to improve small sums of money at a greater interest
than 5 per cent. ? indeed, beyond this rate it is illegal to lend
money, and no leases, annuities, or government securities, can
be purchased with small sums of a few pounds each, which in
general form the excess of interest to replace the capital with
when the income ceases.
* Such being the principle on which all the tables of com-
pound interest for the valuation of leases and annuities for
years or lives are formed, they must be practically wrong
where they exceed the rate of 5 per cent., which being the legal
interest of the country, all calculations to replace the capital at
the end of the term ought to be made in this rate ; and as these
tables form the basis of all the calculations for annuities on
lives, they must follow the same fate ; for the present value of
an annuity certain, for any number of years, is the several
present values of the several sums to be received at the end of
the first, second, third, &c., years to the end of the term, added
together; and he present value of a life annuity is nothing
more than the amount of the said several values, each dimi-
nished in proportion as -the respective probabilities of the person
being alive at the end of the several years to receive them, are
below certainty, and continued to the most probable extent of
life. Now, as the values of annuities for lives depend on the
combinations of these two sets of tables, if one requires new
modelling, and the other is practically wrong, all the results at
rates exceeding 5 per cent, must be doubly incorrect.'
Biden also states that ' the ordinary tables (present value of
i per annum) at high rates are erroneously applied in valuing
leases, &c., because they assume the possibility of making annu-
ally an investment of surplus at those high rates, which is im-
practicable.'
The question of the redemption of capital is of as much im-
portance to the landlord or lessor, as it is to the lessee. For, in
the case of collieries and other mines, the lessee removes annu-
ally so many acres of the minerals contained in the estate.
Unless, therefore, the lessor invests annually a certain sum
derived from the royalty dues at the termination of the lease, or
62 THE ENGINEER'S VALUING ASSISTANT.
exhaustion of the minerals in the royalty area, the c Fee Simple '
in the mineral estate would be entirely lost.
On the contrary, if provision had been made for redemption
at the end of the term of the lease, or when the mineral estate
is exhausted, the annual investment would accumulate to the
original value of the royalty, and the landlord, or lessor, would be
in possession of a sum which could be invested in land or other
property of a permanent character. Thus, the original value of
the mineral estate would be continued in another form.
All terminable annuities, no matter from what source derived,
should be purchased upon a principle, which would allow a
portion of such benefit to be annually invested, and capable of
yielding back the original capital at the termination of the
income.
PART III.
PEACTICAL EXAMPLES
IN THE
VALUING OF COLLIERIES,
IRON AND OTHER MINES,
ROYALTIES, LEASEHOLDS, FREEHOLDS, LIFE INTERESTS, &c-
ALSO
ANNUITIES DEEIVED FROM ANY SOURCE, EITHER
IMMEDIATE OK DEFERRED.
% 66 THE ENGINEER'S VALUING ASSISTANT.
3. In What Time will 650 amount to 858 at 4 per cent.
simple interest ?
Here 650 x -04 = 26*00, and 858 650 = 208.
Then _??- 8 . = 8 years.
26-00
4. What is the Bate per cent., simple interest, when 650
amounts to 858 in 8 years ?
Here 650 x 8 = 5200, and 858-650 = 208.
Then - = "04. And -04 x 100 = 4 per cent.
5200
5. What Discount should be allowed for the present payment
of a bill of 920 due at the end of three months, interest being
at the rate of 5 per cent. ?
Here 3 months = -^-ths of a year = '25.
And '25 x -05 = "0125. Then -0125 + i = 1-0125.
And 9 20 = 908*64197.
Then 920 908-64197 = 11-35803, the discount required.
6. What Will an Annuity of 650 amount to in 12 years at
5 per cent, simple interest ?
Putting a = annuity, or 650,
r = interest, or 5 per cent.,
t = years, or 12,
M = amount.
Then Jf=-
And M = ("("-')-Q5 + 12) 650 = 9945-
7. What Annuity will amount to 9945 in 12 years at 5 per
cent, simple interest ?
Here a =
t (ti
Or a = - . 9945 * 2 -- = 650, the annuity.
12 (12 '
PKACTICAL EXAMPLES IN VALUATION. 67
8. In What Time will an Annuity of 650 amount to ^9945
at 5 per cent, simple interest?
Here t =
2T
And t = Y _ 650
2X 'OS
= 12 years, the time required.
9. At What Rate per cent, simple interest, will an annuity
of 6$o amount to 9945 in 12 years?
( 9 lr-' 2 )
Or r = 2 = 'O5, and -05 x 100 = 5 per cent,
12 X ^ 1 2 ~~ I y
the rate required.
COMPOUND INTEREST.
10. What will ^6500 Amount to in 40 years at 5 per cent,
per annum compound interest ?
Here (i-O5) 40 = 7-039988712. (See Table L)
Then, -
7-039988712x6500= 45759-926628, the amount required.
By logarithms :
log 1-05 . . \ '. ] = 0-021189299070
40
0-847571962800
6500 ; \*,: ^ .= 3-812913356643
n 45759'9266290 . = 4-660485319443
F 2
68 THE ENGINEER'S VALUING ASSISTANT.
11. What Principal will Amount to 45759*926629 in 40
years, at 5 per cent, per annum, compound interest ?
Here - ^- 6500, the principal required.
7-039988712169
By logarithms :
log 1-05x40 . . . . =0-847571962800
45759"9 2662 9 ' -V = 4*660485319443
6500 . .,", ,, . .' =3*812913356643
the principal, as previously determined.
It is evident that by employing Mr. Gray's Logarithmic
Tables to 1 2 places of decimals, we obtain better results than
could be supplied from the common 7-figure table.
12. What is the Rate per cent, when 6500 amounts to
45759-926628 in 40 years ?
Here we have
the amount of 1 in 40 years, and this number will be found
in the column of the amounts under 5 per cent., which is the
rate required.
Or thus :
^7-0399887121 = 1*05, and 1-05 1 = -05.
Then '05x100= 5 per cent.
By logarithms :
log 45759'9 26628 . . = 4-660485319443
6500 .... = 3^12913356643
40)0-847571962800
,,1-05 . . . . = 0-021189299070
And 1-05 1 = -05, then -05 x IOO = 5 per cent., as above.
13. In what Time will 6500 amount to 45759-926628 at
5 per cent, per annum compound interest ?
Here 45759^ = 7 .
PEACTICAL EXAMPLES IN VALUATION. 69
the amount of i at 5 per cent, per annum. Then, by inspect-
ing' the Tables' under 5 per cent., the number 7*039988712 will
be found opposite 40 years, which is the time required.
By logarithms :
log 45759*926628 V v . = 4*660485319443
6500 . ; ':. '~~~ .;" . = 3-812913356643
0*847571962800
and log 1*05 = -02118929907.
Then "847571962800 =
02II8929907
AMOUNT OF ANNUITIES AT COMPOUND
INTEREST.
14. What will an Annuity of 6500 amount to in 40 years,
at 5 per cent, interest being payable annually ?
The amount of i per annum in 40
years, at 5 per cent., see Table (III). = 120*7997742425
6500
785198*5325762500
By logarithms :
log 1*05 = -02118929907
_ 4 U Natural Number.
0*84757196280 = 7*039988712169
6-039988712169
Then,
log 6-039988712169 = 0*781036126991
6500 . . = 3*812913356643
-05 . . = 2-698970004336
5-894979479298 =785 198*5325821,
the amount as above.
Also 6-039988712 169 x 6500 = 785,98-53258197.-
70 THE ENGINEER'S VALUING ASSISTANT.
15. What Annuity will Amount to ^785198-53258197 in 40
years, at 5 per cent, per annum ?
Here 785 198-53258197 x -05 = 39259-9266290985.
The amount of i in 40 years, Table (I) = 7-039987712169,
And 7-039988712169 i = 6-039988712169,
Then 39259-9266290985 = 6 or annuit
6-039988712169
By logarithms :
log 1-05 = 0-02118929907
40
0-84757196280 = 7-039988712169
I
6-039988712169
log (785 198-53258197 x -05) = 4-593949483634
6-039988712169 = 0-781036126991
3-812913356643
= 6500 as above.
By the Tables
The amount of i per annum in 40 years at 5 per cent.,
see Table (III) = 120-7997742425,
Then = ^
120-7997742425
1 6. What will an Annuity of 500 amount to in 10 years,
at 4 per cent, compound interest, the annuity and interest being
payable half-yearly ?
Here, as the time is 10 years, and the rate of interest 4 per
cent, for half-yearly payments, it becomes I o x 2 = 20 half
years, and - = 2 per cent.
Then(i-02) 30 = 1-4859473960,
And 1-4859473960 i = -4859473960, see Table (I) for 2 per
cent, at 20 years.
Also -48594/3960x500 = 6o74 . 34245 .
-O4
PKACTICAL EXAMPLES IN VALUATION. 71
Again, taking the amount of i per annum for 20 years, at
2 per cent., see Table (III) = 24-2973697989.
And = 250;
Then 24*2973697989x250 = 6074-34245.
If, however, payments were made quarterly, then we should
have 10x4= 4^o quarter years, and = I per cent.
4
Then (i-oi) 40 = 1-4888637336, the amount, see Table (I);
And 1-48886373361 = -4888637336;
'4888637336X500 =
04
By employing the amount of i per annum for 40 years, at I
per cent., see Table (III) = 48-8863733588.
And =. 125.
4
Then 48-8863733588 x 125 = 61107966985,
practically the same as above.
17. Required the Time in which an annuity of 6500 will
amount to 785198-53257625, interest being at 5 per cent.
Here 785 198-53258197 x -05 = 39259-9266290985,
I And 39259^266290985 = 6 . 0399887I2l69j - ;
And 6-039988712169+ i = 7-039988712169
Then log 7-039988712169 = 0-847571962800
And 1-05 = 0-021189299070
Whence ' 8 4757i9 (5 28oo _ the time requirei
0-021189299070
By the Tables
785l9 65 5 oo 58197 = I20 *7997742425, - - :
the amount of i per annum, at 5 per cent.; and in Table (III)
under 5 per cent., this number corresponds to 40 years, the
time required.
18. An Annuity of 6500 amounts to 785198-53258197 in
40 years ; required the rate per cent.
72 THE ENGINEEE'S VALUING ASSISTANT.
Here 785198-53258197 = ,207997742425,
or the amount of i per annum in 40 years, at the rate required ;
and upon finding this number in the Tables opposite 40 years,
the rate per cent, will be found at the head of the column in
which the number 120*7997742425 is found. In this case the
rate is 5 per cent.
Much has been written upon the theory of this problem, but,
after all, such investigations have only led to approximate
results by a no very direct method, which is neither convenient
or facile. Dual Arithmetic, however, according to Mr. Byrne,
is said to furnkh direct means for its solution.
PKESENT VALUE OF SUMS AT COMPOUND
INTEREST.
19. What is the Present Value of 500 due at the end of
30 years, allowing interest at the rate of 5 per cent. ?
By Table (I), (i-os) 80 = 4-3219423752, the amountof i in
30 years, at 5 per cent.
Then - - = 115-6887243266,
4-3219423752
the value required.
Again - l - - = -2313774486,
4-3219423752
and -2313774486 x 500 = 115-6887243, the present value as
before. The number -231373486 may be obtained direct from
Table (IV) opposite 30 years and under 5 per cent, to 8 places
of decimals.
By logarithms :
log 500 ..... = 2-698970004336
1-05 = -02118929907x30 = 0-635678972100
115-6887243181 . ..;.,. . =2-063291032236,
practically the present value, as before.
PRACTICAL EXAMPLES IN VALUATION. 73
20. What Sum may be Secured at the end of 30 years by a
present payment of 115-68872433, interest to be allowed at
the rate of 5 per cent. ?
By Table (I), (i'O5) 30 = 4-3219423752, and 4-3219423752
x 115-68872433 = 500, the sum required.
Also ^5-6887243266 = 5oo?asbefore .
2313774486
By logarithms :
log 1-05 = 0-021189299070
30
0-635678972100
115-6887243181 *.' . =2-063291032236
500 * : .' . v . ."' =2-698970004336
21. At the End of a Certain Term the sum of 500 has to be
paid in discharge of a debt, but allowing 5 per cent, discount
from the sum then due, a settlement may be effected by a pre-
sent payment of ^115-6887243181 ; what was the number of
years at the expiration of which the 500 should have been
paid?
log 500 .* . .. . . ' .- =2-698970004336
115-6887243181 .._.>, =2-063291032236
0-635678972100
Log 1-05 = 0-021189299,
, 0-6356789721 ,, ,. . ,
And JD ' ^' =30 years, the time required.
0-02118929907
22. If 500 is due at the end of 30 years, and may be dis-
charged by a present payment of ^115-6887243181, what rate
of interest per cent, was allowed ?
log 500 .^* . v . = 2-698970004336
115-6887243181 .' ' . . = 2-063291032236
30 ) 0-635678972100
1-05 . 'V = 0-03118939907
Then 1-051 = -05, and -05 x 100 = 5 per cent.,
the rate required.
74 THE ENGINEER'S VALUING ASSISTANT.
PKESENT VALUE OF ANNUITIES AT COMPOUND
INTEREST.
23. The Lease of an Estate has 30 years to run, the annual
value of which is 805, but is held subject to the payment of
270 per annum ; what is the present value of the title, allow-
ing interest at the rate of 5 per cent. ?
By Table (IV) the present value of i due 30 years hence,
at 5 percent. = -23137745, and I--23I37745 = 76862255.
Then 805 -270 = 535,
,;-. And 76862255 x 535 = 8224 . 26I285 ,
the present value of the title.
Again, a similar result may also be obtained by employing
the present value of i per annum for 30 years, at 5 per cent.
Thus, the present value of i per annum in 30 years, assuming
redemption of capital can be effected at the same rate,
= 15-372451.
And 15-372451 x 535 = 8224-261285,
the present value, as before. Table (XII) gives values of this
class to 5 places of decimals.
24. What Annuity to be continued 30 years, may be purchased
for 8224*261285, allowing interest to the purchaser at 5 per
cent, per annum ?
The present value of i per annum, at 5 per cent., redeem-
ing capital at the same rate, for 30 years = 15-372451.
And 822 4' 26l28 5 = 535, the annuity required.
'
We may also determine the annuity by employing the pre-
sent value of i due 30 years hence. Thus by Table (IV), the
present value of i due 30 years hence = -23137745, and the
arithmetical complement of this quantity = I '23137745
= -76862255.
A , 8224-261285 x -05
And ^^- f = - - - = 535, as above.
76862255
PRACTICAL EXAMPLES IN VALUATION. 75
25. An Annuity of 535 was purchased for 8224*261285,
interest being allowed at the rate of 5 per cent. ; required the
duration of the annuity.
Here 8224-261285 x -05 = 411-21306425,
And 535-411-21306425 = 12378693575.
Then log 535 ~log 12378693575
log 1-05
2-7283537820212-092674812446 __ '635678969575
02 i i 8929907 -02 i i 8929907
= 30 years, the time required.
PEEPETUITIES.
Perpetual Annuities are those which are to continue for
ever, and are consequently treated in a different manner from
annuities which are to continue for determined periods.
26. What is the Present Value of an estate in fee simple of
1200 per annum, interest of money being at the rate of 5 per
cent. ?
Here - = 20, and 1200 x 20 = 2400^
the present value required, or
1 200
= 24000, the value as before.
27. What Perpetuity will 24000 purchase, interest of
money being at the rate of 5 per cent. ?
Here 24000 x -05 = 1200,
the annuity required ; or
= 20 and 24 00 = 1200, as above.
5 20
28. What Rate of Interest is realized when 24000 will
purchase an annuity in perpetuity of 1200 ?
Here I2OOX 100 = 120000,
And - - = 5 per cent., the rate of interest required.
24000
76 THE ENGINEER'S VALUING ASSISTANT.
EEVEESIONS.
Keversionary or Deferred Annuities, are those which are not
to be entered upon until after the expiration of a certain denned
period. This subject has been fully entered into in the fore-
going part of this work ; it is therefore unnecessary to enlarge
upon it here, except by example.
29. What is the Present Value of a deferred annuity of
650, to continue 20 years, but not to be entered upon until
after the expiration of 6 years, allowing interest at the rate of
4 per cent. ?
The present value of i per annum for 26 years, at 4 per
cent., assuming capital can be redeemed at the same rate per
cent., = 1 5 -98 2769, and for 6 years = 5-242137.
Then 15-982769-5-242137 = 10-740632,
And 10-740632x650 = 6981-4108,
the present value deferred. This example is given to show the
mode generally adopted in solving the problem.
Again, the present value of i per annum for 20 years, at
4 per cent., = 13*590326, and the present value of i due in
6 years, at 4 per cent. = "79031453.
Then 13-590326x79031453x650 = 6981-4108,
present value as before.
Also, the present value of i per annum in 6. years, at 4 per
cent. = 79031453,
And for 26 years = -36068923,
And 79031453 -36068923 = -4296253.
Then ^96253x650 = 6 gl 8>
04
There is, therefore, an agreement in the present value de-
ferred, deduced by three independent processes ; but this could
not have occurred if two different rates of interest had been
involved in the years' purchase.
30. What Annuity, to continue 20 years after the expiration
of the next 6 years, may be purchased for 6981-4108, in-
terest being allowed at the rate of 4 per cent. ?
PKACTICAL EXAMPLES IN VALUATION. 77
Here(i-04)- 6 ..... = 7903145257
And (i-04)- 26 . . .. = -3606892329
4296252928
Then 6981-4108 x -04 = 279-256432,
And 279 ' 256432 = 650, the annuity.
4296252928
31. The Sum of 6981*4108 is expended in the purchase
of an annuity of 650, commencing after the expiration of 6
years. What length of time will the annuity continue when
the rate of interest is 4 per cent. ?
Here the amount of I in 6 years = (rO4) 6 = 1-2653190185,
A -, 6981-4108 x '04 x 1-2653190185
And I - TT -
650
650
= i -5436130378 = -4563869622.
-log -45638696 = -340666770752 = 2Q
log 1-04 -017033339299
the time required.
It may be here remarked that the logarithmic tables ge-
nerally employed in these cases are those before referred to,
by means of which the natural number can be easily found to
1 2 places of decimals.
The French mathematician, Callet, has a limited but very
valuable Table of Logarithms in his work, to 20 decimal places,
but the natural number can only be obtained to a few figures
from it.
32. What is the Present Value of the reversion of a per-
petuity of 650 per annum, after 6 years' deferment, interest
allowed being at the rate of 5 per cent ?
By Table (IV), the present value of i due in 6 years
= 74621540x650 =
-05
Or thus :
- = 20, and 20 x 650 x -74621540 = 9700-8002,
as before.
78 THE ENGINEER'S VALUING ASSISTANT.
By logarithms :
log 650 = 2-812913356643
-05 = 2-698970004336
13000 . . . =4'ii3943352307
value of perpetuity.
Then,
log of perpetuity . > ' . = 4-113943352307
1-05x6 . . ,. . = 0-127135794420
9700-8002 . . . . = 3*986807557887
value as before.
33. The Reversion of an estate in fee simple, after 6 years'
deferrence, is sold for 9700-8002 ; what annuity should it pro-
duce, so as to allow the purchaser 5 per cent, upon his purchase
money ?
By Table (IV), the present value of i due in 6 years
= 7462154-
rpn 9700-8002 X -O5 485-04001 Qfi . ,, .,
Then -^ ^ = ^ 3 H - = 650, the annuity.
74621540 -74621540
34. If a Perpetual Annuity of 650 is purchased for
9700*8002, allowing interest at the rate of 5 per cent., what
period of time must the annuity be deferred before being
entered upon?
Here
9700^002 x -05
Then
- log -7462 1 540 _ -127135792462 = 6 g
log 1-05 -02118929907
the deferred period.
35. Thirty years having expired of a lease having 40 years'
duration, what sum should be paid for renewing such lease for
the lapsed period, supposing the estate to produce a clear rental
of 200 per annum, interest being allowed at the rate of 5 per
cent, per annum ?
PEACTICAL EXAMPLES IN VALUATION. 79
Here the case is that of a deferred annuity, commencing 10
years hence, and to continue 30 years afterwards. If it were
possible to redeem capital at the rate of 5 per cent., the fol-
lowing is the usual mode of treating the question :
The old present value of i per annum for 40 years is
17-159086, and that for 10 years is 7*721735 ;
Then 17-159086 7721735 = 9-437251, or years' purchase.
Also 9-437251 x200 = 1887-450200,
the present value or sum to be paid down.
The old present value of i per annum for 30 years, at 5
per cent. = 15-372451 ; and this deferred 10 years = 9*43730.
Then 9*43730 x 200 = 1887-4600, the present value.
If, however, the capital can only be redeemed at 3 per cent,
per annum, the present value of. i per annum, allowing 5 per
cent, upon the capital for a duration of 30 years = j 4*08068 8,
but deferred 10 years = 8-644417. (See Table X.)
Then 8-644317 x 200 = 1728-8634,
the present value or sum to be paid down.
It will be observed, that in the examples given in this sec-
tion, no rate of interest has been employed higher than 5 per
cent., and then only upon the assumption that any capital sum
expended may be redeemed at the same rate per cent, as that
allowed on the purchase.
It is a question of the value of money at the time of
purchase, or the highest possible rate of interest available to a
purchaser for the redemption of his capital for the future
period, taking into consideration, however, the extra attendant
risk always incurred, when any sum invested is believed to be
capable of being redeemed at high rates of interest.
Most monetary transactions should undoubtedly be governed
by the average rate of interest realised from a fluctuating
market, over a series of years ; at least this would be the wisest
course. But if higher rates are required, and accepted upon
any transaction, the probability of an eventual realisation is
much further removed. Generally, therefore, the higher we
ascend the scale from the normal rate of interest, or 3 per cent.,
so is the risk of the redemption of capital increased propor-
tionally.
80 THE ENGINEER'S VALUING ASSISTANT.
VALUATION OF MINES.
36. What is the Present Value of a Colliery extending over
1 200 acres, and yielding 1 60,000 tons of coal per annum, to
continue 60 years ? The average annuity derived from the
Colliery during the last 10 years has amounted to 16,520, and
that arising from the surface, let as a farm, is 2400. The in-
terest allowed on the purchase of the Colliery to be at the rate
of 14 per cent, per annum, and to redeem the capital at the
rate of 3 per cent, per annum. Working plant to be included
in the purchase. Interest allowed on the purchase of the rough
farm land to be at the rate of 4 per cent.
Here, as previously laid down, we have
P n = present value, or purchase money.
r / = rate of interest allowed on ditto.
r = rate of interest allowed for redemption.
M n = the amount of an annuity of i at r per cent.
p = the annuity.
Then, from (19), we have
Substituting the numerical values for these symbols, we
also have,
/ =14 per cent.
M n = 163-05343680
p 16520.
Then,
163-05343680 x 16520 _ 2693642776^
i+ (-14x163-05343660) 23-82748115"
or 113047 146". Sd.,
the present value.
The present value of an annuity of i, at 14 per cent, for
60 years, and to redeem the capital at the rate of 3 per cent, is
6-84308324, or, in other words, the years' purchase. (See Table
VII, correct to 8 places of decimals.)
PKACTICAL EXAMPLES IN VALUATION 81
Then 6-843083 24 x 165 20 = 11304773512480,
or 113047 I4s.^8c.,
practically the same as before.
To find the Redemption Fund, we also have
M n = the amount of an annuity of i at r per cent, for
n years.
p = the annuity.
r' = the interest allowed on purchase money.
s n = redemption fund.
Then
"
and by substitution we also have
M n = 163-05343680,
p =. 16520,
r' =-14 per cent.
Then
i oo x 16520 1652000 jp r
i oo +(14x163-05343680) ~ 2382-748115 =
or 693 6s. 4d.j or s n .
Again, from (8) we have
^=S^= 5 .8 9I 6o3io 4 i-i = - 06I 3 2 9587,
which is the same as found in Table (V), and which will produce
i in 60 years at 3 per cent.
Then 113047-735 12480 x -0061329587 = 693-31709066,
or 693 6s. 4^.,
practically the same as before.
Then, for the disposal of the annuity, we have
The yearly interest on 113047-7351248, at
14 per cent, per annum . . i - = 15826 13 7f
And the annual redemption fund to replace
the purchase money within the 60 years
would be ..... = 693 6 4^
Together equal to annuity as above . . 16520 o o
G
82 THE ENGINEER'S VALUING ASSISTANT.
Then, if we multiply the amount of i per annum for 60
years by the annual redemption fund, the original capital will be
reproduced.
Thus 1 63*05 343680x6933 1 709066 = 113047 143. 8c.,
the purchase money or capital invested.
The land being in perpetuity, and 4 per cent, being allowed
to a purchaser, it is worth 25 years' purchase.
Then 2400 x 2 5 = 60000, the present value.
The present value of the Colliery . .= 113047 14 8
The present value of the estate . * . = 60000 o o
Total present value . :/ - . . . = 173047 14 8
37. What is the Present Value of the unexpired term of a
lease of a Colliery of 40 years, subject to a royalty to the lessor
of 6d. per ton upon all coal raised ? The present output is
90,000 tons per annum, and the average gross annuity derived,
10125. Interest on the purchase money to be allowed at the
rate of 1 6 per cent., and to redeem the capital at the rate of
3 per cent. The rate of interest upon the royalty to be allowed
at 8 per cent. The estimated worth of permanent plant and
stock is 45,000, to be sold at the end of the term for say
12,000, upon which a discount of 5 per cent, is to be allowed.
Here by Table (VII), the present value of an
annuity of i for 40 years, so as to allow
a purchaser 1 6 per cent, upon his purchase
money, and to redeem the same within the
time at 3 per cent, compound interest . = 5*77159342
Annuity ..... = 10125
Total present gross value . . . = ^58437*38337750
or 58437 73. 8d.
For proof we have the interest on58437'
at 1 6 per cent, per annum . . = 9349 19
And the annual redemption fund to replace
the gross value within the 40 years would
be 775 Q
The gross annuity as above . . . =10125 o
PRACTICAL EXAMPLES IN VALUATION.
83
The annuity resulting from the royalty on 90,000 tons per
annum, at 6d. per ton = 2250.
And by Table (VII), the present value of an
annuity of l for 40 years, at 8 per cent.,
and to redeem the capital at 3 per cent.= 10*72243731
Annuity . . . . . = 2250
Present value
. = 24125-48394750
or 24125 gs. Sd.
Also, for the value of the plant, we have
The present value of i due at the end of
40 years, at 5 per cent., by Table (IV) =
14204568
12000
Present value
. = 1704-54816000
or 1704 los. nd.
From the present gross value of the Colliery
lease .....
Must be deducted the present value of the
royalty .....
58437 7 8
= 24125 9 8
To which must be added the present value
of the plant =
34311 18 o
1704 10 ii
Total present net value of the Colliery lease = 36016 8 u
For proof of the value of the royalty
we have,
The interest on 24125-4839475 at 8 per
cent, per annum = 1930-038715
And the annual redemption fund to replace
the value at the end of 40 years
= 24125-4839475 x -0132623779 . = 319-96128$
Lessor's gross annuity. . . = 2250-000000
84
THE ENGINEER'S VALUING ASSISTANT.
For proof of the lessee's value we also
have,
The interest on 3431 1-89943 at 16 per
cent, per annum = 5489*9039088
And the annual redemption fund to replace
the lessee's value at the expiration of 40
years = 343 1 1-89943 x -oi 32623779 = 455*0573767
Lessee's gross annuity
5944-9612855
Then for proof of lessor and lessee's
gross annuity we have,
1930-038715x2 .. , , ' .' = 3860-077430
Lessor's redemption fund ' . = 319*961285
Lessee's gross annuity . . . = 5944*9^1285
The gross annuity as deduced on page 80 = 10125-000000
Again we also have,
3 19-961 285 + 445-0573767
Or 775 os. 4^d. as before.
775-018662
38. What is the Present Value of a Colliery yielding 60,000
tons of coal per annum, subject to a royalty to the lessor of 8d.
per ton upon all coals raised? The estimated duration is 25
years, and the annuity accruing 6000. Interest on the pur-
chase money to be at the rate of 16 per cent, per annum, and
to redeem the capital at 3 per cent, per annum, plant and stock
included. The annuity arising to the lessor and lessee, how-
ever, to be paid quarterly.
Here the rate of interest to redeem being 3 per cent., we
have - = -0075 for the quarterly ratio.
4
Then
- - - = ' 7 5 Q = -006750165676,
(i-oo75) lo i 1-11108384
the quarterly redemption fund (amount taken from Table II).
PRACTICAL EXAMPLES IN VALUATION. 85
And -006750165676x4 = -027000662704,
the annual redemption fund, with increase due to the quarterly
increments.
Also -02 7000662 704 -f-i6 = -187000662704,
Therefore l - = 5*347574631,
187000662704
the years' purchase, or present value of an annuity of i, for
25 years, when paid quarterly.
Then we have 5*347574^3 1
Annuity = 186000
Present gross value of the Colliery . = 32085-447786000
or 32085 8s. n^d.
The annuity accruing to the lessor = 60,000 tons at 8d.
= 2,000, and the years' purchase being as above,
We have. 5'347574 6 3 I
Annuity . . . . . = 2000
Present value of the royalty . . = 10695-149262000
or 10695 28. n%d.
The present gross value of the Colliery . = 32085 8 u
The present gross value of the royalty . = 10695 2 11}
Present net value of Colliery. . * = 21390 5 nj-
The present value of an annuity of i, at 16 per
cent, per annum, and to redeem the capital at
3 per cent, per annum, for 25 years, when the
annuity accrues annually . . . = 5'3353^579 2
Ditto ditto, when the annuity is paid quarterly = 5-347574631
Difference = -012188839
or nearly $d. in every i annuity purchased, an excess in value
due to quarterly payments.
39. What is the Present Value of a Colliery Lease having
44 years to run, and producing 200,000 tons per annum ? But
86 THE ENGINEER'S VALUING ASSISTANT.
in order to continue this yield during the whole term, it will be
necessary to expend 40,000 in additional works, extending
over a period of 3 years. The average annuity derived from
the Colliery during a series of years in the past has been, and still
is 20,000, and the lease is held subject to a royalty to the
lessor of 6d. per ton during the ensuing 2 1 years, and gd. per
ton for the remainder of the term, or 23 years. Interest
on the purchase to be allowed at the rate of 12 per cent, per
annum, and to redeem the capital at 3 per cent, per
annum. The interest allowed to a present purchaser of the
royalty to be at the rate of 7 per cent, per annum, and to
redeem the capital at 3 per cent. The plant is estimated to
have cost 100,000 when the Colliery was opened, but to be
sold at the end of the term for say 1 6,000, and upon this sum
a discount is allowed at the rate of 5 per cent per annum.
The present value of an annuity of i per
annum for 44 years, at 1 2 per cent., and
to redeem the capital at 3 per cent, per
annum, is by Table (VII) . . = 7-62021768
Annuity . . . . . ,' = 20000
Total present gross value . , = 152404-3536000
or 152404 js. ofd.
Then it is customary for a valuer to say :
6 From this gross value of . . . :. 152404 7 of
Must be deducted the cost of ad-
ditional works . . . 40000
And interest thereon at 5 per
cent, for 3 years' . . 6000 46000 o o
Present gross value of Colliery, after de-
ducting outlay, and interest as determined
by the customary mode -, -. . = 106404 75. ojc/.
Further on, special reference will be made to the customary
mode of allowing interest at the rate of 5 per cent, upon any
sum of money set apart, or estimated by a valuer for maintain-
ing a certain yield from mines for a definite period. An inde-
pendent mode of solution will also be introduced.
- *-' c:> n>q/j)N v
or rue ^^
tvDC.
/7 ^ O
PRACTICAL EXAMPLES IN VALUATION. 87
For the royalty we have 6d. per ton for the first period of
21 years, and gd. per ton for 23 years afterwards; the correct
value may therefore be more readily determined by assuming
that the royalty is fixed at gd. per ton for the whole period of
44 years, and deducting therefrom the present value due to the
excess of royalty, or $d. per ton for 21 years. This is evident,
as an average of the two royalties could not give the correct
value, neither could it be obtained accurately by two separate
valuations, that is, first upon that due to the annuity arising
from 6d. per ton for 2 1 years, and secondly to that due to the
annuity arising from gd. per ton for 23 years afterwards.
The reason for this is obvious.
The years' purchase due to 21 years at 7 per cent.
= 9*535453995 an( i if we treat that number as the basis of a
distinct valuation, and then proceed to value the second period
of 23 years similarly, we should find the years' purchase
= 9*919266819, which is only removed in point of time 2 years
from the former period, i.e. 21 years, whereas the termination of
the second period of 23 years is removed 44 years from the
commencement of the first period, and the years' purchase for
the period of 44 years = 12*31074584.
Therefore, by Table (VII), the present value
of an annuity of i per annum for 44
years, allowing interest at the rate of
7 per cent, per annum, and to redeem
the capital at the rate of 3 per cent, per
annum . i . * . = 12-31074584
7500
Present value if the royalty were at gd. per
ton for the whole period of 44 years = 92330*59380000
And by Table (VII), the present value of
an annuity of i for 21 years, allowiug
interest at 7 per cent., and to redeem
the capital at 3 per cent. . . = 9*535453993
2500
Present value of excess of royalty for 21
years at $d. per ton . . = 23838-634982500
88 THE ENGINEER'S VALUING ASSISTANT.
From the present value of the royalty at gd.
per ton for 44 years = 92330*59380000
Must be deducted the present value of the
royalty at $d. per ton for 21 years . = 23838-63498250
Present net value of royalty . . .= 68491-95881750
or 6849 1 195. 2d.
Then for the machinery, we have the present
value of i due at the end of 44 years at
5 per cent. ;. * = -11686133
16000
Present value of machinery . . ... . = 1869-78128000
or 1869 155, 7^.
KEDUCTION FKOM GKOSS TO NET VALUES.
To the present gross value of the Colliery,
after deducting outlay and interest . = 106404 7 of
Must be added the present value of the
machinery * . = 1 869 1 5 7^
108274 2 8
From which must be deducted the present
value of the royalties . , , 68491 19 2
Present net value of Colliery Lease . = 39782 3$.
40. What is the Present Value of a Colliery, the lease of
which has 21 years to run, subject to a royalty to the lessor of
4.d. per ton on all coals raised, but which royalty is now worth
Sd. per ton during the whole term ? The output from the Col-
liery is 170,000 tons per annum, and the annuity derived is
17,000, and that due from the royalty (which is to be deducted
from the lessee's gross annuity) is 2833 6s. 8d. Interest allowed
on the purchase of the Colliery at the rate of 14 per cent, per
annum, and to redeem the capital at the rate of 3 per cent, per
annum. The interest allowed on the royalty to be at the rate of
8 per cent, per annum, and to redeem at 3 per cent. The excess
PRACTICAL EXAMPLES IN VALUATION. 89
of royalty to be at the same rate. Plant and stock included in
the sale of the Colliery.
The present value of an annuity of i for
21 years, so as to allow a purchaser 14 per
cent, upon his purchase money, and to
redeem the capital at 3 per cent, per
annum ... . . ' . = 5718475674
Annuity . . . . . ' = 17000
Present gross value of Colliery . . =97214-086458000
or 97214 is. 8^d.
And for the lessor's royalty, we have,
The present value of i per annum at 8 per
cent., and to redeem at 3 per cent, for 2 1
years . ''.'" . = 8705358535
Annuity due to lessor >, = 2833-333
Present value of lessor's royalty . . =24665 '1796 140472
or 24665 3s. fd.
Also, for the excess of the value of the royalty, at 4$. per
ton, we have
The years' purchase as above . . = 8705358535
Annuity due to excess of royalty . = 2833*333
Present value of excess of royalty . =24665*1796140472
or 24665 3s. 7<i.
From the present gross value of the Colliery
lease . . _V . . _ . . . = 97214 I 8^
Must be deducted the present value of the
lessor's royalty = 24665 3 7
72548 18 i
To which must be added the present value
of the excess of royalty . . . = 24665 3 7
Present net value of Colliery lease . = 97214 is.
UO THE ENGINEEK'S VALUING ASSISTANT.
Proof of the accuracy of the valuation of the Colliery may
be thus obtained :
The yearly interest at 14 per cent, upon
97214-086548 . . . = 13609 19 54
And the annual redemption fund that will
produce i in 21 years = -0348717765;
then 97214-086548 x -03487 1 7765 . = 3390 o 6J-
Together equal to annuity , ' . . = 17000 o o
And the amount of i per annum for 21 years, at 3 per cent.,
by Table (III) = 28-67648572, and if this number is multiplied
into the annual redemption fund, the original purchase money
would be reproduced. Thus, 28-67648572 x 3390-027899
= 97214 is. S^d.y the original capital invested.
For proof of the valuation of the royalty, we also have,
The yearly interest at 8 per cent, upon
24665-1796140472 . . . = 1973 4 3i
And the annual redemption fund that will
produce i in 21 years is, by Table (V),
= -0348717765 ; then 24665 -i 796 1 40472
x -0348717765 .^ ^ . . . = 860 2 41
Annuity derived from royalty . . = 2833 6s. 8d.
Also, 860-11886x28-67648 = 24665 35. 7<1, the original
present value of the royalty, as previously deduced. That is to
say, if 860 28. 4^d. were laid by annually, at 3 per cent, com-
pound interest, the original sum paid for excess of royalty
would be reproduced.
The last preceding case assumes an incoming tenant, who,
upon purchasing the lease of the Colliery and everything there-
with connected, subjects himself to all the conditions entered
into by the lessee. At the onset, therefore, he is entitled to
have a deduction made from the present value of the Colliery
lease. In this case it is taken at ^.d. per ton, and the resulting
annuity upon the output is treated in the usual way ; the ques-
tion being, what is its present value, presuming it were about to
be sold ? This must be taken as a minus quantity, inasmuch
PEACTICAL EXAMPLES IN VALUATION. 91
as the purchaser of the Colliery, or representative of the lessee,
subjects himself to the payment of the royalty to the lessor. On
the other hand, the lessee has possessed himself of a valuable
lease, the royalty of which, as fixed for the ensuing 2 1 years, is
under its real value ; that is, it is considerably less than that
charged upon the surrounding collieries. The lessee is, therefore,
entitled to sell his Colliery lease at an enhanced value, equiva-
lent to what is due to the difference existing in royalty between
his and the surrounding collieries. Certain questions, however,
would arise, such as whether the Colliery would be exhausted in
2 1 years ? and if not, what would be the probable amount of
royalty for the next term of extension of lease ? This should be
provided for as far as possible in the lease ; but, if left an open
question, then the incoming tenant may fairly raise objections,
and seek to effect a compromise, which probably would result in
diminishing the value of the excess of royalty. Of course all
such questions involve a consideration of the basis upon which
royalties are determined, which may always be open to dispute
and reference ; and here experience and judgment would
weigh materially in settling the matter. Then, again, as to the
determination of the amount of royalty of any particular
Colliery, from that of the surrounding ones, the question as to
whether such collieries are working under similar conditions
must undoubtedly be taken into consideration.
4 1 . What is the Present Value of an undeveloped freehold
Colliery extending over an area of 1000 acres, containing several
workable seams of excellent coal, capable of yielding 420,000 tons
per annum for a period of So years, and producing by estimation
an annuity of 42,000 ? The time occupied in developing the
Colliery is estimated at 4 years, at the expiration of which time
it is expected the above yield will commence. The Colliery is
obtained under favourable circumstances, there being very little
water, and good rock roofs exist over the different seams of coal.
The interest allowed is 18 per cent, per annum, and to redeem
the capital at the rate of 3 per cent, per annum, and the esti-
mated cost of developing, with plant, is 80,000, with the
customary rate of 5 per cent, interest thereon for 4 years, or
during the time of development. The overlying estate, held in
fee simple, is also to be sold with the minerals, the rate of
92 THE ENGINEER'S VALUING ASSISTANT.
interest allowed being 5 per cent., and is let out as farms, pro-
ducing an annuity of 3000.
Here the present value of an annuity of i for 80 years,
allowing a purchaser 1 8 per cent, upon his purchase money, and
to redeem the same at the rate of 3 per cent, per annum
= $'46114612. But as this annuity is deferred 4 years, from
(14) page 34, or (16) page 36, we have
The deferred value = 2-816798415.
The deferred value may be more easily obtained from :
Thus P 8( X = $'46114612 x -5157888751 = 2-816798415, as
before.
Again, by Table (X), the years' purchase = 2-816798, true
to 6 places.
Also . . . : . , . . 2-816798415
Annuity , . . f . .* . = 42000
Present gross value of Colliery . . =118305-53343000
Then a valuer would say :
' From which must be deducted the
estimated cost of development 80000
And the customary interest thereon
at 5 percent, for 4 years' 16000 96000-00000000
Present net value of Colliery, after
deducting outlay, and customary
interest thereon . = 22305-53343000
or 22305 los. Sd.
The interest allowed on the purchase of the estate being
5 per cent., it is worth 20 years' purchase. We therefore have
3000x20 .. . . . * . = 60000 o o
Present net value of Colliery . . -.. , ( = 22305 10 8
Total present net value of Colliery and Estate = 82305 los. 8d.
PRACTICAL EXAMPLES IN VALUATION. 93
The accuracy of the calculations referring to the last pre-
ceding case may be further corroborated thus :
By Table (I), the amount of i in 4 years at 18 per cent.
= I-93877776.
Then 1*93877776 x 1 18305-5334 = 229368-13704,
or that sum to which the deferred years' purchase will amount
during the deferred period.
Then the annual interest at 18 per cent, on
229368-13704 = 41286 5 3j
And the annual redemption fund to replace
the same within the time at 3 per cent, com-
pound interest , ,. , , . . .. . = 713 14 8J
Together equal to the annuity ;> * . 42000 o o
If, however, the payments of the annuity in the last pre-
ceding case were half-yearly, or quarterly, in order to ascertain
the present value deferred 4 years, we must proceed as follows :
The interest allowed to redeem the capital being at the rate
of 3 per cent per annum, the pro rata half-yearly and quarterly
rates would be represented by
^ = -oi 5 half-yearly,
and 3 = -0075 quarterly.
4
Then
' 15 ' OI 5
(i-oi5) 160 -i 10-828461-1 9-828461
= '00152626992, the half-yearly redemption fund.
Then -00152626992x2 = -00305253984, the yearly re
demption fund, and -00305253984+ -1 8 = '18305253984,
.830525398
the years' purchase immediate. The redemption fund for half-
94 THE ENGINEER'S VALUING ASSISTANT.
yearly and quarterly payments may be obtained direct from
Table (V).
As the annuity is deferred 4 years, and payments are made
half-yearly, the problem must be subjected to the principle
involved in (5) and (/a.), pages 25 and 28.
The rate of interest being 18 per cent, per annum, the half-
yearly and quarterly ratios
= , and = -09 and '045.
2 4
Then,
( i + -09) 8 = i '992 5 6264 ;
and (i +'O45) 16 = 2-02237015, or the
amounts due to half-yearly and quarterly payments.
These numbers are readily obtained from Table (I), under
9 and 4^ per cent, for 8 and 16 years.
Then for the present value of i due 4 years hence, at 18
per cent., for half-yearly payments we have,
-50186628;
1-99256264
which is, as it should be, less than the value found in Table (IV)
for the same rate per cent, and period of deferment. The present
value deferred, is now readily deduced from
the relation of which has been fully explained on page 35.
Thus,
P 80 = 5-462912457; and-y 4 = -50186128, and
P*0+4 = PvP 4 = 5-462912457 X -50186628 = 274I65I553,
or the years' purchase deferred.
For proof, we have,
1-99256264x2-741651553 = 5-462912457,
or the immediate value or sum to which ^2-741651553 would
PKACTICAL EXAMPLES IN VALUATION. 95
have accumulated at -18 per cent during the 4 years of
deferment.
Then ....... 2741651553
Annuity . . . . . = 42000
Present gross value of Colliery . . = i 15149*365226000
giving, for the gross value, a smaller sum by 3156*168204,
when the payments are made half-yearly.
Again, for the quarterly payments, we also have
= -00075567493.
( i -007 5 ) 320 i 1 0-924902 i 9-924902
Then '00075567493x4 = -0030226998,
the annual redemption fund due to quarterly payments,
And -0030226998 + -i8 = - 1830226998,
Therefore . = 5-463803129,
the years' purchase immediate, due to quarterly payments.
But, being deferred 4 years, we have the amount of i
in that period at -18 per cent, due to quarterly payments
= 2-02237015.
Then v 4 = - - - = -4944693235, or the
2-02237015
present value of i due 4 years hence, accruing from quarterly
payments.
Here we have Pgo = 5*463803129, and v 4 = -4944693235 ;
Then 5-463803129 x -4944693235 = 2701683037,^6 present
value deferred 4 years, and due to quarterly payments.
The proof is 2701683037 x 2-02237015 = 5-463803129, or
the immediate value or sum to which 2-701683037 would have
accumulated at 1 8 per cent, during the deferred period of 4
years.
Then ....... 2-701683037
Annuity . . . . . = 42000
Present gross value . . . - =113470*687554000
96 THE ENGINEER'S VALUING ASSISTANT.
Here the difference between the values, when the pay-
ments are made yearly and half-yearly, = 3156*168204; that
between the yearly and quarterly payments = 4834*845876 ;
and that between the half-yearly and quarterly payments,
= 1678-677672.
The case, thus treated, is of considerable importance as
applied to the Valuation of Mines, being greatly in favour of a
purchaser. The principle upon which it is based has been
formerly illustrated, and should always be applied when pay-
ments are made half-yearly and quarterly.
42. What is the Present Value of a mineral property, upon
which two shafts have been sunk within a short distance of
the upper seams of coal ? A full description of which is as
follows :
1st. The lease of a colliery, having 35 years to run from
the time when the upper and lower seams of coal, iron ore, and
clay are successively won, subject to a royalty of $d. per ton
upon all coal or other minerals raised from the mine. It is
known from the surrounding collieries, that the roofs over the
seams of coal are good, and that only a moderate quantity of water
exists in the strata to be passed through. It is estimated that the
first seams of coal will yield 60,000 tons per annum for the
entire term, and that the cost of developing this portion of the
mine, including plant, is 12,500. The time occupied in
performing the work is estimated at 2 years, and the rate
of interest allowed to a present purchaser is at the rate of 16
per cent, per annum, and to redeem the capital at the rate of
2\ per cent., and the annuity estimated to be realized during
the entire period amounts to 6750.
2nd. The lower seams of coal, won by the same shafts, are
capable of yielding 1 20,000 tons per annum for a longer period
than that of the lease, and assessing the profits at a moderately
low rate per ton, it is estimated that an annuity of 15,000
may confidently be expected to be realized. This portion of the
mine will require a further period of 2 years to develop it, at an
extra cost of i 5,000, including plant. Interest to be allowed to
a present purchaser at the rate of 20 per cent, per annum, and
redeeming the capital at the rate of 2\ per cent, per annum.
3rd. By continuing the same shafts a short distance below
PRACTICAL EXAMPLES IN VALUATION. 97
the lower coal seams, it is estimated that an output of 60,000
tons per annum of excellent Hematite iron ore may be secured
at a further outlay of 8,000 at the expiration of 6 years from
the time of commencing operations. The ore contains 50 per
cent, of metallic iron ; it is, therefore, estimated that under the
favourable circumstances by which this property is secured, an
annuity of 12,000 may be realized. Interest to a present
purchaser to be allowed at the rate of 22 per cent, per annum,
and redeeming the capital at the rate of 2\ per cent, per
annum.
4th. Fire clay in beds, of an excellent quality, is also
known to exist over the entire area included in the lease, and
that 45,000 tons may be annually extracted during the entire
period. There is a ready market for its disposal at a constant
price per ton ; it is therefore estimated that an annuity of
5875 will be realized. The additional cost for the develop-
ment and plant will be about 7500, expended at the same
time that the iron ore is won. Interest to be allowed to a
present purchaser at the rate of 14 per cent, per annum,
and redeeming the capital at the rate of 2-J per cent, per
annum.
5th. Wayleave of certain private branch Eailways, and
other accommodations, charged at the rate of id. per ton upon
all minerals conveyed over them, amounting to an annuity of 250
per annum after 2 years. Also an annuity of 500 after a period
of 4 years, and further an annuity of 437 los. after 6 years.
Interest to be allowed at the rate of 10 per cent, per annum,
and to redeem the capital at the rate of 2\ per cent, per
annum.
6th. Ground rents derived from houses and other build-
ings, amounting to 140 per annum. Interest to be allowed
to a present purchaser at the rate of 8 per cent, per annum,
and to redeem the capital at the rate of 2\ per cent, per annum.
7th. Eoyalties to the lessor, amounting to 750 per
annum after 2 years, and to run 10 years afterwards. Interest
at 10 per cent., and to redeem at 2\ per cent.
8th. Royalty to lessor, amounting to 1500 per annum
after 4 years, and to run 10 years afterwards. Interest as in
last preceding case.
Qth. Royalty to lessor, derived from iron ore and clay,
H
98 THE ENGINEEE'S VALUING ASSISTANT.
amounting to 1312 los. per annum after 6 years, and to run
10 years afterwards. Interest as before.
loth. The lessor will not consent to sell the royalty of $d.
per ton on the estimated annual output from the mine, until
after the expiration of 10 years from the time estimated for
winning the upper and lower seams of coal, iron ore, and clay,
in succession. The minerals contained in this property will not
be exhausted in 35 years ; the royalty is, consequently, worth
more than $d. per ton ; the lessor will, however, convey it on
the assumption that it may be exhausted in that time. Interest
to be allowed at the rate of 10 per cent, per annum to a present
purchaser, and to redeem the capital at 2% per cent, per annum.
The lessor consents to accept any bond fide incoming tenant
introduced by the lessee ; and the latter may sell his interest in
the property at any time.
1st Valuation,
Annuity from 60,000 tons of coal per annum = 6750.
Interest allowed at 16 per cent, per annum.
Eedemption of capital at 2 J
The present value of i per annum for 35 years, so
as to allow a purchaser 16 per cent, per annum upon his
purchase money, and to redeem the capital at 2\ per cent, per
annum = 5-61 149650. As the annuity is deferred 2 years, from
Table IV we have / y 2 , or the present value of i due 2 years
hence, at '16 per cent. = -74316290.
Then
^35+2 = Px>V*= 5'6l I49 6 50X743 16290 = 4-170256019,
years' purchase, or present value deferred.
Then, to prove the accuracy of the operation, we also have
4-170256019 x 1*3456 = 5-61149650,
the value immediate, as before.
Then . . . . * 4-170256019
6750
Present gross value = 28149-228128250
PEACTICAL EXAMPLES IN VALUATION. 99
2nd Valuation.
Annuity from 120,000 tons of coal per annum = 15000.
Interest allowed at 20 per cent, per annum.
Eedemption of capital at 2\
The present value of i per annum for 35 years, so as to
allow a purchaser 20 per cent, per annum upon his purchase
money, and redeem the capital at 2\ per cent, per annum
= 4*58283418, and as the annuity is deferred 4 years, from
Table IV we have v 4 , or the present value of i due 4 years
hence, at -20 per cent. = -48225309.
Then
X -48225309 = 2-2I008594,
the present value deferred.
For proof, we have 2-210085927 x 2-0736 = 4-58283418,
the present value immediate.
Then .. ; " .... . . , . 2-210085927
15000
Present gross value : ,Y ' ' = 33151*288905000
3rd Valuation.
Annuity from 60,000 tons of iron ore per annum
= 12,000.
Interest allowed at 22 per cent, per annum.
Redemption of capital at 2\
The present value of i per annum for 35 years, so as to
allow a purchaser 22 per cent, per annum upon his purchase
money, and to redeem the capital at 2\ per cent, per annum
= 4*19805443 ; and as the annuity is deferred 6 years, we have
-PlB+6 = ^35 V 6 = 4-I9805443 X -3032780757 = I-273I77869,
the present value deferred.
Then, for proof, we have
1-273177869x3-297303989 = 4-19805443,
the present value immediate.
H 2
100 THE ENGINEERS VALUING ASSISTANT.
And 1-273177869
12000
Present gross value . . . =15278-134428000
4th Valuation,
Annuity from 45,000 tons of clay per annum = 5875.
Interest allowed at 14 per cent, per annum.
Eedemption of capital at 2\
The present value of i per annum for 35 years, so as to
allow a purchaser 14 per cent, per annum upon his purchase
money, and to redeem the capital at 2\ per cent, per annum
= 6*32088948 ; but, as it is also deferred 6 years, we have
P P ?> 6
35+6 ^35 U *
Then by Table (VI) P 35 = 6-32088948, and by Table (IV)
v 5 = -45558655-
Consequently 6-32088948 x -45558655 = 2-879712216,
the present value deferred.
Then, for proof of the accuracy of the mode of working, we
2-879712216x2-1949726239 = 6-32088948,
the value immediate.
Then ...... - . 2-879712216
^5875
Present gross value . . . = 16918-309269000
5th Valuation, part 1.
Annuity from wayleave of 60,000 tons per annum = 250.
Interest allowed at I o per cent, per annum.
Redemption of capital at 2\
The present value of i per annum for 35 years, so as to
allow a purchaser 10 per cent, per anpum upon his purchase
money, and to redeem the capital at 2 \ per cent, per annum
= 8-45983736; but, as this annuity is deferred 2 years, we have
P 35+2 = P^v\
PEACTICAL EXAMPLES IN VALUATION. 101
By Table (VI) P 35 = 8-45983736, and by Table (IV) v* =
82644628.
Then 8-45983736 x '82644628 = 6-991601118,
the present value deferred.
For proof, we also have
6-991601118x1-21 = 8-45983736,
the years' purchase immediate.
Then . 6-991601118
250
Present net value *", . - . - . = 1747-900279500
5th Valuation, part 2.
Annuity from wayleave of 120,000 tons per annum
= 500.
Interest to purchaser and for redemption, same as in part I.
The present value of i being also 8-45983736, and
as the annuity is deferred 4 years, we have the following ex-
pression : p . p 4
-^35+4 -^35 D
Here P 35 = 8-45983736, and v* = -68301346.
Then 8-45983736 x -68301346 = 5-5:78182744,
the present value deferred.
Then, for proof, we have
5-778182744x1-4641 = 8-45983736,
value immediate.
Then . . .V '. ; ;.. .'". 5778182744
^500
Present net value . . . , = 2889-091372000
5th Valuation, part 3,
Annuity from wayleave of 60,000 tons of iron ore, and
4 5, ooo tons of clay = 437 ros.
102 THE ENGINEERS VALUING ASSISTANT.
Interest to purchaser and for redemption as in parts
I and 2.
The present value of i per annum for 35 years, also, as
before = 8*45983736, but it is deferred 6 years, therefore we
have
^35 = 8-45983736, and v 6 = -56447393.
Then 8-45983736 x '56447393 = 477535764,
the present value deferred.
Also 4-77535764x1-771561 =-- 8-45983736,
the present value immediate.
And ;. ;.. ... . . 4-77535764
437*
Present net value , -.':.. . =2089-218967500
6th Valuation.
Annuity from freehold ground rents = 140.
Interest allowed at 8 per cent, per annum.
Redemption of capital at 2\
The present value of i per annum for
35 years, so as to allow a purchaser 8 per
cent, per annum upon his purchase money,
and to redeem the capital at the rate of
2\ per cent, per annum . . , = 10*18272055
140
Present net value . ' . , . " . . = 1425-58087700
7th Valuation.
Annuity from royalty to lessor = 750.
Interest allowed at 10 per cent, per annum.
Redemption of capital at 2 \
The present value of i per annum for 10 years, so as to
allow a purchaser 10 per cent, per annum upon his purchase
money, and to redeem the capital at 2\ per cent, per annum
= 5*28377119, but, as the annuity is deferred 2 years, we have
P 10 = 5*28377119, and v 2 = -82644628.
PRACTICAL EXAMPLES IN VALUATION. 103
Then, 5-28377119 x -82644628 = 4-366753048,
the present value deferred.
The proof is 4-366753048x1-21 = 5-28377119,
value immediate.
And. Y /' 4*3^6753048
^ 4750
Present net value . . .., . . = 3275-064786000
8th Valuation,
Annuity from royalty to lessor = 1500.
Interest to purchaser and for redemption as before.
The present value of i per annum for 10 years, as pre-
viously given = 5-28377119, and as the annuity is deferred 4
years, we have
PW = 5*28377119, and v 4 = -68301346.
Then 5-28377119 x '68301346 = 3-608886817,
the present value deferred.
For proof we also have 3-608886817 x 1-4641 = 5-283771 19,
present value immediate.
And. . . . . . . . 3608886817
1500
Present net value . . . % ' 1 S . = 5413-330225500
9th Valuation.
Annuity from royalty to lessor on iron ore and clay
= 1312 i os.
Interest to purchaser and for redemption the same as in
7th and 8th Valuations, and the present value of i
per annum for 10 years, as before = 5-283771 19 ; and
as the annuity is deferred 6 years, we have
Ao = 5*28377119, and v 6 = -56447393.
Then 5-28377119 x -56447393 = 2-982551103,
the present value deferred.
104 THE ENGINEER'S VALUING ASSISTANT.
The proof is 2-982551103 x 1771561 = 5*28377119,
value immediate.
Then 2-982551103
Present net value . .' .' / =3914-5983226875
10th Valuation, part 1.
Annuity from lessor's interest in royalty, to be sold at the
expiration of 10 years from the time of winning upper
seams = 750.
Interest allowed at 10 per cent, per annum.
Redemption of capital at 2\
Here, as the lessor receives "royalty for 10 years from the
time of winning the upper seams, and as the winning occupies
2 years, the lessor's interest, in this case, can only be realised or
purchased after a period of 12 years. We therefore have
P 25 by Table (VI) = 773539259, and v 12 by Table (IV)
= -31863082.
Then 773539259 x -31863082 = 2-464734463,
the present value deferred.
For 2-464734463x3- 1 3842838 = 773539259,
value immediate.
Then . . . . _. .. . 2-464734463
^750
Present net value . . :\ '-' . . = 1848-550847250
10th Valuation, part 2.
Annuity from lessor's interest in royalty, to be
sold at the expiration of 10 years from the
time of winning the middle seams . . . i 500
Interest allowed at 10 per cent, per annum.
Redemption of capital at 2\
PKACTICAL EXAMPLES IN VALUATION, K)5
Again, the lessor receives royalty for 10 years from the time
of winning the middle seams, which are won after 4 years ; his
interest for the remaining 25 years can therefore only be pur-
chased after 14 years' deferrence ; we have therefore,
P 25 by Table (VI) = 773539259, and v u by Table (IV) =
26333125,
Then 773539259 x -26333125 = 2-036970630,
the present value deferred.
And 2-036970630x379749834 = 773539 2 59>
value immediate.
Then . . ' w ' * V . 2-036970630
^1500
Present net value * ; i . - . . = 3055-455945000
10th Valuation, part 3.
Annuity from lessor's interest in royalty, to
be sold after the expiration of 10 years
from the time of winning the lower
seams of iron ore and clay . . . 1312 IO O
Interest on capital and for redemption as in last preceding
case.
The lessor receives royalty from these seams for 10 years
also, and sells his interest at the expiration of that time, but, as
it is deferred 16 years, we have
P 25 by Table (VI) = 773539259, and v l by Table (IV)
= -21762914.
Then 773539259 x -21762914 = 1-683446802,
the present value deferred.
And 1-683446802x4-59497299 = 773539259,
value immediate.
Then ..... . 1-683446102
Present net value . . . . = ^2209-5239276250
106
THE ENGINEER'S VALUING- ASSISTANT.
REDUCTION FROM GROSS TO NET VALUES.
1st Valuation of upper coal seams
From which must be
deducted the cost of
developement =
Customary interest
thereon at 5 per
cent, for 2 years =
5th valuation, part I,
of wayleaves . =
7th valuation of
royalty to lessor =
= 28 1 49- 228 128250
I250O-OOOOOOOOO
1250-000000000
1747-900279500
3275-064786000 18772-965065500
Total present net value of the first or
upper seams of coal . . . = 9376-263062750
1 5OOO-OOOOOOOOO
2nd Valuation of middle or lower coal
seams * . , . . V
From which must be
deducted the cost
of developement =
Customary interest
thereon during the
time occupied in
winning the seams,
at 5 per cent, for
2 years . =
5th valuation, part 2,
of wayleaves . =
8th valuation of
royalty to lessor =
= 33151-288905000
1 500-000000000
2889-091372000
5413-330225500 24802-421597500
Total present net value of the middle
seams of coal
= 8348-867307500
PRACTICAL EXAMPLES IN VALUATION.
107
3rd Valuation. Lower seams of iron
ore
15278-1344280000
16918-3092690000
32196-4436970000
= 8000-0000000000
Soo-OOOOOOOOOO
4th Valuation. Lower seams of clay . =
Total gross value of iron ore and clay =
From which must be
deducted the cost
of developement of
iron ore
Customary interest
thereon at 5 per
cent, for 2 years =
Also for the develope-
ment of the clay = 7500*0000000000
And customary inte-
rest at 5 per cent,
for 2 years . = 750*0000000000
5th valuation, part 3,
of wayleaves of iron
ore and clay . = 2089-2189675000
9th valuation of
royalty to lessor on
iron ore and clay = 3914*5983226875 23053-8172901875
Total present net value of iron ore and
clay . .V V ';. .
= '9142*6264068125
SUMMARY OF VALUES.
Total net value of upper seams .
Total net value of middle seams .
Total net value of the lower seams of
iron ore and clay ....
Total net value of ground rents, 6th
valuation . . . *
From which must be deducted the pre-
sent value of the lessor's interest,
which is to be sold after 10 years,
loth valuation, parts i, 2, and 3,
together equal .
Total present net value of mineral pro-
perty ......
9376*2630627500
8348-8673075000
9142-6264068125
1425-5808770000
28293-3376540625
7113*5307198750
= 21179-8069341875
108 THE ENGINEER'S VALUING ASSISTANT.
Under the peculiar conditions of the lease, it was deemed
advisable, either for the purpose of a real or hypothetical sale,
to enter upon a series of valuations, in order to arrive at the
present net value of the mineral property on behalf of the lessee,
who is responsible for the developement of the property, but
who may nevertheless sell it now or hereafter.
The present interest held by different parties under existing
circumstances, which enters into and affects the question, was
to be fully set forth before the works were commenced.
After two, four, and six years, the deferred periods for
winning each successive series of seams, royalty has to be paid
to the lessor, extending to ten years' duration in each case ; the
property is therefore of less value now by the amount or present
value of the estimated or prospective annuity to be paid to the
lessor, which in the valuation is treated as a minus quantity.
This is evident, as- an incoming purchaser must be held to be
responsible to the lessor for the payment of the annuity
accruing on account of royalty. The same remark also applies
to the lessor's interest, which can only be purchased after the
expiration of ten years.
Presuming, however, that the seams were won, and it was
proposed to sell the property at that time, the case would be
very different, for then the party in possession would have a
current going concern, and the present value from the annuity
that has at that time accrued must be taken as immediate.
The lessor receives royalty for four and two years respectively,
upon the output from the upper and middle series of seams, at
the time the other minerals are won, and if taken as an imme-
diate annuity it would then have six, eight, and ten years,
respectively, to run.
Now, assuming that the time the royalty has to be paid to
the lessor has elapsed, and for the remainder of the term of the
lease, it has to be purchased, or the property cleared from such
charge, the property would at that time assume a greater value,
equivalent to the present value of the amount of the annuity
derived from the royalty, but which will now merge into that
due to the profits of the mine.
The party in possession could then fairly charge it to another
purchaser, who would then, in point of fact, be in possession of
a freehold property as far as the minerals are concerned.
PRACTICAL EXAMPLES IN VALUATION. 109
Taking the time of the lease of the mineral property in the
last preceding case at 2 1 years from the commencement of the
works, instead of 35 years from the time the seams are won, all
other conditions being the same, the comparative value will
appear from the following deductions.
Here, the term of the lease being 2 1 years from the time of
commencing the works, and considering the deferred periods for
winning, the time to run afterwards will be represented by
212 = 19 years, 214 = 17 years, and 216 = 15 years,
respectively.
1st Valuation.
The present value of i per annum for
19 years after 2 years, so as to allow a
purchaser 16 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 3*68338935 1
Annuity * = 67 50
Present gross value . . .. . = 24862-878119250
2nd Valuation.
The present value of i per annum for
17 years after 4 years, so as to allow a
purchaser 20 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 1-945 1354 17
Annuity . . . - ' . ' .. ". = 15000
Present gross value . . . .=29177-031255000
3rd Valuation.
The present value of i per annum for
1 5 years after 6 years, so as to allow a
purchaser 22 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 1-099764199
Annuity . . . . = 12000
Present gross value . . . .=13197-170388000
110 THE ENGINEER'S VALUING ASSISTANT.
4th Valuation.
The present value of i per annum for
1 5 years after 6 years, so as to allow a
purchaser 14 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum .= 2*327194131
Annuity ..... =
Present gross value . . .-* .=13672-265519625
5th Valuation, part 1.
The present value of i per annum for
19 years after 2 years, so as to allow a
purchaser 10 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 5*829872283
Annuity '. . . . = 250
Present net value . . . . = 1457-468070750
5th Valuation, part 2.
The present value of i per annum for
17 years after 4 years, so as to allow a
purchaser 10 per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 4-617209168
Annuity .."" . . . . . = 500
Present net value . 'i * .= 2308-604584000
5th Valuation, part 3.
The present value of i per annum for
1 5 years after 6 years, so as to allow a
purchaser I o per cent, per annum upon
his purchase money, and redeem the
capital at 2\ per cent, per annum . = 3-623847804
Annuity . . -,*'.. . .- =
Present net value . . ..' . . = 1585-433414250
PKACTICAL EXAMPLES IN VALUATION. Ill
6th Valuation.
The present value of i per annum for
21 years, so as to allow a purchaser 8
per cent, per annum upon his purchase
money, and redeem the capital at 2\
per cent, per annum . . . . = 8-56257287
Annuity ......= 140
Present net value . * . . . 119876020180
Here the present value of the royalty to lessor for 10 years
will be the same as in the last preceding cases, viz. :
7th Valuation . V . . 3275-0647860000
8th Valuation . . . 5413*3302255000
9th Valuation .... 3914-5983226875
Total present net value = 12602-9933341875
10th Valuation, part 1.
The present value of i per annum for
9 years after 12 years, so as to allow a
purchaser 10 per cent, per annum upon
his purchase money, and redeem the
capital at the rate of 2\ per cent, per
annum . -." . . ",. .= 1*589522903
Annuity . * .' .; . = 750
Present net value . . . . .= 1192-142177250
10th Valuation, part 2.
The present value of i per annum for
7 years after 1 4 years, so as to allow a
purchaser 10 per cent, per annum upon
his purchase money, and redeem the
capital at the rate of 2\ per cent, per
annum is . ... . . .= 1-132629809
Annuity . . . ;,'". . . = 1500
Present net value . >.; . . .= 1698-944713500
112 THE ENGINEER'S VALUING ASSISTANT.
10th Valuation, part 3.
The present value of i per annum for 5
years after 1 6 years, so as to allow a pur-
chaser 10 per cent, per annum upon his
purchase money, and redeem the capital
at the rate of 2\ per cent, per annum = 0-749807026
Annuity . . . .,_....; = 1312^-
Present net value . . . . .= 984*121721625
REDUCTION FROM GROSS TO NET VALUES.
2nd SEKIES.
1st Valuation of upper coal seams . . = 24862-8781 19250
From which must be
deducted the cost of
developement as in
1st series . . = 12500*00000000
Customary interest
thereon at 5 per
cent, for 2 years . = 1250*00000000
5th valuation, part i,
of wayleaves . . = 145746807075
7th valuation of roy-
alty to lessor . .= 3275*06478600 18482-532856750
Total present net value of the first or
upper seams of coal v . .' .= 6380*345262500
2nd Valuation of middle or lower coal seams = 291 77-03 1 25 5000
From which must be
deducted the cost of
developement as in
ist series . .= 15000*0000000
Customary interest
thereon during the
time occupied in
winning the seams at
5 per cent, for 2 years = 15 00*0000000
5th valuation, part 2,
of wayleaves . . = 2308-6045840
8th valuation of roy-
alty to lessor . .= 5413-3302255 24221-934809500
Total present net value of the middle
seams of coal . . . . = 4955*096445500
PRACTICAL EXAMPLES IN VALUATION. 113
3rd Valuation of lower seams of iron ore = .13 197-1703880000
4th Valuation of lower seams of clay . = 1 3672-2655 196250
Total gross value of iron ore and clay . = 26869-4359076250
From which must be
deducted the cost
of developement of
iron ore as in 1st
series . . . = SooO'OOOOOOOOO
Customary interest
thereon at 5 per
cent, for 2 years . = 800*000000000
Also for the develope-
ment of the clay as
in ist series . . = 7500-000000000
Customary interest
thereon at 5 per
cent, for 2 years .= 750*000000000
5th valuation, part 3,
ofwayleaves . .= 1585*433414250
9th valuation of roy-
alty to lessor on iron
ore and clay . . = 3914*5983226875 22550*0317369375
Total present net value of iron ore and
day = 4319-4041706875
SUMMARY OF VALUES.
2nd SERIES.
Total net value of upper coal seams =. 6380*3452625000
Total net value of middle or lower coal
seams ..... = 4955-0964455000
Total net value of the lower seams of
iron ore and clay = 4319-4041706875
Total net value of ground rents, 6th
valuation . . . . = 1198*7602018000
16853-6060804875
From which must be deducted the
present value of the lessor's interest,
which is to be sold after 10 years,
loth valuation, parts I, 2, and 3,
together = 3875*2086123750
Total present net value of mineral
property, 2nd series . . . =12978*3974681125
114 THE ENGINEERS VALUING ASSISTANT.
If several seams of coal and other minerals exist at different
depths (which is a case of common occurrence) in an area
leased, it is highly desirable, and to the interest of the lessee,
that ample time is granted for developement before the royalty
becomes due, and that the time embraced in the lease is suffi-
ciently long to justify the adventure, and expenditure connected
therewith. In the 1st series of valuations the total net value
is 2 1 1 79-8069341 875, the duration being 35 years after the
seams are won ; but, for the sake of comparison, if we confine
the period of a lease to 2 1 years from the commencement of the
works, the present net value is 12978*3974681125; and the
difference is 8201*409466075. The present value of the pro-
perty in the last case is consequently less by that amount, and
due as a matter of course to the shorter period of time.
The cost of winning minerals at any defined depth is the
same, no matter what time is fixed for the lease to run, but the
comparison of values above referred to demonstrates that the
present value is very much affected by the time. It is, therefore,
to be inferred that the time any lease has to run for working-
minerals at great depths should much exceed that granted when
the minerals are much nearer the surface.
On the whole I am inclined to the opinion that 2 1 years'
lease of any mineral property is much too short a period, when the
time of developement extends to three, four, five, and six years.
When, however, a longer period cannot be granted, it should,
if possible, be made compulsory on the part of the lessor, or his
representatives, to extend the time a further period of 2 1 years
upon the lapse of the former period, at a reasonable royalty,
and not to be in excess of the rate per ton as previously
determined, unless the profits of the mine are such as to
justify it.
It is undoubtedly an error in judgment on the part of those
who suppose that, by allowing short periods of time for develope-
ment, fixing the royalty or other dues above the normal or
customary rate in a mining district, or in excess of what any
particular mine will bear, the landlord or lessor's interest is
thereby either permanently augmented or established. In point
of fact the very reverse is the case, and great consideration
should be exercised by the landlord or lessor towards the lessee,
upon whom devolves the risk of the adventure. It is a question of
PRACTICAL EXAMPLES IN VALUATION. 115
no small importance to the ultimate success of a mine ; and I
venture to assert that the high dues demanded have frequently
operated to discourage and frighten away those who would
otherwise have spent their capital in developing such mines.
It should be remembered that, in the majority of cases,
landlords are not disposed or in a position to expend large sums
of money in order to develop the mineral resources of their
estates. While, therefore, such minerals lie dormant, the owner
is in exactly the same position as he would be if the minerals
did not exist at all. The interest of the landlord or lessor is
therefore intimately bound up, if not exactly identical, with that
of the lessee, and upon the degree of success of the latter
entirely depends the income to be received by the former.
An equitable state of things should therefore exist between
the parties, and every facility be offered for the encouragement
of bond fide undertakings ; and instead of raising the royalty or
other dues, it is necessary in very many cases that these should
be reduced, so as to enable capitalists to develop mineral
properties with profit to themselves as well as to the land-
lord.
To attempt to raise the landlord's dues when making a new
grant or assigning a lease, simply on account of temporary good
trade, having the appearance of producing extra profits, is as
unwise as it is unjust, operating as an impediment to future
progress in opening up those mines coming under such restric-
tions.
There is also another point intimately connected with this
question, and that is, the area included or described in the
grant or lease. At first sight this would appear too simple a
matter to require special notice ; but, in reality, it is necessary
that it should be treated as systematically as any other matter
of importance connected with mining engineering ; for, if taken
at random, there may be no proper relation whatever existing
between the area granted and the time the lease has to run.
It may be in excess, to the injury of the landlord, or in defect of
the proper quantity which should have been assigned, and con-
sequently to the detriment of the lessee.
In assigning the area, due regard should be had to the
increasing depth of the minerals, as compared to landworks,
estimated cost of winning, annual output, time fixed for the
I 2
116 THE ENGINEER'S VALUING ASSISTANT.
grant or lease, probable profit per ton to be derived, and a proper
and accurate valuation made before ultimately fixing the area,
which should always be such as to justify the outlay to be
incurred in the developement. In cases where parties are entitled
to have grants of mineral tracts made to them from the lord
of the manor, by virtue of some, right, as in the Forest of Dean,
two distinct interests exist, i.e., that of the Crown, as lord of
the manor, and that of persons called c free miners,' who are
entitled under existing law to have grants of mineral tracts
made to them. The Crown exercises the right to make such
grants conditionally upon certain payments being made by the
grantee, such as dead rent and royalty dues, which are intended
to represent one-fifth of the profits derived, or to be derived, as
the share or interest of the Crown. The galee or grantee
nominally undertakes to develop, or procure to be developed,
the grant in question ; but, as those who are so entitled are not
competent by reason of their being working men to attempt
to open up any of the deeper mines, it is necessary that another
party should be introduced to effect this for them.
Here, then, the representative of the galee is not only
obliged to purchase the grant or interest of the galee, but is
called upon to expend a sufficient sum in the develope-
ment of the mineral tract or grant, and also to pay a dead or
certain rent, after a certain determined period, if the mine is
undeveloped, or royalty or tonnage dues, when the mine is
opened.
If, therefore, the dead rent and royalty are unusually heavy,
a double burden has to be borne by those engaged in opening
up the mines. Under such circumstances the difficulty of pro-
curing capitalists willing to enter into such undertakings is all
the greater.
The result is that, at the expiration of the fixed period
when the dead rent becomes due, if no one is forthcoming to
take the matter up, the grant or grants must lapse to the Crown,
but subject to be re-granted to other persons over and over
again, to the manifest injury of the Crown, the free miner, and
the district in general. There is no remedy apparently for this
state of things, unless the Crown would make grants of the
ungranted tracts of minerals, and then purchase back the
interest of the galee in such grants.
PRACTICAL EXAMPLES IN VALUATION. 117
43. What is the Present Value of the royalty of an iron
mine producing an income of 600 per annum, during the life
of a person A 9 aged 52 ? Interest to be allowed to the purchaser
at the rate of 10 per cent, per annum. Capital to be redeemed
by effecting an insurance upon A* a life at the office rate of, say,
4. i os. 4.d. per 100.
Here the annuity of i is to be purchased on a life aged x 9
to yield v* per cent, on the purchase money P, and to redeem it
at the determination of the contingency, by effecting a policy
in an insurance office at the rate of r per pound ; but while the
annuity (a) is due at the end of the year, the premium must be
paid at its commencement. To prevent, therefore, the possi-
bility of the loss of a year's income in case the annuitant should
die before the completion of a year, the sum to be insured will
be represented by P-f a; and v being the present value of i
due one year hence, we have,
(20). P = - I - - 1.
Substituting the numerical value?, we also have
P = - l - - _ _ -i = 6-348847436
( i - -9090909 1 ) + -045 1 666;
years' purchase.
Then, 6-348847436 x 600 = 3809-3084616,
the present value of A's interest ; but, by the conditions of the
problem,
3809-3084616 + 16600 = 4409-3084616,
the total sum to be insured. The premium necessary to insure
this sum on the death of A will be represented by
(P-f a)x/.
Therefore 4409-3084616 x -04516667 . ; =199-15378
And (3 809-3084616+ 199-1537802) x lop.cent, = 400-84622
Together equal to the annuity . . . 600-00000
118 THE ENGINEER'S VALUING- ASSISTANT.
44. What is the Present Value of the royalty of a mine pro-
ducing an income of 500 per annum during the life of a person
A aged 47 ? The annuity has 60 years to run, and on the death
of A reverts to his successor, whose interest is to be sold at the
present time. Interest allowed to a purchaser on the capital
at the rate of 10 per cent, per annum, and to be redeemed by
effecting an insurance on A's life at the office rate of 3 iSs. id.
per 100. The value of the successor's interest to be redeemed
at the rate of 3 per cent, per annum.
The present value of i per annum for 60 years, allowing a
purchaser I o per cent, per annum upon his purchase money, and
redeeming the same at 3 per cent, per annum = 9-42214381.
And 9-42214381 x 500 = 4711-071905,
the value of the annuity for the total period of 60 years ; and,
as in the last preceding case, the value of A*s interest is
P = , i-r ^ I = 6-694606OII
( I -90909091) + ^3905 208
years' purchase.
Then 6*6946060 1 1 x 500 = 3347*3030055,
the present value of A's interest ; and, by condition,
^3347'303005 5 +500 = 3847-3030055,
the total sum to be insured. The premium to insure this sum
at the death of A is
3847-3030055 x -03905208 . . . =150-24518
And,
(^3 347'3030055-f 1 50-245 1 8476) xi oper cent. = 349-75482
Together equal to the annuity . C). . = 500*00000
The total value of the annuity for 60 years = 471 1*0719050
Value of A. 9 s interest . . . . = 3347*3030055
Value of A* a successor's interest . . 1363-7688995
PRACTICAL EXAMPLES IN VALUATION. 119
I have devoted a considerable amount of time and thought
to the construction of other problems, involving some of the
more general cases of lives with immediate and deferred annui-
ties. Originally it was intended to take up the whole range of
such cases, but after entering fully into the solution of some of
the more difficult deferred cases, I concluded that they were not
of that class likely to be of any great value or service to the
Civil and Mining Engineer, Colliery Proprietor, Colliery Viewer,
or General Manager. It is true, however, that the cases devised
were both curious and difficult ; although probably of more use
to professional Actuaries and Assurance Offices, than for those
for whom this work is more particularly intended.
Being fully aware that ample rules and examples illustrating
the treatment of such cases are to be found in works already
in existence, it would have been entirely out of place on my
part to have gone over the same ground. The subject of lives,
however, is one of great interest, and I confess it was with very
considerable reluctance that I finally determined not to intro-
duce anything further of that nature in this work.
The cases given in the preceding pages referring to the
Valuation of Mines are those usually occurring in practice, but
it is impossible to provide for all the modifications which it
may be necessary to introduce, suitable for all the varying
circumstances that may arise. Such modifications will be
best applied to any such cases by those to whom they may
occur.
It will be observed that throughout the problems where the
condition was introduced that a certain sum was necessary to
be expended upon open or unopened mines, with a view to
obtain an estimated yield of minerals, and constant profit ex-
tending over a definite future period, the ordinary or customary
mode of allowing 5 per cent, upon any such sum has been fol-
lowed. It was considered advisable that this mode of solution
should be fully exhibited, as it is believed to be good prac-
tice by some of the profession.
Others, however, entertain an opposite opinion, the nature
of which will be best understood by putting a case. For this
purpose, therefore, let us assume that a colliery is yielding a
nett income of 8,000 per annum, and that after careful con-
sideration, a valuer has estimated that to place the colliery in a
120 THE ENGINEER'S VALUING ASSISTANT.
position to yield a constant quantity of minerals extending over
a period of 2 1 years, so that in all probability the income will
be uniform for that period, the sum of 12,000 must be ex-
pended upon the works, during a period of 3 years, in equal
sums of 4,000 each year. The interest to be allowed to a
purchaser is 20 per cent, per annum, and the capital is to be
redeemed at 3 per cent, per annum.
Under such conditions the present value
of the colliery would be * . = 34,06 r 13800
The redemption fund to replace this gross
value of 34,061-1380 . . .= 1,18777239
And interest on the gross value of
34,061 *i 380 x 20 per cent, per annum = 6,812-22761
The proposed annuity . . = 8,000*00000
Then, it is customary to say,
From the gross value of the colliery . = 34,061*1380
Must be deducted the estimated
cost of works . . . . = 12,000
And also interest thereon at
the rate of 5 per cent, for 3
years .' .. * - .= 1,800
= 13,800*0000
Nett present value of the colliery . = 205261*1380
Now, it is held that the gross value of the colliery is made
up of two parts, i.e. 22,061*1380 and 12,000; because these
two sums together = 34,061*1380, or the gross value; also,
that the purchaser, or party in possession, is receiving 20 per
cent, per annum upon 22,061*1380, and upon 12,000, the
latter sum being contained in and part of the gross value.
Further, that the vendor receives a less sum for the colliery
than the gross value, by the difference between that value and
12,000, or 20,261*1380; and, therefore, that the purchaser
is not entitled to be allowed 5 per cent, for 3 years upon
12,000, nor indeed the full sum of 12,000, but only such a
sum as would, if it were invested at 3 per cent., accumulate to
12,000 at the end of 3 years. According to this view, by
PRACTICAL EXAMPLES IN VALUATION. 121
Table (XIII), the present value of 4,000 per annum for 3
years, allowing interest at 3 per cent, per annum = i 1,3 14*445.
The present value of the colliery, as pre-
viously stated . . . > : . = 34,061*1380
From which must be deducted the present
value of 4,000 per annum for 3 years
at 3 per cent, per annum , . *= 11,3 14-44 50
Present nett value of the colliery accord-
ing to the new mode . /.; 7 ; >V . = 22,746*6930
Present nett value of the colliery first de-
duced f ; . * . * . . = 20,261*1380
Difference in value . * .= 2,485*5550
The difference between the values as found by the two
modes is not large, but it is apparent that if the time over
which the expenditure was distributed amounted to 8 or 10
years, the difference would be very considerable.
It will be seen in Parts I. and II,, especially on pp. 10-14,
19-20, and 58-60, what elements are necessary to be con-
sidered in arriving at a valuation ; but after the valuer has
exercised his best judgment in determining all the necessary
elements, involving of course the rate per cent, to be allowed,
and the probable annuity to be derived over any fixed period in
the future ; then opinion as to the deduction and mode of
valuation ceases, or ought to cease altogether.
When we have no better means for determining any point
involved in a question than that of opinion, undoubtedly it
must be accepted ; but where science will aid us in arriving at
any conclusion, it must be taken as definite, and must not be
displaced by mere opinion.
DEDUCING VALUES FROM TABLES OF MULTIPLES
OF YEARS' PURCHASE, ETC.
For those who prefer to arrive at the value of either im-
mediate or deferred annuities, derived from any property,
simply by adding the quantities together, instead of performing
122 THE ENGINEER'S VALUING- ASSISTANT.
a long multiplication of the years' purchase by the annuity, ad-
ditional Tables for a few percentages may be prepared to effect
this.
For each percentage so treated there must be 10 columns of
figures ; the annuity in each may be found at the top of each
column, as i, 2, 3, 4, &c., up to 10. These numbers
may be conceived to have as many noughts attached to them
as there are decimal places in each column of figures. Thus
i, 2, &c., may represent i to 100,000,000, 2 to
200,000,000, up to 10 or 1,000,000,000. It is therefore
evident that the numbers in the column under i are the years'
purchase or values of that annuity, and that those in the other
9 columns are simply multiples of it.
The numbers i, 2, 3, &c., to 10 may be called 10 or
100, 20 or 200, 30 or 300, or any other number of tens
up to the limits before assigned.
In order, therefore, to find the proper value of any proposed
annuity, the decimal point must be removed as many places to
the right of the position it at first occupied to unity, as there
may have been tens or noughts attached to the annuity digit.
This mode of pointing off so as to form each number into whole
pounds and decimals of a pound, under or for any annuity, may
be best illustrated by. example.
Taking, therefore, the interest to be allowed to a present
purchaser at 2 1 per cent, per annum, and to redeem the capital
at 3 per cent, per annum, for 30 years' duration, with an
annuity of i, the present value would be equivalent to
4/3 2 8643434; this number, therefore, stands as it is found,
without alteration, but, by calling the i annuity 10, the
present value would be changed to 43 '2 8643434, and by as-
suming the annuity to be still greater, or 100 and 1000,
the present value would be changed to 432*8643434, and
4328*643434 respectively. We may, therefore, continue this
process of adding noughts to the original number corresponding
to unity until we get up to 100,000,000 ; and the equiva-
lent, as present value, would be 432864343*4. If instead,
however, of attaching noughts to the annuity of i, they are
prefixed, the value will be decreased in the same ratio as they
were increased in the former case.
Calling, therefore, i annuity *i, the present value or
PRACTICAL EXAMPLES IN VALUATION.
123
years' purchase would be .-4328643434, and supposing it to
be -01, -001, -0001, and -00000001 respectively, the
present value would be '04328643434, '004328643434,
0004328643434, and -00000004328643434 respectively,
which mode of working would hold good throughout.
Everything that is necessary to be obtained within the
limits of the rates of interest per cent, the Tables should be
calculated for, may be deduced from the first five columns, but
with a ten-column Table the lines of figures to be taken out
find added together are considerably diminished.
Supposing the annuity consisted of four figures, or say
8448, before applying the five-column Table it would be best
to divide it into parts, as
5000 + 3000 + 400 4- 40 + 5 4- 3 ;
but if we were to employ the ten-column Table, the figures would
be broken up into sections thus
8000 -f 400 + 40 + 8.
Thus, assuming the annuity derived from any property is
8448, to last for 20 years, interest to be 21 per cent, per
annum, and to redeem the capital at 3 per cent, per annum,
the work would stand thus (See Table XIV) :
SPECIMEN TABLE No. i.
H
20
Annuity
i, 10, 100,
1000; or -1,
'or, 'ooi, &c.
Annuity
2, 20, 200,
2000 ; or '2,
'02, '002, &C.
Annuity
3, 30, 300,
3000 ; or -3,
'03, '003, &c.
Annuity
4, 40, 400,
4000 ; or '4,
'04, '004, &c.
Annuity
5, 50, 500,
5000 ; or '5,
'05, '005, &c.
'
Ji
30
4-045050412
8-090100824
I2-I35I5I236
16-180201648
20-225252060
1
Annuity
6, 60, 600,
6000 ; or '6,
'06, '006, &c.
Annuity
7, 70, 700,
7000 ; or '7,
'07, '007, &c.
Annuity
8, 80, 800,
8000; or '8,
'08, 'oo8, &c.
Annuity
9, 90, 900,
9000 ; or '9,
'09, '009, &c.
Annuity
10, 100. 1000,
10000 ; or 'oi,
'ooi, *oooi, &c.
"
20
24-270302472
28-315352884
32-360403296
36-405453708
40-450504120
20
124 THE ENGINEER'S VALUING- ASSISTANT.
Annuity From Specimen Table No I
5000 20225-252060
3000 12135-151236
/JOG 1618*0201648
40 161*80201648
5 20-22525206
3 12-135151236
8448 34172-585880576
Employing the above specimen Table, using ten columns
instead of five, we shall obtain the value more readily.
Annuity From Specimen TaLle
8000 32360-403296
4OO 1618*0201648
4O 161*80201648
8 32-360403296
8448 34172-585880576
Although valuation may be performed by this simple mode,
it would nevertheless render this work too bulky and cumbrous
to compute additional tables for all the rates per cent, in a
similar manner, that is, to form tables of every rate per cent,
for which the present values have been calculated.
When the time of duration of a mine, the rate per cent., and
present value are given, to find the annuity, it may be deduced
from the same Table by the following process, and may be thus
expressed :
Rule. Find in the Tables in line with the number of years'
duration, and at the given rate per cent., the nearest value to
the one proposed, and take their difference ; the nearest value to
this difference must again be found in one of the columns in
line with the same number of years, and deducted as before.
This operation of seeking a value nearest to every new difference
must be repeated until the required or corresponding annuity
is obtained.
At each operation of finding such a value nearest to any
difference, the corresponding annuity to it, as found at the head
of the column of figures from whence each value was obtained,
must be noted down in a tabular form, and made to occupy a
PKACTICAL EXAMPLES IN VALUATION. 125
proper position with reference to the preceding figures ; then
the sum of all the lines or parts will express the annuity.
This rule will appear more clear from the following ex-
ample :
Kequired the annuity, all the other elements being as in the
last preceding case.
Corresponding
Annuity From Specimen Table No. I
34i72*58588o576 = given value.
8000 32360*403296 nearest value.
1812-182584576= ist difference.
400 1618*0201648 nearest value.
1 94* 1 624 1 9776 = 2nd difference.
40 161*80201648 nearest value.
32*3 6040 3 2 96 = 3 rd difference.
8 32*360403296 the value.
8448
The annuity required is therefore 8448.
If, however, an annuity composed of whole numbers, and
decimals, for a period of 30 years, and rates per cent, as in the
last preceding case, were required to be valued, it would present
no greater difficulty than a simple number.
Assuming it, therefore, to be 24362-29463, it must be dis-
posed of thus :
Annuity From Table (XIV)
20000-00000 86572*86868
4000*00000 I73i4'5737$6
300-00000 1298*5930302
60*00000 2 5 9*7 1 860604
2*00000 8-657286868
20000 -8657286868
09000 '38957790906
00400 -017314573736
00060 -002 5 97 1 860604
00003 '00012985930302
24362-29463 105455-68668732295942
126
THE ENGINEER'S VALUING ASSISTANT.
The proof is 4-328643434 x 24362*29463 = the above result,
or io5455'68668732295942.
The annuity may also be found from the present value as
illustrated above, thus :
From Table (XIV)
105455-68668732295942 =s given value.
86572-86868 nearest value.
1 8882-8 1 800732295942 ist difference.
17314-573736 nearest value.
1 568-24427 1 32295942 = 2nd difference.
1298-5930302 nearest value.
269-65 1 241 1 2295942 = 3rd difference.
259-7 1 860604 nearest value.
9-93 263 508295942 = 4th difference.
8-657286868 nearest value.
Corresponding
Annuity
2OOOO-OOOOO
40OO-OOOOO
300-00000
6O'OOOOO
2-OOOOO
20000
09OOO
00400
OOO6O
00003
24362-29463
The value of a deferred annuity may also be determined in
a similar manner, but it would first be necessary to construct a
table which should be multiples of the years' purchase deferred
under each rate per cent., according to the following Specimen
Table:
I -275 3482 1495942 = 5th difference.
8657286868 nearest value.
409619528 1 5942 = 6th difference.
38957790906 nearest value.
02004 1 6 1 909942 = 7th difference.
017314573736 nearest value.
002727045 36342 = 8th difference.
002 5 97 1 860604 nearest value.
00012985930302 = 9th difference.
00012985930302 the value.
PKACTICAL EXAMPLES IN VALUATION.
127
SPECIMEN TABLE No. 2.
!
Annuity
r, 10, 100,
1000 ; or 'i,
'oi, 'ooi, &c.
Annuity
2, 20, 200,
2000 ; or '2,
'02, '002, &C.
Annuity
3, 30, 300,
3000 ; or '3,
'03, '003, &c.
Annuity
4, 40, 4 oo,
4000; or '4,
'04, '004, &c.
Annuity
5, 50, 500,
5000; or -5,
'05, '005, &c.
30
2-I8I95053
4-36390106
6-54585I59
8-72780212
10-90975265
A nnuity
6, 60, 600,
6000; or '6,
06, '006, &c.
Annuity
7, 70, 700,
7000 ; or '7,
'07, '007, &c.
Annuity
8, 80, 800,
8000 ; or '8,
'08, '008, &c.
Annuity
9, 90, 900,
9000 ; or '9,
'09, '009, &c.
Annuity
10, 100, 1000,
10000 ; or 'oi,
'ooi, 'oooi, &c.
I
30
30
1 3-09 1 703 1 8
I5-2736537I
17-45560424
19-63755477
21-81950530
Thus an annuity of 18,254, to continue 30 years after
4 years, allowing 20 per cent, per annum to a present purchaser,
and to redeem the capital at the rate of 3 per cent, per annum,
would be dealt with by the following process :
Annuity
10000
8000
200
50
4
18254
From Specimen Table No. 2
21819-5053
I7455-60424
436-390106
109-0975265
872780212
39829-32497462
The accuracy of this deduction may be proved thus : The
present value of i per annum deferred 4 years
= 2-18195053 x 18254 = 39829-32497462,
the present value as before.
When all the other elements are given except the annuity,
and it is required to be -found, it may be readily deduced by the
converse operation, as previously illustrated for immediate
annuities.
Deferred values may also be obtained directly from the
table of the Present Value Immediate, with the assistance
of the table of values due at a future period, or the present
value of i due in n years
128
THE ENGINEER'S VALUING ASSISTANT.
Thus, presuming it were required to find the present value
of i per annum at 15 per cent, per annum, redeeming the
capital at the rate of 3 per cent, per annum, and to continue
35 years after 10 years' deferrence, we should have,
By Table (IV) the present value of i due 10 years hence
= '24718471, and considering it as an annuity, the present
value deferred may be deduced from a conversion of Table (VII)
as in Specimen Table No. 3.
SPECIMEN TABLE No. 3.
35
Assumed
Annuity of
1, 'oi, 'ooi,
&c.
Assumed
Annuity of
'2. '02, '002.
&c.
Assumed
Annuity of
3, '03, '003,
&c.
Assumed
Annuity of
4, '04, '004,
&c.
Assumed
Annuity of
'5, '05, '005,
&c.
i
H
600458901
1-200917802
1-801376703
2-401835604
3-002294505
35
Assumed
Annuity of
6, '06, '006,
&c.
Assumed
Annuity of
'7, '07, '007.
too.
Assumed
Annuity of
8, "o8, -008,
&c.
Assumed
Annuity of
-9, '09, '009,
&c.
Assumed
Annuity of
'oi, -001,
'ooor, &c.
35
3-602753406
4-203212307
4-80367 1 208
5-404130109
6-004589010
35
Assumed Annuity
*2
04
007
oooi
00008
000004
0000007
ooooooo i
Present Value deferred 10 Years
(From Specimen Table No. 3)
24718471
2401835604
04203212307
000600458901
0004803671208
00002401835604
000004203212307
000000060045 890 1
1-4842425931060371
or the present value of 'i per annum for 35 years, deferred 10
years.
The immediate value of 1 per annum corresponding to the
given elements in the last preceding case is 6-00458901, and
the proof of the above conclusion is 6-00458901 x -24718471
PRACTICAL EXAMPLES IN VALUATION.
129
= 1-4842425931060371, the present value deferred as before.
The converse of this will result by operating as previously ex-
plained.
Bub taking an example, and assuming it were required to
find the present value of i due in 10 years, by having given
the present value of i per annum deferred 10 years,
= i -484242 593 1 06037 1 , the work must be arranged as follows :
Assumed Annuity
04
007
oooi
00008
000004
0000007
oooooooi
From Specimen Table No. 3
1-4842425931060371 = given value.
1-200917802 = nearest value.
2833247911060371 = ist difference.
240 1 8 3 5 604 = nearest value.
0431412307060371 = 2nd difference.
04203212307 = nearest value.
0011091076360371 = 3rd difference.
000600458901 = nearest value.
0005086487350371 = 4th difference.
000480367 1 208 = nearest value.
0000282816142371 = 5th difference.
00002401835604 = nearest value
0000042632581971 = 6th difference.
000004203212307 = nearest value.
0000000600458901 = 7th difference.
0000000600458901 = the value.
247 1 847 1 the value sought.
We may also determine by similar means the annuity which
may be purchased for a given sum, at a certain rate per cent,
and for a given time. Thus the present value of 1 per annum,
allowing 20 per cent, interest, and redeeming at 3 per cent, per
annum, for a period of 50 years = 4-78777025, and,
- = -2088654943,
4-78777025
or the annuity which i will purchase.
130
THE ENGINEER'S VALUING ASSISTANT.
A table may be then formed, having such numbers for ;
basis, according to the following specimen for the fiftieth year.
SPECIMEN TABLE No. 4.
JH
Annuity
i, 10, 100,
1000; or -1,
'oi, 'ooi, &c.
Annuity
2, 20, 200,
2000 ; or -2,
'02, '002, &C.
Annuity
3, 30, 300,
3000 ; or '3,
03, '003, &c.
Annuity
4, 40, 400,
4000; or -4,
04, '004, &c.
Annuity
5, 50, 500,
5000 ; or -5,
'05, '005, &c.
I
50
50
2088654943
4177309886
6265964829
8354619772
I-04432747I5
>*
5
Annuity
6, 60, 600,
6000 ; or -6,
'06, '006, &c.
Annuity
7, 70, 700,
7000 ; or -7,
'07, '007, &c.
Annuity
8, 80, 800,
8000 ; or .8,
08, '008, &c.
Annuity
9, 90, 900,
9000 ; or *9,
'09, -009, &c.
Annuity
10, 100, 1000,
10000; or i,
'i, 'oi, 'ooi.
&c.
N
50
1-2531929658
1-4620584601
1-6709239494
1-8797894487
2-0886549430
Required the annuity which may be purchased for the sum
of 46,842, interest to be at the rate of 20 per cent, per annum,
and to redeem the same at the rate of 3 per cent, per annum,
to continue 50 years.
Sum to be In-
vested in Pur-
chasing Annuity
6OOO
800
40
2
Annuity to be
Purchased
8354-619772
1253-1929658
167-09239544
8-354619772
4177309886
From Specimen Table No. 4.
46842 9783-6774840006
Again, as a proof, we have
46842 x -2088654943 = 9783-6774840006,
the annuity as before.
By reversing the operation, the purchase sum may be
deduced by employing the annuity.
f/\-
ff'tJNlVBK'
PEACTICAL EXAMPLES IN VALUATION. 131
Purchase Money
40000
9783*6774840006 = given annuity.
8354*619772 = nearest value.
6000
800
1429-0577120006 = ist difference.
1253-1929658 = nearest value.
175-8647462006 = 2nd difference.
167-09239544 = nearest value.
87723507606 = 3rd difference.
8-354619772 = nearest value.
4177309886 = 4th difference.
4177309886 = the value.
40
2
46842
For proof, we also have,
4-78777025x9783-6774840006 = 46842,
as before, and also
The same rule may also be applied in determining the
deferred annuity which i or any other sum will purchase at a
certain rate and for a given period.
Thus the present value of i per annum, allowing 20 per
cent, per annum, deferred 3 years, and to continue 50 years
afterwards = 2-77070036 (see Table X).
Then
2-77070036
= "3609195763, the annuity
which i will purchase after 3 years. Then, by forming a table
with this number as one of its bases, we have the following
results for the fiftieth year :
K 2
132
THE ENGINEER'S VALUING ASSISTANT.
SPECIMEN TABLE No. 5.
%
50
Annuity
i, 10, 100,
1000, Sac., &c.,
&c.
Annuity
2, 20, 200,
2000, &c., &c.,
&c.
Annuity
3, 30, 300,
3000, &c., &c.,
&c.
Annuity
4, 40, 400,
4000, &c., &c.,
&c.
Annuity
5, 50, 500,
5000, &c., &c.,
&c.
1
50
3609195763
7218391526
1-0827587289
1-4436783052
1-8045978815
%
50
Annuity
6, 60, 600,
6000. &c., &c.,
&c.
Annuity
7, 70, 700,
7000, &c., &c.,
&c.
Annuity
8, 80, 800,
8000, &c., &c.,
&c.
Annuity
9, 90, 900,
9000, &c., &c.,
&c.
Annuity
10, 100, iooc,
10000, &C., &C.,
&c.
I
2-1655174578
2-5264370341
2-8873566104
3-2482761867
3-6091957630
50
Kequired the annuity that may be purchased, deferred 3
years, and to continue 50 years afterwards, allowing interest at
20 per cent, per annum, and to redeem the capital for 3 per
cent, per annum for the sum of 64,242.
Purchase Money Annuity Purchased
60000 21655-174578 From Specimen Table No. 5.
4000 1443-6783052
200 72-18391526
40 14-436783052
2 7218391526
64242 23186-1954206646
Then, the proof is
64242 x '3609195763 = 23186-1954206646,
the annuity as before.
And, conversely, we have
PEACTICAL EXAMPLES IN VALUATION.
133
Purchase Money
Kequired
60000
4Ooo
200
40
2
64242
From Specimen Table No. $
23186-1954206646
21655-174578
1531-0208426646
1443-6783052
72-18391526
15-1586222046
14-436783052
7218391526
7218391526
= given annuity.
= nearest value.
= 1st difference.
= nearest value.
= 2nd difference.
= nearest value.
= 3rd difference.
= nearest value.
= 4th difference.
= the value.
For proof, we have
2-77070036 x 23186-1954206646 = 64242, as before ;
also 23186^954206646 =6
3609195763
The redemption fund necessary to be set aside annually in
order to redeem any capital sum, may also be determined by
the same rule ; but in this case also it would be necessary first
to construct a table of redemption funds, which should be mul-
tiples of those corresponding to unity or I , at different rates
per cent. See Table (XV).
Thus, supposing it were necessary to redeem 38105*25 at
3 per cent, per annum, at the expiration of 30 years, we should
thus proceed :
SPECIMEN TABLE No. 6.
1
H
Redemption
Fund for
i, 10, ,100,
1000 ; or %
'oi, 'ooi, &c.
Redemption
Fund for
2, 20, 200,
2000 ; or -2,
'02, '002, &C.
Redemption
Fund for
3, 30, 300,
3000 ; or '3,
03, '003, &c.
Redemption
Fund for
4, 40, 400,
4000 ; or '4,
04, -004, &c.
Redemption
Fund for
5, 50, 500,
5000 ; or -5,
05, '005, &c.
30
30
02IOI92593
0420385186
0630577779
0840770372
1050962965
e
rH
30
Redemption
Fund for
6, 60, 600,
6000 ; or -6,
'06, '006, Sue.
Redemption
Fund for
7, 70, 700,
700x3; or -7,
'07, '007, &ic.
Redemption
Fund for
8, 80, 800,
8000 ; or -8,
08, 'oo8, &c.
Redemption
Fund for
9, 90, 900,
9000; or -9,
09, '009, &c.
Redemption
Fund for
10, 100, 1000,
10000 ; or 'oi,
'ooi, '0001, &c.
>4
I26II55558
I47I348I5I
1681540744
I89I733337
2IOI92593O
3
134 THE ENGINEER'S VALUING ASSISTANT.
Capital to be redeemed Redemption Fund
from Specimen Table No. 6
630-577779
8000-OO 168-1540744
100-00 2-10192593
5-00 -1050962965
20 -00420385186
O5 -001050962965
38105-25 800-944130441325
We may obtain a proof of this conclusion thus : The redemp-
tion fund necessary to produce i in 30 years is -02 10192593,
and -0210192593 x 38105-25 =800-944130441325, as
before.
The capital sum which may be redeemed in any particular
time at a certain rate per cent., and at a given redemption fund,
may also be found by the converse operation to that given
above ; thus :
Required the capital sum which may be redeemed in 30
years, when the rate is 3 per cent, per annum, and the Redemp-
tion Fund = 800-944 1 3 044 1325.
Corresponding Capital From Specimen Table No. 6
30000-00 ^630-577779 = nearest value.
170-366351441325 = 1st difference.
8000*00 168-1540744 = nearest value.
2*212277041325 = 2nd difference.
I OO'OO 2-10192593 = nearest value.
1 1 03 5 1 1 1 1 3 2 5 = 3rd difference.
5-00 -105096296500 = nearest value.
005254814825 = 4th difference.
20 -004203851860 = nearest value.
001050962965 = 5th difference.
05 -001050962965 = the value.
38105-25
PRACTICAL EXAMPLES IN VALUATION.
135
It may probably be considered by some of my readers that
the scheme for the Specimen Tables of Multiples, and the
examples worked by their means are needlessly diffuse ; but I
preferred allowing the decimals to run to the greatest number
of places possible, in order to exhibit more fully the general
arrangement of the mode and power of the Tables. When the
plan of working is understood, the labour of writing down so
many figures can be abbreviated ; indeed, it would not be con-
venient or advantageous to retain in the work more than four
or five places of decimals.
Tables of multiples of value may be arranged in a different
manner to those previously given. Thus in Specimen Table
No. 7, nine values will be found sufficient for each rate per cent,
and number of years.
SPECIMEN TABLE No. 7.
Interest on Capital 10 per cent. Kedernption 3 per cent.
An-
nuity
10 years
12 years
13 years
14 years
15 years
Au-
nuity
!
5-34100996
5-86640717
6-09646272
6-30810001
6-5033637I
I
2
10-68201992
1173281434
12-19292544
I2-6l620002
13-00672742
2
3
16*02302988
I7-59922I5I
18-28938816
18-92430003
19-51009113
3
4
21-36403984
23-46562868
24-38585088
25-23240004
26-01345484
4
5
26-70504980
29-33203585
30-48231360
31-54050005
32-51681855
5
6
32-04605976
35-I98443 2
36-57877632
37-84860006
39-02018226
6
7 37-38706972
8 !42728o7968
41-06485019
46-93125736
42-67523904
4877170176
44-15670007
50-46480008
45'52354597
52-02690968
8
9
48-06908964
52-79766453
54-86816448
56-77290009
58-53027329
9
The annuity being 7428-375, to last 15 years, interest
being at 10 per cent, per annum, and redeeming the capital at
3 per cent, per annum, we have the following deductions from
Specimen Table No. 7.
Annuity Value
7000 45523-546
400 2601-345
20 1 30-067
8 52*027
3 1-951
07 -455
005 '033
7428-375 48309-424
136 THE ENGINEER'S VALUING ASSISTANT.
This may be written in abbreviated form as follows :
Proposed annuity = 7428-375
2601-345
130-067
52-027
i95i
'455
Q33
Equivalent present value = 48309-424.
SPECIMEN TABLE No. 8.
Present Value of '1 per Annum. Redemption of Capital 3 per cent.
per Annum.
Years
3i per cent.
4 per cent.
4$ per cent.
5 per cent.
7 per cent.
Years
I
096618357
096153846
095693780
095238095
093457943
!
2
189533635
187754347
186008155 -184294144
177742755
2
3
278916405
275080186
271348062 ! -267715853
254109998
3
4
364927483
358388l 9 8
352079148 j -345988383
323596273
4
5
447718618
437915472
428532423
419543034
387064953
5
6
527433115
513881215
501008279
488764524
445240930
6
7
60420641 1
586488408
569779941
553997H9
4987373! 2
7
8
677766575
655925283
635096491
615549815
548076177
8
9
749434980
722366639
697185463
673700745
593704863
9
10
818126365
785974980
756255138
728700946
636008890
10
Years
10 per cent.
12 per cent.
15 per cent.
18 per cent.
20 per cent.
Years
j
090909090
089285714
086956522
084745762
083333333
I
2
168744805
163235767
155615178
I4867438I
144381223
2
3
236110581
225463707
2III79700
198597756
191010889
3
4
294961719
278530549
257051537
238648080
227776400
4
5
346795265
324301986
295547950
27H77559
257496647
5
6
392776833
364169375
328302103
298866548
282009884
6
7
433827521
399191472
356498164
322054601
302566044
7
8
470684834
430188219
381015682
341931323
320044664
8
9
503946260
457804488
402521626
359151725
335082624
9
10
534100996
482554435
421530947
374208773
348152434
10
All the numbers contained in the Tables in this work may
be arranged to read as pure decimal numbers. Thus, in Table
VII for 10 per cent, and for 10 years' duration by reading i
PRACTICAL EXAMPLES IN VALUATION.
137
as !, the corresponding present value would be changed from
5*34100996 to '534100996, and by the same rule if we read i
as *oi, the corresponding value of i per annum would be
changed to -0534100996, etc.
Specimen Table No. 8 illustrates this principle.
The present value of an annuity of 3,000 for 8 years,
allowing interest at the rate of 10 per cent, per annum, and
redeeming the capital at 3 per cent, per annum, may be deduced
from the above table as follows :
The present value of ! at 10 per cent, for 8 years
= 470684834.
Then, '470684834 x 3OOO = i4i2'O545O2ooo. We must
now remove the decimal point one place to the right (which is
equivalent to multiplying by 10), and we shall then have
i4i2O'545O2OOO for the present value.
This Table may also be arranged in another way, i.e. by
.considering i to have a cypher affixed to it, so as to read 10,
the corresponding present value would be changed.
Thus in Table VII for 10 years' duration, and at 10 per
cent, per annum, the present value of 1 = 5 '341 00996, but for
10 per annum for a similar period the value would be changed
to 53*4100996; if we were to affix two cyphers to i and
make it read 100, then the value would be changed from
5*34100996 to 534*100996. This method is shown in Speci-
men Tables No. 9 and 10.
SPECIMEN TABLE No. 9.
Present Value of 10 per Annum. Keclemption of Capital 3 per cent.
per Annum.
Years
3| per cent.
4 per cent.
4* per cent.
5 per cent.
7 per cent.
Years
I
9-6618357
9-6153846
9-5693780
9-5238095
93457943
I
2
l8'9533635
187754347
18-6008155
18-4294144
177742755
2
3
27-8916405
27-5080186
27*1348062
267715853
25-4109998
3
4
36-4927483 35-8388I98
35-2079148
34-5988383
32-3596273
4
5
44-7718618 : 43-7915472
42-8532423
4 T '9543034
38-7064953
5
6
52-7433115
51-3881215
50-1008279
48-8764524
44-5240930
6
7
60-4206411
58-6488408
56-9779941
55-3997119
49' 8 7373!2
7
8
67-7766574
65-5925283
63-5096491
61-5549815
54-8076177
8
9
74-9434980
72-2366639
697185463
67-3700745
59-3704863
9
10
81-8126365
78-5974980
75-6255138
72-8700946 1 63-6008890
10
138
THE ENGINEER'S VALUING ASSISTANT.
SPECIMEN TABLE No. 10.
Present Value of 100 per Annum. Redemption oi Capital 3 per cent.
per Annum.
Years
10 per cent.
12 per cent.
15 per cent.
18 per cent.
20 per cent.
Years
I
90-909090
89-285714
86-956522
84745762
83-333333
I
2
168744805
163-235767
155-615178
148-674381
144-381223
2
3
236-110581
225-463707
2II-I79700
198-597756
191-010889
3
4
294-961719
278-530549
257-05I537
238-648080
227776400
4
5
346795264
324-301986
295-547950
27I-477559
257-496647
5
6
3927/6833
364-169375
328-302103
298-866548
282-009884
6
7
433-827521
399-191472
356-498164
322-054601
302-566044
7
8
470-684834
430-188219
381-015682
341-931323
320-044664
8
9
503-946260
457-804488 i 402-521626
359-151725
335-082624
9
10
534-100996
482-554435 421-530947
374-208773
348-152434
10
The annuity being 3426, to continue 8 years, allowing
10 per cent, per annum, and redeeming the purchase money
at 3 per cent, per annum, the present value is deduced from
Specimen Table No. 10, as under.
The present value of 100 per annum under the conditions,
is 470-684834.
Then 470-684834 x 3426 = 1612566' 241 284.
By the decimal rule we have only cut off six decimal places,
which gives the result 100 times greater than it should be ; we
must therefore remove the decimal point two places to the left
to obtain the required value, i.e. 1612 5 '66241 284.
In working with the Tables it may be sufficient for ordinary
purposes to employ a less number of decimal places than will
be found in the Tables. This is of course effected by writing-
down the required number of decimal places, not forgetting to
add an unit to the last place retained, when the first figure in
the portion cut off is 5 or more. For instance, by Table VII
the present value of i for 8 years' continuance, at 5 per cent,
interest, and 3 per cent, redemption, is 6' 15 5498 15 ; but if we
employ only 4 decimal places, the value will read 6-1555.
Specimen Tables No. 1 1 and 1 2 give values to 3 and 4 places of
decimals respectively.
PBACTICAL EXAMPLES IN VALUATION.
139
SPECIMEN TABLE No. u.
Present Value of 1 per Annum. Redemption 3 per cent.
Years
3^ per cent.
4 per cent.
4i per cent.
5 per cent.
7 per cent.
Years
!
0-966
0-962
0-957
0-952
0'935
,
o
1-895
1-878
1-860
I-843
1777
O
3
2789
2751
2713
2-677
2-541
3
4
3^49
3-5^4
3-521
3-460
3-236
4
S
4777
4-379
4-285
4-195
3-870
S
6
5-274
5-I39
5-010
4-888
4-452
6
7
6-042
5-865
5-6 9 8
5-540
4-987
7
8
6778
6-559
6-351
6-155
5-480
8
9
7'494
7-224
6-972
6737
5-937
9
10
!
8-181
7-860
7-563
7-287
6-360
. I0
fears
10 per cent.
12 per cent.
15 per cent.
18 per cent.
20 per cent.
Years
I
0-909
0-893
0-870
0-847
0-833 I
2 I -687
1-632
1-556
1-487
1-444
2
3
2-361
2-255
2'II2
1-986
1-910
3
4
2-950
2785
2-571
2-386
2-278
4
3-468
3-243
2-955
2715
2-575
5
6
3-928
3-642
3-283
2-989
2-820
6
7
4-338
3-992
3-565
3-221
3-026
7
8
4-707
4-302
3'8lO
3-419
3-200
8
9
5^39
4-578
4-025
3-599
3-351
9
10
5341
4-826
4-2I5
3742
3-482
10
SPECIMEN TABLE No. 12.
Present Value of 1 per Annum. Redemption 3 per cent.
Years
3i per cent.
4 per cent.
4i per cent.
5 per cent.
7 per cent.
Years
I
0-9662
0-9615
0-9569
0-9524
0-9346
I
2
1-8953
1-8775
r86oi
I '8429
17774
2
3
27891
27508
27135
2-6772
2-5411
3
4
3-6493
3-5839
3-5208
3-4599
3-2360
4
5
4-4772
4-3792
4-2853
4'1954
3-8706
5
6
5-2743
5-1388
5*0101
4-8876
4-4524
6
7
6-0421
5-8649
5-6978
5-5400
49874
7
8
6-7777
6-5593
6-3510
6-1555
5-4808
8
9
7'4943
7-2237
6-9719
6-7370
5-9370
9
10
8-1813
7-8597
7-5626
7-2870
6-3601
10
140
THE ENGINEER'S VALUING ASSISTANT.
Years
10 per cent.
12 per cent.
15 per cent.
18 per cent.
20 per cent.
Years
I
0*9091
0-8929
0-8696
0-8475
0-8333
I
2
1-6874
1-6324
1-5562
1-4867
1-4438
2
3
2-3611
2-2546
2-III8
1-9860
1-9101
3
4
2-9496
27853
2-5705
2-3865
2-2778
4
5
3-4680
3-2430
2-9555
27148
2-5750
5
6
3-9278
3-6417
3-2830
2-9887
2-8201
6
7
4-3383
3-9919
3-5650
3-2205
3-0257
7
8
4-7068
4-3019
3-8I02
3-4I93
3-2004
8
9
5-0395
4-5780
4-0252
3-59I5
33508
9
10
53410
4-8255
4-2I53
37421
3-48I5
10
I am not aware that any special advantage is obtained by
arranging the Tables as in Specimen Tables No. 7, 8, 9, 10, 1 1,
and 12, but they may have the effect of preventing persons
pirating my Tables by adopting any of the modes of arrange-
ment I have exhibited. Unpleasant reminiscences of having
suffered by the dishonourable conduct of others in the past,
have induced me to take this course, with a view of guarding as
much as possible against such a contingency in the future.
KEMAEKS ON LOGARITHMIC CALCULATIONS.
In the last preceding division of this work I have given a
few practical examples of the mode of solving some of the more
difficult propositions in compound interest by Logarithms.
Had it been necessary, this mode of conducting computations
could also have been applied to the solution of the cases in
Valuation of Mines ; but it was not desirable to encumber that
portion of the work by introducing other rules, which, of neces-
sity, would have been subject to frequent repetition.
The following rules are of very great importance in deducing
results of an exceedingly accurate order, and may therefore be
applied as an occasional test to the numbers composing the
Tables.
The property of logarithms available for the facilitation of
arithmetical operations is, that the sum of the logarithms of
two or more numbers is equal to the logarithm of the product
of those numbers. From this, it follows that,
PEACTICAL EXAMPLES IN VALUATION. 141
ist. The difference of two logarithms is the logarithm of
the quotient of the corresponding numbers. A particular case
of this is, that the remainder arising from the subtraction of a
logarithm from o, is the logarithm of the reciprocal of the cor-
responding number. For, the product of a number and its
reciprocal being always I, the logarithm of which is o, the sum
of their logarithms is consequently o.
The indexes of the logarithms of two numbers reciprocal to
each other are necessarily affected with contrary signs, the sign
of the one being positive and that of the other negative ; and
it simplifies work to remember that, apart from their signs, the
negative index always exceeds the positive by an unit.
2nd. Another consequence of the property above enunciated
is, that n times the logarithm of a number is the logarithm of the
71 th power of the number. Thus n log a = log a n ; and in like
manner one n ili part of the logarithm of a number is the
logarithm of the n ih root of that number :
log a
n
= log
Tables of /-figure logarithms, which suffice for most pur-
poses, are very accessible. When results of more than seven
figures are wanted, recourse may be had to Gray's Tables of
logarithms to twelve places.*
I now give a few examples.
I. Kequired the amount of i at 3^ per cent, in 100 years.
The required amount here is .R 100 , where R is the amount at
the specified rate, of i in one year, = 1*035.
Hence,
logE 100 = 1 00 log It;
that is,
Iog(i ; o35) 100 = IO lg 1*035 = 0-0149403 x 100 = I '4940300
and the number corresponding to this is, 31 '191 5, which is the
amount required.
It is to be observed that two places in the logarithm being
in effect lost in the multiplication by 100, the result cannot be
depended on to more than five or six places in all.
* Published l>y C. and E. Lay ton, London.
142 THE ENGINEER'S VALUING ASSISTANT.
Using the 12-figure logarithms we find,
i oo log i -03 5 = 1-494034979300,
the number corresponding to which, to 10 places, beyond which
it is useless to go, is 31-19140798.
2. Required the present value of i per annum, the rate of
interest on the purchase money being 16 per cent, per annum,
and that for redemption being 3 per cent, per annum, for a
duration of 40 years.
The formula for solution here is, p r 31,
i
P -
* n ~~~
^ +
that is,
16
(Table V) = -01326238
16 = -16
17326238 log 1-2387043
P 40 . . = 5771593 0-7612957 complement,
The complement (which is the logarithm of the reciprocal)
is obtained by subtracting the logarithm here formed from o ;
and the subtraction is most readily performed by deducting
each figure in the decimal portion from 9, except the last,
which is deducted from 10. And the index of the logarithm
being i, that of the complement is o, in accordance with what
has been said.
Using the 1 2-figure tables we get for the logarithm
0-761295729529,
and for the corresponding number
577I5934I6075.
By Table VII the required value is 5-77159342, agreeing, as
far as it goes, with that last found.
3. Required the present value of I per annum deferred 4
years, and to continue 40 years thereafter, allowing interest
at 20 per cent, per annum, and for redemption 3 per cent, per
annum.
PEACTICAL EXAMPLES IN VALUATION. 143
The formula here is
Pt+n = PnV* ; that is P 4+40 = P^v*.
P 40 , (Table VII) . = 4-6890596 log 0-6710858
v 4 , (Table IV) . = -4822531 1-6832750
P 4+40 .' . " = 2-261313 0-3543608
By the 12-figure table we have,
P 4+40 = 2-261313463908;
the value by Table X being 2-26131348.
4. Required the redemption fund that will amount to i in
20 years at the rate of 3 per cent, per annum.
The formula here is, p. 29,
= Kr~i' that is '
Q3
(1-03)"- i"
03 log 2-4771213
( I -03) 20 - I, (Table I) = -8061112 1-9063949
s 20 . . = -03721571 2-5707264
The value by Table V is -03721571. The 12 -figure pro-
cess gives -0372157075953.
5. Required the present value of i due 20 years hence.
The value here required is the reciprocal of the amount of
i in the same time, being denoted by i> 20 . We therefore have
v = JL, and log v 20 = co log # 20 .
JTt
# 20 , (Table I) = 1-8061 1 1 log 0-2567444
v 20 . . = -5536759 17432556 complement.
The 1 2-figure process gives -553675754178 ; and the value
given by the tables is -55367575.
6. Required the annuity which i will purchase, the ele-
ments being as in (2).
The annuity that i will purchase is, in all cases, the re-
ciprocal of the present value of the same annuity. Hence the
144 THE ENGINEER'S VALUING ASSISTANT.
annuity here required will be found by forming the reciprocal
of P 40 found in example 2.
^40 =5771593 log 07612957
Annuity = '1732624 1*2380043 complement.
By the 12-figure tables we have for the required value
173262377895.
7. Required the annuity, deferred, which i will purchase,
the elements being as in (3).
The value here sought is the reciprocal of that found in
example 3.
By the 7-figure process it comes out '4422208, and by the
12-figure process, '4422208667492.
PART IV.
SOUECES FOE EEDEMPTION OF CAPITAL
BY
EEINVESTMENT OF SURPLUS ANNUITY;
WITH REMARKS ON THE ADVANTAGES OF HOME AND
FOREIGN MINING, ETC. ETC.
PAET
SOUECES FOE EEDEMPTION OF CAPITAL BY
EE INVESTMENT OF SUEPLUS ANNUITY.
WHEN a proper Valuation has been made, and a mineral property
purchased upon its basis, with a view to its ultimate develop-
ment, it is of the greatest consequence to be in a position to
thoroughly examine into all available sources for the redemption
of any capital sum so invested, and select that which under all
the circumstances is most reliable and profitable.
This being settled, any values may be obtained from the
Tables having corresponding rates of interest for redemption at
2 25 3? 3i> an d 4 per cent, per annum.
For the sake of comparison, and to illustrate the difference
in value at different rates of redemption^ we may employ- the
years' purchase or present value of i per annum at a given
constant rate of interest and time ; thus, the present value of
i per annum, or years' purchase, allowing 20 per cent, to a
purchaser for a period of 20 years, and to redeem the capital at
rates of interest of 4, 4^, and 5 per cent., is 4-281156377,
4-312647 1 80, and 4*343245149 respectively.
The difference between the first and second years' purchase
is -031490803 or 71 pence, that between the second and third,
*3O5 9/969 or 7^ pence, and that between the first and third is
062088772, or 1 5 pence. Presuming, therefore, the interest
allowed on any purchase to be at the same rate, and for the
same time of duration as stated, it appears that the present
value of i per annum, or years' purchase, is augmented as the
rate per cent, for redemption is increased. Thus, at 20 per
cent, per annum upon a purchase, at 4^ per cent, for redemp-
tion, and for 20 years' duration, every i annuity purchased
would cost more by about 7^ pence, than it would, presuming
t 2
148 THE ENGINEERS VALUING ASSISTANT.
the redemption rate of interest had been fixed at 4 per cent.
per annum. The difference between the years' purchase at
redemptive rates of interest at 4 and 5 per cent, per annum,
comes out more prominent, amounting to 1 5 pence more than
would be paid for each i annuity in case the capital were
redeemed at the rate of 4 per cent, per annum. High rates of
interest for redemption, therefore, are against the interest of a
purchaser, and in favour of that of a vendor. On the other
hand, however, as the rate of interest for redemption increases,
the redemption fund necessary to re-produce i in the given
time, decreases ; which is of course due to the increase at
compound interest of I in any number of years.
Thus, - - = '0335817503, or s 20 ,
' 2-19112314303-1
2-4II7H024-I
The redemption fund being s 20 , and corresponding to the
rates of interest at which the years' purchase were computed.
If we pay down the present sums of 4-281 156377,
4-3 1 2647 1 80, and 4-343245149, and expect to realise 20 per
cent, per annum for 20 years, and redeem such capital sums at
rates of interest of 4, 4-^, and 5 per cent., we shall have the
available and capitalisation sums thus derived and represented :
4*281 156377 at 20 per cent, per annum = -8562312755
4-281 1 56377 x -0335817503 . . = -1437687245
Annuity purchased =1-0000000000
And,
4-312647180 at 20 per cent, per annum = -8625294362
4-312647180 x -0318761443 * . = -1374705638
Annuity purchased = 1-0000000000
Also,
4-343245149 at 20 per cent, per annum = -8686490298
4-343245 149 x -033581750 . . = -1313509702
Annuity purchased =1-0000000000
SOURCES FOR REDEMPTION OF CAPITAL. 149
which, as previously mentioned, shows a decreasing redemption
fund for reproducing each capital sum in twenty years.
Perhaps one of the most reliable sources for investments at
low rates of interest is presented by the English Grovernment
Funds. The Consolidated 3 per Cent. Annuities are, however,
subject to much uncertainty as to the price to be realised by
them in the market. The highest rate of interest ever obtained,
occurred I believe in 1797, when Consols were sold at 52, the
rate percent, on the purchase being ? -=^5 l$s. 4d. The
least rate realised upon purchase appears to have been in 1737,
when Consols were sold as high as 106, the rate being ^ =
100
2 i6s.
One of the chief causes which operate to influence the price
of stock is the limitation in the demand in proportion to the
supply, and vice versa. Consols, as well as most other kinds of
stocks, are also affected by a variety of circumstances, such as
the storing or withdrawal of gold from the Bank, political
changes, apprehensions of the disturbance or restoration of
peace, and many other causes influencing the condition of the
money market, known best to stock brokers, their agents, and
jobbers, who are adepts not only in understanding, but some-
times in producing certain fluctuations in the value of stock for
special benefit. Indeed any excitement of public feelings, due
either to real or imaginary causes, is sufficient to produce a
temporary change at least in the value of furided property.
Those whose business it is to deal in stocks endeavour to
make a profit by purchasing at low prices, and selling out at
higher rates, at favourable opportunities.
The money market is also much influenced by the press ;
and it is curious to note with what anxiety and expectancy City
and other business men will turn to the Money Article in the
day's newspapers, and the eagerness they exhibit in exchanging
comments and eliciting opinions upon it, evidently with a view
to extend or curtail their financial operations, according as the
general tone may seem favourable or otherwise.
At the time of writing this portion of the work the sale of
stock in about 28 of the British railways was producing from 2
to 51 per cent.; the best in the list being the Bristol and Exeter,
150 THE ENGINEER'S VALUING ASSISTANT.
Furness, North-Eastern, Shropshire Union, and the Taff Vale,
which were selling at rates of interest of 5f, 5^, 5j, 5|, and 5^
per cent, respectively. Railway preference stocks were selling
to realise from 4 to 5 J per cent, per annum ; railway debenture
stock was also selling to realise from 3j to 5j per cent, per
annum, and is considered to be a safe investment.
The stock of 13 Indian railways were selling to realise
from 3^ to 4 per cent, per annum, and are considered very
safe ; the interest on the issue being at the rates of 4^ and 5
per cent , which, with the principal, is guaranteed by the
Secretary of State for India in Council.
Of 43 colonial railways, 27 were selling stock which realises
from 3 to 9 per cent, per annum. The highest percentage
represents the European and North American 6 per cent, issue
first mortgage bonds, redeemable at par in 1 898 ; but it appears
that the most reliable are the Melbourne and Hobson's Bay
united 6 per cent, bonds, payable in 1880, and 5 per cent,
bonds redeemable in 1895, the latter having 20 years to run.
Also Tasmania Main Line, Limited, guarantees 5 per cent., the
stocks of which were selling to realise 5 1, 5, and 6J percent,
per annum respectively.
Of 85 American railways, the shares in 44 of them were sell-
ing to realise from 4! to 9 per cent., the former rate repre-
senting that obtained by the sale of the shares in the Illinois
Central redemption mortgage, payable in 1875, and the latter
the Paris and Decanture.
The sale of the shares in Baltimore and Potomack Main
Line first mortgage, and the Gralveston and Harrisburgh
first mortgage, were selling to realise 6J and 8J per cent, per
annum, and redeemable in 191 1, having 31 years to run.
Of foreign railway obligations, the bonds in the Central
Argentine first issue 7 per cent, were selling to realise 5 J per
cent, per annum ; and out of 20 others, the bonds of 16 of them
were selling to realise from 4 to 7 per cent, per annum.
Out of 30 colonial government investments, the stock in 29
of them were sold at from 4 to 5| per cent, per annum.
The shares in 12 Insurance Companies were realising 6J, 7,
6J, 5i, 6, 5j, 5f, 4f, 4^, 5, and 6| per cent, per annum
respectively, the highest rate being realised by the c Universal
Marine ' insurance company, limited, and the lowest by the
SOUKCES FOR REDEMPTION OF CAPITAL. 151
6 Koyal ' insurance company, limited. The highest and lowest
rate obtained by the sale of shares in 1 2 land companies was
7f and 4} per cent. ; in 7 dock companies 5f and 4 per cent. ;
and in 8 shipping companies it was 8J and 6 per cent, per
annum.
The shares in the Globe Telegraph and Trust Company
were realising 8J per cent, per annum. Those in n other
telegraph companies were realising from 5f to 7f per cent,
per annum upon the market value of stock.
Of other industrial companies, the sale of shares in Hooper's
Telegraph Works, Limited, realised as much as 13^ per cent,
at the then market value. The shares in most other com-
panies were selling to realise from 5 to 10 per cent, per annum.
There are a great variety of foreign stocks, loans, and bonds,
which were realising rates in the market from 3 j to nf per
cent, per annum, such as Argentine, Columbian, and Costa
Rica 6 per cents., Paraguay 8 per cents., and many others of
an uncertain character belonging to the South American States.
Indeed, mention may be made of many not far removed from
an entire collapse.
Great care, and the exercise of sound judgment, are of
necessity required on the part of an intending purchaser of
stocks, if. they are to be regarded as a means of profitable
investment.
Indian railways, Indian debenture bonds, colonial govern-
ment investments, safe home railway debenture stock, and joint
stock limited banks, &c., working on a safe basis, and possessing
firm guarantees and good management, are very inviting, and
would doubtless yield a good percentage upon the capital
invested in such undertakings.
Surplus annuities derived from mining may therefore be
employed to advantage in the purchase of stock or shares in
such of these undertakings as may be considered to be absolutely
safe, and so from time to time redeem any capital sum, or at
least a portion of such sum invested elsewhere, at a higher rate
of interest than could be realised by investing in 3 per cent.
Consols. On the average 4, 4-J-, or probably 5 per cent, may be
realised for limited periods. A considerable advantage is also
connected in possessing property of this class, as it may always
be turned into ready cash, at the market value.
152 THE ENGINEER'S VALUING ASSISTANT.
EEMAKKS ON FOREIGN AND HOME MINING.
As to Foreign Mines on the whole with some exceptions
I consider it to be a great mistake to invest in them indiscrimi-
nately, as the majority of them are of such uncertain character
as to render it a very unsafe venture. Much, however, depends
on the part of the world in which they exist, the surrounding
circumstances, and other associations. Very valuable beds of
coal of great thickness, and iron ore deposits in immense masses
exist, and are of such frequent occurrence in the different mineral
basins in the United States, as to entitle them to be considered
as the future storehouses of untold wealth; but the isolated
condition, and want of transit of many of them, renders it very
improbable that they will receive much attention from English
capitalists, at least for some years to come. Those, however,
who can afford to lock up a considerable amount of capital in
the purchase of large tracts of minerals in the States, for the
benefit of their successors, might do a more unwise thing.
With regard to the silver, and gold mines of the far West,
some of them are unworthy the attention of English capitalists,
as it is not in the nature of things considering their great
distance from home, and all the surrounding circumstances
that any permanent profit can be realised from many of those
offered in the market, even supposing that such mines are really
in existence. Many of these mines are too much in the hands
of a class of men whose chief aim in a general way is to interest
English persons in their behalf with a view to carry on some illegi-
timate speculation. It is also a most surprising fact that persons
of apparent respectability are to be found in London to co-operate
in such barefaced schemes, some of which are now and then
exposed and held up to the light in the law courts. If, instead
of taking up with all the mines introduced in England from
Colorado, Utah, California, and places similar to the late salted
diamond fields, the English public were to turn their attention to
portions of the Argentine Eepublic, they would find some of
the silver mines of those regions far more worthy of their
attention,
At the time I was appointed Engineer to survey, and draw
EEMAKKS ON FOKEIGN AND HOME MINING. 153
up a report, estimate, and valuation, for the purpose of carrying
out an immense drainage scheme, projected for the Argentine
Government, and intended to unwater the silver mines of the
Cero-de-Pasco, high up in the Andes, I had ample opportunity
of collecting information as to the great riches existing in
that district, and from further evidence, since published by
Major Rickard, it is ascertained beyond a doubt that many
portions of the mountainous districts of the Argentine Eepublic
are replete with rich silver ore deposits, containing a greater
percentage of silver than can be obtained from similar mines in
many other parts of the world.
The chief drawback to mining being carried on in this
Eepublic, is the want of special and speedy means of transit
from the mines to the Towns, and seaboard, but the great eleva-
tion, dangerous passes, and gorges, have hitherto prevented this,
other than what may be performed by pack-mules , the load of
each being from } to one hundred weight. This difficulty may,
however, be remedied to some extent, by extracting the metal
at the mines upon an improved principle, and then conveying it
to its destination by mules. If it is necessary to adventure capi-
tal in American mining at all, the Argentine Republic should
undoubtedly have the preference, on account of the unusually
high profits expected to be derived from the silver mines there.
To obtain a large concession in this region, and colonise it
with English people, would be a far more wise and profitable
scheme than scores of those laid before the public from time to
time.
My professional visit to the Brazils in 185 1 did not strongly
impress me with the idea that it would ever be likely to prove
a legitimate and permanent mining field for the expenditure of
English capital. Indeed, the small amount of labour to be
obtained from the natives, naturally an indolent race under a
burning tropical sun, is not such as to encourage English adven-
turers to speculate in such a place.
Australia has undoubtedly created and is still creating con-
siderable interest as a mining colony, being rich in tin, copper,
iron, coal, and the precious metal, gold ; but I am not of opinion
that the quantity of the latter to be found there in the future will
ever affect the value in the currency so as to cause a depreciation.
I visited Australia professionally in 1853, and at that time
154 THE ENGINEER'S VALUING ASSISTANT.
there seemed to exist such a tendency, but it soon became
manifest, that, even to obtain a moderate supply of gold, the
search would have to be continued in a more regular mining
way, involving of course more labour, and the expenditure of
adequate capital in order to obtain fair or corresponding returns.
I anticipate great things for Australia, from the future yield of
her mineral fields.
India, and also New Zealand, are legitimate fields for mining
enterprise ; they are British Possessions so to speak, and therefore
it is natural Englishmen should turn their attention in these
directions. It is only a question of colonising these places with
young English people, so that they may become acclimatised,
and the more general introduction of rail ways, and then capitalists
may fearlessly venture their cash in developing the mineral
resources in conjunction with manufactories. On the whole,
New Zealand, as a mineral field, is in some respects pre-
ferable to some of the other colonies, on account of its splendid
climate.
Spain has from very ancient times been far famed for her
mineral wealth, it is much nearer home than any of the places
previously referred to. Many parts abound in different kinds of
minerals, such as silver, copper, lead, quicksilver, sulphur, iron
ore, and coal. The English obtained concessions in Spain and
caused a great excitement there in 1825, but the speculators
in a general way were so ill advised, that the mania soon
subsided to its proper level. Since that time very valuable
concessions have been obtained, and worked by English companies
to a very great profit. The nation has hitherto been much
crippled by its internal disorganisation, producing a re-action
in speculation to a considerable extent. Mercantile relations
are thus injured, and thrown out of proper order. Spain, however,
obtains a large revenue from her mines, and should the new
government secure permanent peace to the nation, the tide of
English speculators would again flow in that direction, and the
export of minerals from there to England would undoubtedly
prove large. I am quite persuaded that by perseverance, there
is ample opportunity to amass large fortunes from working
Spanish mines.
There are, however, great profits to be gained from legitimate
Home Mining, and it will no doubt be preferred by many to
KEMARKS ON FOREIGN AND HOME MINING. 155
foreign adventure ; England, however, creates rich men, and in
too many instances, foreigners reap the benefit of them.
However, it is the nature of Englishmen to desire to become
rich, and as the population increases so enormously, and this
passion will always exist, they will naturally seek that field of
enterprise most likely to enable them to achieve their object ;
hence, we shall always find English capitalists adventuring, some
in one thing, and some in another, in different parts of the
world.
There are many good mines in every mining district
throughout the United Kingdom, and there are also a good
many inferior ones ; but it is known to many persons that there
are thousands and thousands of acres of virgin ground, containing
iron ore, lead, tin, coal, and other minerals, not yet explored.
When however the time comes for winning, a rich harvest will
be yielded to those embarking in it. Coal, iron, and other
minerals will always be in requisition for the purpose of carrying
on the commerce of the world, no matter what may be urged
against new undertakings, consequent upon fluctuations of trade.
There are at all times capitalists who will purchase properties
for the purpose of working the minerals, and the proper time to
make these purchases is when trade is dull, and prices are low.
It is only in a season of great commercial excitement and pros-
perity, that all sorts of persons join together in order to float
bubble companies, endeavour to pocket the cash obtained,
perhaps upon glaring and false representations, ruin the share
holders, and bring legitimate mining into ill repute. Of all
places for palming off shams, and hatching swindles, there is
none equal to London.
It always has been, and will still be the case, that those capable
of producing the best article in the greatest abundance, and at
the cheapest rate, must win the day ; but whether it is a colliery,
iron, silver, or other mine, a good one in the first instance must
be possessed, that is, it must contain minerals in sufficient
quantity, and quality, to justify the contemplated outlay, other-
wise it will be so much capital lost. When a good property is
obtained, it is only a question of time, and capital judiciously
expended, in order to produce proportionate results as to profit.
In these times, too, it is necessary to obtain a very large and
constant annual output or yield from the mine, and with regard
156 THE ENGINEER'S VALUING ASSISTANT.
to the expected profit per ton, or annual income, it is also a
question of importance to consider whether, on the whole, it
would not be the wisest plan at the commencement of a new
winning, to arrange all the works above and below ground, so
as to be in a position to raise from the mine two or three times
as much as is being raised from any single colliery or iron mine
in the same district, or indeed as may be required from such
new colliery by the demand of trade during the first few years
of its life. If 800 or 1000 tons per diem could be considered a
good output from any one of the several mines surrounding the
winning about to be developed, the machinery should be calcu-
lated to raise at least three times that quantity, or from 2400 to
3000 tons per day, and arrange all the surface and underground
works to correspond.
The position would then be this, that if at 800 or loootons
per diem, and say is. 6d. or 2s. per ton profit, the smaller
collieries in the district would but just or scarcely pay at
the rate of profit named or that actually realised, the larger
colliery would live, and flourish at a less profit per ton than
the smaller ones, because a large colliery properly laid out
would cost less in working expenses in proportion, than those
of less capacity. Another advantage would also accrue
from laying out a new winning according to this plan, and it
is this : in a time of great demand, and with high rates of profit,
the larger quantity could be obtained, supposing the colliery
had not been worked up to its full capacity, consequently a
greater annual revenue would result. I believe it is a great
mistake, in laying out a new winning of ample area, to copy even
the best example in the same neighbourhood, its capacity being
only equal to that of an ordinary going concern.
Provisions should be always made in surface arrangements
for future underground extension, at any time it may be required
to double or triple the output, but if the machinery is under
power this cannot be accomplished without making additions,
which are always more expensive, and incomplete, besides pro-
ducing vexation from delay.
As to the underground works, if there are good seams of coal
to work upon, provision can always be made in times of moderate
demand, to have a reserve ready, to be extracted as an additional
supply, at the least notice. I am of opinion that if all new
HEM ARKS ON FOREIGN AND HOME MINING. 157
collieries were laid out as suggested, it would tend to equalise
trade, and place the proprietors in a position to meet a downward
market: I think this is clear, as 1000 tons per diem at is. per
ton profit would produce the same annuity as 500 tons per diem
at 2s. per ton profit, and although more capital would of necessity
be employed, nevertheless a colliery so circumstanced would pay
a dividend, when those of more limited capacity would be
struggling for life, or perhaps would be closed altogether.
In the case where proprietors require a certain definite
and invariable income from their mines, no matter whether
times are good or bad, I think they would be more likely to
succeed by adopting the plan proposed.
The unprecedented struggle of labour against capital ex-
perienced of late throughout the United Kingdom, has created,
and laid severe infliction upon all the parties involved. Whether
English proprietors will, with neighbouring countries, be content
to accept in the future less profit than heretofore, is not easy to
judge ; but as labour can be commanded on the Continent at a
much cheaper rate than at home, enabling the firms established
there to produce the raw and manufactured article at a cheaper
price than we can, under present circumstances, necessity seems
to force itself upon us, to adopt some measures for preventing
a destructive competition, and to retain and increase the trade
of this country. The only way to this which seems to com-
mend itself, is, reasonable wages for men, such indeed as the
demand of trade seems to warrant, and smaller profits to the
employers.
I have no doubt the plan of working I have suggested, that
is, to produce large vends and receive small profits, would meet
with considerable opposition from proprietors of limited means,
but the policy is undoubtedly a sound one. I am also of opinion
that gentlemen of limited means are not the proper persons to
embark in such adventures ; in point of fact, it is only those
private persons who can afford to risk from 50,000 to i 50,000
if necessary, in mining, that should enter into it, and then if
success crowned the efforts put forth, it would be very pleasing,
and highly satisfactory ; on the contrary, the loss of the capital
would not prove an entirely ruinous matter. It is a great
mistake for gentlemen who do not understand mining to embark
their all in it, especially as is too commonly the case, when their
158 THE ENGINEER'S VALUING ASSISTANT.
capital is limited to a few thousands, and they enter into the
undertaking for the sake of a managing salary, and a living.
The issue generally is, that the development is carried on by feeble
attempts ; gets crippled, and drags on to a premature death ;
but if by any chance it survives, it only yields respectable poverty
to all connected with it : whereas, if sufficient capital had been
put into it, under more favourable auspices, it would have proved
a lucrative undertaking.
One great drawback to the success of a mine is that gentlemen
proprietors, some of whom are only half educated in mining
matters, are continually interfering in the management, leading
to neglect and disappointment on the part of those in charge,
and disastrous government.
Persons in the possession of limited means, are, therefore, fit
subjects for joining a Limited Liability Company, where their
dominant spirit can only be exercised in direct ratio to the
amount of capital they are able to throw into the concern.
When foreign mines are found to compare favourably in
productiveness and estimated worth with our best home mines
of a similar class, more risk is undoubtedly incurred in the pur-
chase of the former than of the latter. A purchaser is therefore
entitled to be allowed a greater rate per cent, per annum upon
the Capital he may invest in foreign than in home mines.
Extra contingencies, which are impossible to be foreseen, arising
out of the policy or internal disorganisation of foreign Grovern-
ments, may frequently operate to prejudicially affect the value
of the interest held by home capitalists in foreign mines. This
must be evident, especially when it is necessary to ship the
minerals to this country. If, then, 20 or 25 per cent, per
annum may be considered to be the maximum rate allowed upon
the purchase of home metalliferous mines, foreign mines should
be purchased at least from 10 to 15 per cent, per annum higher.
Since printing Tables I to XVIII, I have been called upon to
consider this question ; and, after mature deliberation, have
arrived at the above conclusion.
A small Table (C) of Immediate Values for 30, 35, 40, and
45 per cent., and also a Table (D) of Deferred Values for the same
rates per cent., Deferred I, 2, 3,4, and 5 years, have been prepared,
and will be found of special use to purchasers of foreign mines
at high rates of interest ; but it is probable that such mines
PUKCHASING FOREIGN MINES.
159
would find little favour with the English public when the time
for development and consequent delay of dividends extended to
or beyond 3 or 4 years. Table A was calculated for the purpose
of constructing Table B, and the latter was employed in defer-
ring the values in Table C.
In Table C, at 45 per cent, per annum for 40 years, the
years' purchase is 2*1586, and for the same rate and time, but
deferred 3 years, Table D gives a years' purchase of '7081 ; and
for 4 or 5 years' deferrence it is "4883 and '3368 years' purchase
respectively. These values are apparently small, but when it is
considered that gold, silver, and other foreign mines are fre-
quently purchased upon representations which assume that the
annual income will be very large, it is clear that the value
would amount to a very considerable sum. For instance,
assuming that a gold mine were to be offered which, according
to representation, would yield an Annuity of 60,000, but to
prepare for this 3 years must be spent in development. Then,
at 45 per cent., the Value would be 708 1 x 60,000 = 42,486
= the Grross Value ; but if deferred 4 years, it would be '4883
x 60,000 = 29,298 = the Grross Value; if deferred 5 years,
3368 x 6o,OOO = 20,208 = the Grross Value. Of course the
cost of opening the mines must be deducted from the Grross
Value.
As a constant yield from gold, silver, and some other
metalliferous mines is very uncertain for any length of time, it
is highly desirable that they should be purchased upon the most
advantageous terms.
TABLE A.
Amount of 1 in n years, up to 5 years, at the following rates
per cent. :
n
Years
30 per cent.
35 per cent.
40 per cent.
45 per cent.
n
Years
I
2
3
4
5
1-30000
1-69000
2 19700
2-85610
371293
I-35000
1-82250
2-46038
332I53
4-48407
1-40000
1-96000
274400
3-84160
5-37824
I -45000
2-IO25O
3-04863
4-42051
6-40974
I
2
3
4
5
160
THE ENGINEER'S VALUING ASSISTANT.
TABLE B.
Present Value of 1 in n years, up to 5 years, at the following
rates per cent. :
n
Years
30 per cent.
35 per cent.
40 per cent.
45 per cent.
n
Years
I
2
3
4
5
76923
59172
45517
35013
26933
75074
54869
40644
30107
22302
71429
5I02O
36443
26031
18593
68965
47562
32802
22622
15602
2
3
4
5
TABLE C.
Present Value of 1 per Annum in n years. Redemption of
Capital being at 3 per cent., with Interest allowed to a Purchaser at
the following rates per cent. :
n
Years
30 per cent.
35 per cent.
40 per cent.
45 per cent.
n
Years
I
7692
7407
7143
6897
j
3
I '6038
1-4847
1-3821
1-2928
3
5
2-0477
1-8575
1-6997
I-5665
5
6
2-1997
1-9818
1-8031
I '6540
6
8
2-4245
2-1624
I-95I4
17779
8
10
2-5826
2-2871
2-0524
1-8614
10
12
2-6993
2-3783
2-1256
1-9214
12
15
2-8267
2-4767
2-2038
I -9850
15
20
2-9655
2-5825
2-2877
2-0525
20
22
3-0053
2-6127
2-3108
2-0715
22
25
3-054I
2-6495
2-3396
2-0946
25
27
3-0811
2-6698
2-3554
2-I072
27
30
3-II5I
2-6953
2-3752
2-I23I
30
32
3-I343
2-7097
2-3864
2-I320
32
35
3-1592
27282
2-3915
2-1434
35
37
3 -I 735
27389
2-4090
2*1500
37
40
3-1922
27528
2-4198
2-1586
40
42
3-2032
27610
2-4261
2-1636
42
45
3-2177
27702
2'4344
2-I7O2
45
47
3-2262
27781
2-4393
2-I74I
47
5
3-2377
2-7866
2-4458
2-1793
50
52
3-2445
27916
2-4497
2-1824
52
55
3-2536
2-7984
2-4549
2-1865
55
57
3-2591
2-8024
2-4580
2-1890
57
60
3-2666
2-8079
2-4622
2-I923
60
65
3-2771
2-^157
2-4682
2-I97I
65
70
3-2858
2-8222
2-4732
2-2010
70
75
3-2931
2-8275
2-4773
2-2043
75
80
3-2991
2-8320
2-4807
2-2070
80
90
33085
2-8388
2-4866
2'21 1 1
90
IOO
3-3i5i
2-8438
2-4898
2-2I4I
IOO
PURCHASING FOREIGN MINES.
161
TABLE I).
Present Value (or Years' Purchase) of ,\ per Annum in
n years, after t years' Deferrence. Redemption of Capital being at
3 per cent., with Interest allowed to a Purchaser at 30 per cent.
n
Years
Deferred
1 Year
Deferred
2 Years
Deferred
3 Years
Deferred
4 Years
Deferred
5 Years
n
Years
I
5917
4552
3501
2693
2072
I
3
1-2337
9490
7305
5615
4320
3
5
I-5752
I-2II7
9321
7205
5515
5
6
I-692I
1-3016
1-2374
7702
5924
6
8
I -8650
I-4346
1-1036
8489
6530
8
10
1-9866
1-5282
I-I755
9042
6956
10
12
2-0764
1-5972
1-2290
9451
7270
12
15
2-1744
1-6726
1-2866
9897
7613
15
20
2-28I2
17547
I-3500
1-0383
7987
20
22
23Il8
17783
1-3679
I-0522
8094
22
25
23493
I-8072
I-390I
I -0693
8226
25
27
2-370I
1-8231
I -4024
I -0788
8298
27
30
2-3962
1-8433
I-4I79
1-0907
8393
30
32
2-4IIO
1-8546
I -4266
I -0974
8442
32
35
2-4302
1-8694
I -4380
1-1061
8509
35
37
2-44I2
I-8778
1-4445
I-IITI
8547
37
40
2-4555
1-8889
I-4530
1-1177
8598
40
42
2-4639
1-8953
1-4580
1-1215
8627
42
45
2-4752
1-9040
i -4646
1-1266
8666
45
47
2-4817
1-9659
1-5122
1-1632
8689
47
So
2-4905
1-9666
1-5128
1-1637
8720
5o
52
2-4958
I -9670
1-5131
1-1639
8738
52
55
2-5028
1-9676
I-5I35
1-1643
8763
55
57
2-5070
1-9679
- I-5I38
1-1645
8778
57
60
2-5128
1-9684
1-5141
1-1647
8798
60
65
2-5214
1-9690
1-5146
1-1651
8825
65
70
2-5275
1-9695
1-5150
1-1654
8850
70
75
2-5332
I -9700
I-5I54
1-1657
8869
75
80
2-5378
I-9704
1-5157
1-1659
8885
80
90
2-5450
1-9709
1-5161
1-1662
8911
90
100
2-5501
I-97I3
1-5146
1-1665
8929
100
162
THE ENGINEER'S VALUING ASSISTANT.
TABLE D.
Present Value (or Years' Purchase) o 1 per Annum in
n years, after t years' Deferrence. Redemption of Capital being at
3 per cent., with Interest allowed to a Purchaser at 35 per cent.
n
Years
Deferred
1 Year
Deferred
2 Years
Deferred
3 Years
Deferred
4 Years
Deferred
5 Years
n
Years
I
556l
4064
3011
2230
1652
,
3
1-1146
8146
6034
4470
3311
3
5
1*3945
I-OI92
7550
5592
4142
5
6
i -4878
1-0874
8055
5967
4420
6
8
1-6234
1-1865
8789
6510
4822
8
10
17170
1-2549
9296
6886
5100
10
12
1-7855
1-3049
9666
7160
5504
12
15
1-8594
1-3589
I -0066
7457
5523
15
20
1-9388
1-4170
I -0496
7775
5759
20
22
1-9615
I-4336
1-0619
7886
5827
22
25
1-9891
1-4538
I -0769
7977
5909
25
27
2-0043
1-4610
I-0822
8017
5938
27
30
2-0235
1-4789
1-0955
8115
60 1 1
30
32
2-0343
I -4868
I-IOI3
8158
6043
32
35
2-0482
1-4969
1-1088
-8214
6084
35
37
2-0562
1-5028
1132
8246
6108
37
40
2-0666
1-5104
1188
8288
6139
40
42
2.0728
I-5I49
1222
8313
6157
42
45
2-0797
I'520O
1259
8340
6178
45
47
2-0856
I'5243
1291
8364
6196
47
50
2-0920
1-5290
1326
8390
6214
50
52
2-0958
I-53I7
1346
8407
6226
52
55
2-1009
1-5355
1374
8425
6241
55
57
2-1039
1-5376
I-I390
8436
6250
57
60
2-1080
1-5407
I-I4I2
8454
6262
60
65
2-1139
1-5449
I-I444
8477
6279
65
70
2-1187
1-5485
I-I47I
8497
6294
70
75
2-1227
1-5514
I-I492
8513
6306
75
80
2-1261
1*5539
I-I5II
8527
6316
80
90
2-1312
I-5576
I-I538
8547
6331
90
100
2-1350
1-5604
I-I558
8562
6342
100
PURCHASING FOREIGN MINES.
163
TABLE D.
Present Value (or Years' Purchase) of 1 per Annum in
n years, ai'ter t years' Deferrence. Redemption of Capital being at
3 per cent., with Interest allowed to a Purchaser at 40 per cent.
n
Deferred
Deferred
Deferred
Deferred
Deferred
n
Years
1 Year
2 Years
3 Years
4 Years
5 Years
Years
I
5102
3644
2603
1859
1328
j
3
9872
7052
5037
3598
2570
3
5
2141
8672
6194
4424
3160
5
6
2880
9200
6571
4694
'3353
6
8
'3939
9956
7III
5080
3628
8
10
4660
I -0470
7480
"5343
3818
10
12
5183
1-0845
7746
5533
3952
12
15
'5747
1244
8031
'5737
4098
15
20
1-6344
. -1672
8337
'5953
4254
20
22
1-6508
1790
8421
6015
4296
22
25
I -67 1 2
1937
8526
6090
'435
25
27
I-6824
20l6
8584
6131
'4379
27
30
1-6986
2119
8656
6183
4416
3
32
I -7046
2177
8697
6212
"4439
3 2
35
17082
2202
8715
6225
'4447
35
37
I-7207
2291
8779
6271
'4479
37
40
17284
2346
88l8
'6300
'4499
40
42
17329
2378
8841
6315
4511
42
45
17389
2421
8872
6337
4526
45
47
I -7424
2446
8890
6350
"4535
47
50
I -7470
1-2479
8913
6367
'4547
5
52
I-7498
1-2499
8927
6384
4555
52
55
17535
I-2525
8946
6390
4564
55
57
17557
I-254I
8958
6398
4570
57
60
17587
1-2562
8973
6409
4578
60
65
17630
1-2593
8995
6425
4589
65
70
17666
1-2619
9013
6438
4598
70
75
17695
1-2639
9028
6449
4606
75
80
I77I9
1-2656
9040
6458
4612
80
90
17757
I -2684
9060
6471
4622
90
100
17784
1-2703
9074
6481
4629
100
164
THE ENGINEERS VALUING ASSISTANT.
TABLE D.
Present Value (or Years' Purchase) of 1 per Annum in
n years, after t years' Deferrence. Redemption of Capital being at
3 per cent., with Interest allowed to a Purchaser at 45 per cent.
n
Years
Deferred
1 Year
Deferred
2 Years
Deferred
3 Years
Deferred
4 Years
Deferred
5 Years
n
Tears
I
'4757
3280
2262
1560
1084
I
3
8916
6149
4241
2925
2017
3
5
i -0803
"745 i
5138
3544
2444
5
6
1-1407
7867
5425
3742
2 5 8l
6
8
1-2261
8456
5832
4024
2774
8
10
1-2837
8853
6106
4211
2904
10
12
1-3251
9139
6303
'4347
2 99 8
12
15
1-3690
9441
6511
4490
3097
15
20
1-4155
9762
6733
4643
3202
20
22
1-4286
9852
6793
4686
3232
22
25
1-4445
9962
6871
4738
3268
25
27
1-4532
1-0022
6912
4767
3288
27
3
1-4642
I -0098
6964
4803
3312
30
32
1-4703
I-OI40
6993
4823
3326
32
35
i -4782
I-OI94
7031
4849
'3344
35
37
1-4827
I -0226
7052
4864
'3354
37
40
i -4887
I -0267
7081
4883
3368
40
42
1-4927
I-029I
7097
4894
3376
42
45
1-4967
I-0322
7119
4909
3386
45
47
1-4994
I -0340
7131
4918
3392
47
50
1-5030
I -0365
7149
4930
3400
50
52
1-5051
I -0380
7159
4937
3405
52
55
1-5079
1-0399
7172
4946
34ii
55
57
1-5096
I-04I6
7l8o
4952
3415
57
60
1-5119
I-0427
7191
4961
3420
60
65
1-5152
I -0450
7207
4970
3428
65
70
1-5172
I -0468
7220
'4979
'3434
70
75
1-5202
I -0484
7231
4987
'3439
75
80
1-5221
1-0497
7239
5003
'3443
80
90
1-5249
1-0516
7253
5008
3450
90
100
1-5270
I-053I
7263
5009
'3454
100
RECAPITULATION OF FORMULAE. 165
NOTATION.
?' = Interest on i (or any other
monetary unit, say on I )
for one year.
r = Kate of interest for redemp-
tion.
n = An integral number of years
R = Amount of i in one )
h = 1+ r
year, J
R n =5 Amount of i in n years j
(Compound interest), j = ( l
/Present value of i due n
years hence,
v n =1
If interest can be realised m
times in a year,
i * i
\ m
V n = Present value of a perpetuity j
of i, payable once in [= /r V ^ O r -^
j i
every tith year,
=
V * """*" ^ )
j v
D rt = Present value of a perpetuity j _ 4
of i deferred n years, J r
e = Base of Napierian Loga-
rithms = 27182818, and
its Logarithm = -43429448
e r _ Amount of i in one year,
9*
the rate being per mo-
ment.
e rn = Amount of i in n years at
that rate.
166
THE ENGINEER'S VALUING ASSISTANT.
Amount of i per annum in ) __ R n
n years, j r
Amount of 1 per annum if)
M,, =
interest can be converted
m times in a year at the
r
rate
m '
/ r \
(14--) -
. V mJ
T
m
s n =
Redemption Fund to be in- j
vested at the end of the f = -^~ , or -
R"i M n
year to realise i,
If interest can be realised m
times in a year,
m
I
p n = Present value of i per)
annum, calculated at one I -,or- v .
rate of interest, j
f Present value of i per
R"r
P =
t+n'
annum in n years, interest
on capital being at one
rate,/, and for redemption
another rate, r, per cent. ,
Present value, if interest can } _
be realised m times in a
At
year at the rate ,
m
Present value of i per
annum for a duration of
n years after t years,
allowing interest on capital
at one rate, r', and for re-
demption another rate, r,
per cent.,
or
'+*
R n -i
M
R n -i
i
-f/
or
v n .
RECAPITULATION OF FORMULAE.
167
I Annuity immediate which ) _
&i will purchase j
Annuity deferred which :6l)_
will purchase j
Present value of i per
annum on a single life,
allowing interest on capi-
tal at one rate, r', per cent,
and to redeem the capital
by an assurance on the life
[^ at theoffice rate,r, percent.,
r
(i v)
i.
TABLE I.
The sum to which 1 will amount in n years up to
one hundred at the rates of J, f, i, i, ij, if, 2, 2^ r 2j,
2f, 3> 3i 4? 4<b 5? 5i> 6, 7, 8, 9, 10, n, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, and 25 per
Calculated to 10 places of decimals for each percentage
to 9 per cm. ; to 6 places to 15 per cent, owcZ to 5 places
to 25 per cent.
a
TABLE 1.
Amount of 1 in n years at the following rates per cent.
iii
Years
i per cent.
Years
i per cent.
Years
J per cent.
Years
| per cent.
I
1-005
51
1*2896419440
I
1-0075
51
1-4638541068
2
I-OI0025
52-
1-2960901537
2
1-01505625
52
1*4748330126
3
1-015075125
53
1*3025706045
3
1*0226691719
53
1*4858942602
4
1*0201505006
54
1*3090834575
4
1*0303391907
54
1-4970384672
5
1-0252512531
55
1-3156288748
5
1*0380667346
55
1*5082662557
6
1-0303775094
56
1*3222070192
6
1*0458522351
56
1*5195782526
7
I-0355293969
57
1*3288180543
7
1*0536961269
57
I '5309750895
8
I -0407070439
58
1*3354621446
8
1*0615988478
58
1*5424574027
9
1-0459105791
59
1*3421394553
9
0695608392
59
1*5540258332
10
1-0511401320
60
1-3488501526
10
0775825455
60
1*5656810269
ii
1-0563958327
61
I'3555944033
ii
0856644146
61
1*5774236346
12
1-0616778119
62
1*3623723753
12
0938068977
62
1*5892543119
13
I -0669862009
63
1*3691842372
13
1020104494
63
1-6011737192
14
1-0723211319
64
1-3760301584
14
1102755278
64
1*6131825221
15
1-0776827376
65
1-3829103092
15
1186025942
65
1*6252813911
16
1-0830711513
66
1*3898248607
16
1269921137
66
1*6374710015
i?
I -0884865070
67
1-396773985
17
1354445545
67
1*6497520340
18
I -0939289396
68
1-4037578550
18
1439603887
68
1-6621251743
J 9
1-0993985843
69
1-4107766442
19
1525400916
69
1*6745911131
20
1-1048955772
70
1*4178305275
20
1611841423
70
1*6871505464
21
1-1104200551
71
1*4249196801
21
1698930234
71
1-6998041755
22
1-1159721553
72
1*4320442785
22
1786672210
72
17125527068
23
1-1215520161
73
1*4392044999
23
1875072252
73
17253968521
24
1-1271597762
74
1*4464005224
24
1964135294
74
17383373285
25
1-1327955751
75
1*4536325250
25
2053866309
75
17513748585
26
1-1384595530
76
i -4609006876
26
2144270306
76
1*7645101699
27
1-1441518507
77
1*4682051911
27
2235352333
77
17777439962
28
1-1498726100
78
1*4755462170
28
2327117476
78
1*7910770762
29
1-1556219730
79
i -482923948 1
29
2419570857
79
1-8045101542
30
1-1614000829
80
1*4903385678
30
2512717638
80
1-8180439804
31
1-1672070833
81
1-4977902607
31
2606563021
81
1-8316793102
32
1-1730431187
82
1*5052792120
32
2701112243
82
1-8454169051
33
1-1789083343
83
1-5128056080
33
2796370585
83
I-85925753I9
34
1-1848028760
84
1*5203696361
34
2892343364
84
1-8732019633
35
1*1907268904
85
1*5279714843
35
2989035940
85
1*8872509781
36
1-1966805248
86
1*5356113417
36
3086453709
86
1-9014053604
37
1*2026639275
87
1*5432893984
37
3184602112
87
1-9156659006
38
1-2086772471
88
1*5510058454
38
1-3283486628
88
I-9300333949
39
1-2147206333
89
1*5587608746
39
3383112778
89
1-9445086453
40
1-2207942365
90
1*5665546790
4O
3483486123
9O
1*9590924602
4i
1-2268982077
91
1*5743874524
41
1*3584612269
91
1*9937856536
42
1-2330326987
92
1*5822593896
42
1*3686496861
92
1-9885890460
43
1-2391978622
93
1-5901706866
43
1-3789145588
93
2-0035034639
44
45
1-2453938515
1-2516208208
94
95
1-5981215400
1-6061121477
44
45
1*3892564180
1-3996758411
94
95
2-0185297398
2-0336687129
46
1-2578789249
96
1-6141427085
46
1*4101734099
96
2-0489212282
47
1-2641683195
97
1-6222134220
47
1*4207497105
97
2-0642881375
48
1-2704891611
98
1-6303244891
48
1*4314053333
98
2*0797702985
49
1-2768416069
99
1-6384761116
49
1*4421408733
99
2-0953685757
50
1-2832258149
100
1-6466684921
50
1*4529569299
100
2*1110838400
THE ENGINEEE'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
1 per cent.
Years
1 per cent.
Years
1J per cent.
Years
1 J per csnt.
I
I '01
51
1-6610781401
I
I-OI25
51
1*8842851532
2
I '020 1
52
1-6776889215
2
1-02515625
52
1-9078387177
3
I '03030 1
53
1-6944658107
3
1-0379707031
53
1-9316867016
4
1-0406040!
54
1-7114104688
4
1-0509453369
54
1-9558327854
5
I-05IOI0050I
55
17285245735
5
1-0640821536
55
1-9802806952
6
1-0615201506
56
1-7458098192
6
I "077383 1 805
56
2-0050342039
7
I-072I35332I
57
17632679174
7
I -0908504703
57
2-0300971315
8
1-0828567056
58
17809005966
8
1-1044861012
58
2-0554733456
9
1-0936852727
59
1-7987096025
9
1-1182921774
59
2-0811667624
10
I-I04622I254
60
1-8166966986
10
1-1322708297
60
2-1071813470
ii
1-1156683467
61
1-8348636655
ii
1-1464242150
61
2-1335211138
12
1-1268250301
62
1-8532123022
12
1-1607545177
62
2-1601901277
13
1-1380932804
63
1-8717444252
13
1-1752639492
63
2-1871925043
H
I-I494742I32
64
1-8904618695
14
1-1899547486
64
2-2145324106
15
1-1609689554
65
1-9093664882
15
1-2048291829
65
2-2422140657
16
1-1725786449
66
1-9284601531
16
1-2198895477
66
2-2702417416
17
1-1843044314
67
1-9477447546
17
1-2351381670
67
2-2986197633
18
1-1961474757
68
1-9672222021
18
1-2505773941
68
2-3273525104
19
1-2081089504
69
I -9868944242
19
1-2662096116
69
2-3564444168
20
I-220I900399
70
2-0067633684
20
1-2820372317
70
2-3858999720
21
1.2323919403
71
2-0268310021
21
1-2980626971
71
2-4157237216
22
1-2447158597
72
2*0470993121
22
1-3142884808
72
2-4459202681
23
1-2571630183
73
2-0675703052
23
1-3307170868
73
2-4764942715
24
1-2697346485
74
2-0882460083
24
1-3473510504
74
2-5074504499
25
1-2824319950
75
2-1091284684
25
1-3641929385
75
2-5387935805
26
1.2952563150
76
2-1302197530
26
1-3812453503
76
2-5705285003
27
1-3082088781
77
2-1515219506
27
1-3985109172
77
2-6026601065
28
1-3212909669
78
2-1730371701
28
1-4159923036
78
2-635I933578
29
1-3345038766
79
2-1947675418
29
1-4336922074
79
2-6681332748
3O
1-3478489153
80
2-2167152172
3O
1-4516133600
80
2-7014849408
31
1-3613274045
81
2-2388823694
31
1-4697585270
81
27352535025
32
1-3749406785
82
2-2612711931
32
1-4881305086
82
27694441713
33
1-3886900853
83
2-2838839050
33
1-5067321400
83
2-8040622234
34
1-4025769862
84
2-3067227440
34
1-5255662917
84
2-8391130012
35
1-4166027560
85
2-3297899715
35
1-5446358703
85
2-8746019137
36
1-4307687836
86
2-3530878712
36
1-5639438187
86
2-9105344377
37
1-4450764714
87
2-3766187499
37
I-583493II65
87
2-9469161181
38
I-459527236I
88
2-4003849374
38
1-6032867804
88
2-9837525696
39
1-4741225085
89
2-4243887868
39
1-6233278652
89
3-0210494767
40
1-4888637336
90
2-4486326746
40
1-6436194635
90
3-0588125952
41
I-5037523709
91
2-4731190014
41
1-6641647068
9 1
3-0970477526
42
1-5187898946
92
2-4978501914
42
1-6849667656
92
3-1357608495
43
I-5339777936
93
2-5228286933
43
1-7060288502
93
3-1749578602
44
I-5493I757I5
94
2-5480569803
44
17273542108
94
3-2146448334
45
1-5648107472
95
2'573537550I
45
17489461384
95
3-2548278938
46
1-5804588547
96
2-5992729256
46
1-7708079652
96
3-2955132425
47
1-5962634432
97
2-6252656548
47
1-7929430647
97
3-3367071580
48
1-6122260777
98
2-6515183114
48
1-8153548531
98
33784159975
49
1-6283483385
99
2-6780334945
1 49
1-8380467887
99
3-4206461975
50
1-6446318218 100
2-7048138294
SO
1-8610223736
100
3-4634042749
TABLE I.
Amount of 1 in n years at the following rates per cent.
Years
1J per cent.
STears
1 J per cent.
Years
If per cent.
Years
If per cent.
I
i 'oi 5
51
2-1368210569
I
I-OI75
51
2-4224527382
2
1-030225
52
2-1688733728
2
1-03530625
52
2-4648456611
3
1-045678375
53
2-2014064734
3
1-0534241094
53
2-5079804602
4
1-0613635506
54
2-2344275705
4
1-0718590313
54
2-5518701182
5
1-0772840039
55
2-2679439840
5
1*0906165643
55
2-5965278453
6
1-0934432639
56
2-3019631438
6
1-1097023542
56
2-6419670826
7
1-1098449129
57
2-3364925909
7
1-1291221454
57
2-6882015065
8
1-1264925866
58
2-37I5399798
8
1-1488817830
58
2-7352450329
9
1-1433899754
59
2-4071130795
9
1-1689872142
59
27831118210
10
i '1605408250
60
2-4432197757
10
1-1894444904
60
2-8318162778
n
1-1779489374
61
2-4798680723
ii
1-2102597690
61
2-8813730627
12
ri956i8i7i5
62
2-5170660934
12
1-2314393149
62
2-9317970913
13
1-2135524440
63
2-5548220848
13
1-2529895030
63
2-9831035404
14
1-2317557307
64
2-5931444161
14
1-2749168193
64
3-0353078523
15
1-2502320667
65
2-6320415823
15
1-2972278636
65
3-0884257398
16
1-2689855477
66
2-6715222061
16
1-3199293512
66
3-1424731902
17
1-2880203309
67
27115950391
17
1-3430281149
67
3-1974664710
18
1-3073406358
68
2-7522689647
18
1-3665311069
68
3-2534221343
19
1-3269507454
69
27935529992
19
1-3904454012
69
3-3103570216
20
1-3468550065
70
2-8354562942
20
1-4147781958
70
3-3682882695
21
1-3670578316
71
2-8779881386
21
1-4395368142
71
3-4272333142
22
1-3875636991
72
2-9211579607
22
1-4647287084
72
3-4872098972
23
1-4083771546
73
2-964975330I
23
1-4903614608
73
3-5482360704
24
1-4295028119
74
3-0094499600
24
1-5164427864
74
3-6103302017
25
1-4509453541
75
3-0545917094
25
1-5429805352
75
3-6735109802
26
1-4727095344
76
3-1004105851
26
1-5699826945
76
37377974223
27
1-4948001774
77
3-1469167439
27
I-59745739I7
77
3-8032088772
28
1-5172221801
78
3-1941204950
28
1-6254128960
78
3-8697650326
29
1-5399805128
79
3-2420323025
29
1-6538576217
79
3-9374859206
30
1-5630802205
80
3-2906627870
3O
1-6828001301
80
4-0063919243
31
1-5865264238
81
3-3400227288
31
1-7122491324
81
4-0765037829
32
1-6103243202
82
3-3901230697
32
17422134922
82
4-1478425991
33
1-6344791850
83
3-4409749158
33
17727022283
83
4-2204298446
34
1-6589963727
84
3-4925895395
34
1-8037245173
84
4-2942873369
35
1-6838813183
85
3-5449783826
35
1-8352896963
85
4-3694373958
36
1-7091395381
86
3-5981530583
36
1-8674072660
86
4-4459025503
37
1-7347766312
87
3-6521253542
37
I -9000868932
87
4-5237058449
38
i -7607982806
88
3-7069072345
38
I-9333384I38
88
4-6028706972
39
1-7872102548
89
3-7625108430
39
1-9671718361
89
4-6834209344
to
1-8140184087
9O
3-8189485057
40
2-0015973432
90
4-7653808007
41
1-8412286848
91
3-8762327333
4i
2-0366252967
91
4-8487749647
42
1-8688471151
9 2
3*9343762243
42
2*0722662394
92
4*9336285266
43
1-8968798218
93
3-99339I8676
43
2-1085308986
93
5-0199670258
44
1-9253330191
94
4-0532927457
44
2-1454301893
94
5-1078164488
45
1-9542130144
95
4-1140921368
45
2-1829752176
95
5-1972032366
46
1-9835262096
96
4-1758035189
46
2-2211772839
96
5-2881542933
47
2-0132791028 97
4-2384405717
47
2-2600478864
97
5*3806969934
48
2-0434782893 98
.4-3020171803
48
2-2995987244
98
5-4748591908
49 j 2-0741304637 99
4-3665474380
49
2-3398417021
99
5-5706692266
so 2-1052424206 100
4-4320456495
50
2-3807889319
100 5*6681559381
THE ENGINEEB'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
2 per cent.
Years
2 per cent.
Years
21 per cent.
Years
2i per cent.
I
I'02
51
2-7454197897
I
I-0225
51
3-1104924437
2
I -0404
52
2-8003281855
2
1-04550625
52
3-1804785237
3
I -06 1 208
53
2-8563347492
3
1*0690301406
53
3-2520392904
4
1-08243216
54
2-9134614441
4
1-0930833188
54
3-3252101745
5
1-1040808032
55
2-9717306730
5
1-1176776935
55
3-4000274034
6
1-1261624193
56
3-0311652865
6
1-1428254416
56
3-4765280200
7
1-1486856676
57
3-0917885922
7
1-1685390140
57
3-5547499004
8
1-1716593810
58
3-1536243641
8
1-1948311418
58
3-6347317732
' 9
1-1950925686
59
3-2166968513
9
1-2217148425
59
3-7165132381
10
1-2189944200
60
3-2810307884
10
1-2492034265
60
3-8001347859
ii
1-2433743084
61
3-3466514041
ii
1-2773105036
61
3-8856378186
12
1-2682417946
62
3-4135844322
12
1-3060499899
62
3-9730646695
13
1-2936066305
63
3-4818561209
13
I'335436lI47
63
4-0624586246
H
1-3194787631
64
3-5514932433
14
1-3654834272
.64
4-1538639437
15
I-3458683383
65
3-6225231081
15
I -3962068044
65
4-2473258824
16
1-3727857051
66
3-6949735703
16
1-4276214575
66
4-3428907148
17
1-4002414192
67
37688730417
17
1-4597429402
67
4-4406057558
18
1-4282462476
68
3-8442505025
18
1-4925871564
68
4-5405193853
19
1-4568111725
69
3-9211355126
19
1-5261703674
69
4-6426810715
20
I'4859473960
70
3-9995582229
20
1-5605092007
7O
47471413956
21
1-5156663439
71
4-0795493873
21
1-5956206577
71
4-8539520770
22
1 -545979 6 708
72
4-1611403751
22
1-6315221225
72
4-9631659988
23
1-5768992642
73
4-2443631826
23
1-6682313703
73
5-0748372337
24
1-6084372495
74
4-3292504462
24
17057665761
74
5-1890210715
25
1-6406059945
75
4-4158354551
25
1-7441463240
75
5-3057740456
26
1-6734181144
76
4-5041521642
26
17833896163
76
5-4251539616
27
1-7068864766
77
4-5942352075
27
1-8235158827
77
5-5472199258
28
I74I0242062
78
4-6861199117
28
1-864544990!
78
56720323741
29
17758446903
79
47798423099
29
1-9064972523
79
5-7996531025
30
1-8113615841
80
4-875439I56I
3O
1-9493934405
80
5-9301452973
31
1-8475888158
81
4-9729479392
31
I-9932547929
81
6-0635735665
32
1-8845405921
82
5-0724068980
32
2*0381030258
82
6-2000039717
33
1-9222314039
83
5-I738550360
33
2-0839603439
83
6-3395040611
34
1-9606760320
84
5-2773321367
34
2-1308494516
84
6-4821429025
35
1-9998895527
85
5-3828787794
35
2-1787935642
85
6-6279911178
36
2-0398873437
86
5-4905363550
36
2-2278164194
86
67771209179
37
2-0806850906
87
5-6003470821
37
2-2779422889
87
6-9296061386
38
2-1222987924
88
57123540237
38
2-3291959904
oo
OO
7-0855222767
39
2-1647447683
89
5-8266011042
39
2-3816029002
8 9
7*2449465279
40
2-2080396636
9O
5 '943 i 33 1 263
4O
2-4351889654
90
7-4079578248
41
2-2522004569
91
6-0619957888
41
2-4899807171
91
7-5746368759
42
2-2972444660
92
6-1832357046
42
2-5460052833
92
7-7450662056
43
2343I893553
93
6-3069004187
43
2-6032904022
93
7-9193301952
44
2-3900531425
94
6-4330384271
44
2-6618644362
94
8-0975151246
45
2-4378542053
95
6-5616991956
45
27217563860
95
8-2797092149
46
2-4866112894
96
6-6929331795
46
2-7829959047
96
8-4660026722
47
2'5363435I52
97
6-8267918431
47
2-8456133126
97
8-6564877324
48
2-5870703855
98
6-9633276800
48
2-9096396121
98
8-8512587063
49
2-6388117932
99
7-1025942336
49
2-9751065934
99
9-0504120272
5O
2-6915880291 loo
7-2446461183
5O 3-0420463997 100: 9-2540462979
TABLE I.
Amount of 1 in n years at the following rates per cent.
vii
Years
2| per cent.
STears
2| per cent.
Years
2| per cent.
fears
2f per cent.
I
I '02 5
51
3*5230364377
I
1-0275
51
3-9890856203
2
1*050625
52
3-6111123486
2
1-05575625
52
4-0987854749
3
I -076890625
53
37013901574
3
I*o847895469
53
4-2115020754
4
I '1038 1 28906
54
3-7939249113
4
1*1146212594
54
4-3273183825
5
1-1314082129
55
3-8887730341
5
1*1452733440
55
4-4463196380
6
1-1596934182
56
3-9859923599
6
1*1767683610
56
4-5685934281
7
1-1886857537
57
4-0856421689
7
1*2091294909
57
4-6942297474
8
i '2 1 8402897 5
58
4*1877832231
8
1*2423805519
58
4-8233210654
9
1*2488629699
59
4-2924778037
9
1*2765460171
59
4-9559623947
10
1*2800845442
60
4-3997897488
10
1*3116510326
60
5-0922513606
ii
1*3120866578
61
4-5097844925
ii
1*3477214360
61
5*2322882730
12
1-3448888242
62
4-6225291048
12
I-3847837755
62
5*3761762005
13
1-3785110449
63
4-7380923325
13
1*4228653293
63
5*5240210460
H
1*4129738210
64
4-8565446408
14
1*4619941259
64
5-6759316248
15
1*4482981665
65
4-9779582568
15
1*5021989643
65
5-8320197444
16
1*4845056207
66
5-1024072132
16
1*5435094358
66
5-9924002874
17
1*5216182612
67
5-2299673936
17
I-5859559453
67
6*1571912953
18
1-5596587177
68
5-3607165784
18
1-6295697338
68
6*3265140559
19
1-5986501856
69
5-4947344929
19
1-6743829015
69
6*5004931925
20
1*6386164403
7O
5-6321028552
2O
1*7204284313
70
6-6792567553
21
1-6795818513
71
5-7729054266
21
1*7677402131
71
6*8629363160
22
1-7215713976
72
5-9172280622
22
1*8163530690
72
7-0516670647
23
1-7646106825
73
6-0651587638
23
1*8663027784
73
7-2455879090
24
1-8087259496
74
6-2167877329
24
1-9176261048
74
7*4448415765
25
1*8539440983
75
6-3722074262
25
1*9703608227
75
7*6495747199
26
1-9002927008
76
6-5315126118
26
2-0245457453
76
7-8599380247
27
1-9478000183
77
6-6948004271
27
2-0802207533
77
8-0760863203
28
1-9964950188
78
6-8621704378
28
2*1374268240
78
8-2981786942
29
2-0464073942
79
7*0332246988
29
2*1962060617
79
8-5263786082
30
2-0975675791
80
7*2095678162
3O
2*2566017284
80
8-7608540200
31
2-1500067686
81
7-3898070116
31
2*3186582759
81
9-0017775055
32
2-2037569378
82
7-5745521869
32
2-3824213785
82
9*2493263869
33
2*2588508612
83
7-7639159916
33
2'4479379664
83
9-5036828626
34
2-3153221327
84
7-9580138914
34
2*5152562605
84
9-7650341413
. 35
2-3732051861
85
8-1569642387
35
2-5844258077
85
10-0335725802
36
2-4325353157
86
8-3608883446
36
2-6554975174
86
10*3094958261
37
2-4933486986
87
8-5699105533
37
2*7285236991
87
10-5930069613
38
2-5556824161
00
OO
87841583171
38
2*8035581008
88
10-8843146528
39
2-6195744765
89
9-0037622750
39
2*8806559486
89
11-1836333057
40
2-6850638384
90
9*2288563319
10
2-9598739872
90
11-4911832216
4i
2-7521904343
91
9'4595777402
4i
3-0412705218
91
11-8071907602
42
2-8209951952
92
9-6960671837
42
3-1249054612
92
12*1318885061
43
2*8915200751
93
9-9384688633
43
3*2108403614
93
12*4655154401
44
2-9638080770
94
10-1869305849
44
3*2991384713
94
12*8083171147
45
3-0379032789
95
10-4416038495
45
3-3898647793
95
13-1605458353
46
3-1138508609
96
10-7026439457
46
3-4830860607
96
13-5224608458
47
3*1916971324
97
10-9702100444
47
3-5788709274
97
13-8943285190
48
3-2714895607
98
11-2444652955
48
3*6772898779
98
14-2764225533
49
3-3532767997
99
11*5255769279
49
3-7784153495
99
14-6690241735
50
3-4371087197 ,100
11-8137163511
50
3-8823217716
1OQ
15-0724223383
viii THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
3 per cent.
Years
3 per cent.
Years
3 J per cent.
Years
3 J per cent.
I
1-03
51
4-5154231993
!
1-035
51
57803992956
2
I -0609
52
4-6508858952
2
1-071225
52
5-9827132709
3
1-092727
53
47904124721
3
1-108717875
53
6-1921082354
4
1-12550881
54
4-9341248463
4
1-1475230006
54
6-4088320237
5
1-1592740743
55
5-0821485917
5
1-1876863056
55
6-6331411445
6
1-1940522965
56
5-2346130494
6
1-2292553263
56
6-8653010846.
7
-1-2298738654
57
5-3916514409
7
1-2722792628
57
7-1055866225
8
1-2667700814
58
5-5534009841
8
1-3168090369
58
7-3542821543
9
* '304773 1 838
59
5-7200030136
9
1-3628973533
59
7-6116820297
10
-1-3439163793
60
5-8916031040
10
1-4105987606
60
7-8780909008
ii
1-3842338707
61
6-0683511972
ii
1-4599697172
61
8-1538240823
12
1-4257608868
62
6-2504017331
12
1-5110686573
62
8-4392079252
13
1-4685337135
63
6'4379 I 3785i
13
i '5639560604
63
87345802026
H
-1-5125897249
64
6-6310511986
14
1-6186945225
64
9-0402905096
15
1-5579674166
65
6-8299827346
15
1-6753488308
65
9-3567006775
16
1-6047064391
66
7-0348822166
16
17339860398
66
9-6841852012
17
1-6528476323
67
7-2459286831
17
1-7946755512
67
10-0231316832
18
1-7024330612
68
7-4633065436
18
1-8574891955
68
IO-37394I292I
19
17535060531
69
7-6872057399
19
1-9225013174
69
10-7370292374
20
1-8061112347
70
7-9178219121
20
1-9897888635
70
11-1128252607
21
1-8602945717
71
8-1553565695
21
2-0594314737
71
11-5017741448
22
1-9161034089
72
8-4000172666-
22
2-1315115753
72
11-9043362399
23
I'9735865III
73
8-6520177846
23
2-2061144804
73
12-3209880083
24
2-0327941065
74
8-9115783181
24
2-2833284872
74
127522225886
2$
2-0937779297
75
9-1789256676
25
2-3632449843
75
I3-I985503792
26
2-1565912675
76
9-4542934377
26
2-4459585587
76
13-6604996424
27
2-2212890056
77
9-7379222408
27
2-5315671083
77
14-1386171299
28
2-2879276757
78
10-0300599080
28
2-6201719571
78
14-6334687295
29
2-3565655060
79
10-3309617053
29
2-7118779756
79
15-1456401350
30
2-4272624712
80
10-6408905564
3O
2-8067937047
80
I5-6757375397
31
2-5000803453
81
10-9601172731
31
2-9050314844
81
16-2243883536
32
2-5750827557
82
11-2889207913
32
3-0067075863
82
16-7922419460
33
2-6523352384
83
11-6275884151
33
3-1119423518
83
17-3799704141
34
27319052955
84
11-9764160675
34
3-2208603342
84
17-9882693786
35
2-8138624544
85
12-3357085495
35
3'333594459
85
18-6178588068
36
2-8982783280
86
12-7057798060
36
3-4502661115
86
19-2694838651
37
2-9852266778
87
13-0869532002
37
3-5710254254
87
1 9*9439 158004
38
3-0747834782
OQ
OO
i3-47956i79 6 2
38
3-6960113152
88
20-6419528534
39
3-1670269825
8 9
13*8839486501
39
3-8253717113
89
21-3644212032
40
3-2620377920
90
14-3004671096
40
3-9592597212
90
22-1121759453
41
3-3598989258
91
14-7294811229
41
4-0978338114
91
22-886I02I034
42
3-4606958935
92
15-1713655566
42
4-2412579948
92
23-6871156771
43
3-5645167703
93
15-6265065233
43
4-3897020246
93
24-5161647258
44
3-6714522734
94
16-0953017190
44
4-54334I5955
94
25-3742304912
45
3-7815958417
95
16-5781607705
45
4-7023585513
95
26-2623285583
46
4-8950437169
96
17-0755055936
46
4-8669411006
96
27-1815100579
47
4-0118950284
97
17-5877707615
47
5-0372840392
97
28-1328629099
48
4-1322518793
98
18-1154038843
48
5-2135889805
98
29-1175131118
49
4-2562194356
99
18-6588660008
49
5-3960645949
99
30-1366260707
50
4-3839060187
100
19-2186319809
50
5-5849268557
100
31-1914079831
TABLE I.
Amount of 1 in n years at the following rates per cent.
Years
4 per cent.
Years
4 per cent.
Years
4| per cent.
Years
4 1 per cent.
I
1-04
51
7 -390950680 1
I
1-045
51
9-439I049048
2
I -0816
52-
7-6865887073
2
1-092025
52
9-8638646255
3
1-124864
53
7-9940522556
3
1-141166125
53
10-3077385337
4
1-16985856
54
8-3138143454
4
1-1925186006
54
107715867677
5
1*2166529024
55
8-6463669197
5
1-2461819377
55
11-2563081722
6
1-2653190185
56
8-9922215965
6
1-3022601248
56
117628420400
7
I-3I593I7792
57
9-3519104603
7
1-3608618305
57
12-2921699318
8
1-3685690504
58
97259868787
8
1-4221006128
58
12-8453175787
9
1-4233118124
59
10-1150263539
9
1-4860951404
59
13-4233568698
10
1-4802442849
60
10-5196274080
10
1-5529694217
60
14-0274079289
ii
I'5394540563
61
10-9404125044
ii
1-6228530457
61
14-6586412857
12
1-6010322186
62
1 1 -3780290045
12
1-6958814328
62
15-3182801435
13
1-6650735073
63
11-8331501647
13
17721960972
63
16*0076027500
H
17316764476
64
12-3064761713
H
1-8519449216
64
16-7279448738
15
1-8009435055
65
127987352182
15
1-9352824431
65
17-4807023931
16
1-8729812457
66
13-3106846269
16
2-0223701530
66
18-2673340008
17
1-9479004956
67
13-8431120120
17
2-1133768099
67
19-0893640308
18
2-0258165154
68
14-3968364925
18
2*2084787664
68
19-9483854122
19
2*1068491760
69
14-9727099521
19
2-3078603108
69
20-8460627557
20
2-1911231430
70
15-5716183502
20
2-4117140248
70
217841355797
21
2-2787680688
71
16-1944830842
21
2*5202411560
71
227644216808
22
2-3699187915
72
16-8422624076
22
2*6336520080
72
237888206565
23
2-4647155432
73
17-5159529039
23
27521663483
73
24-8593175860
24
2-5633041649
74
18-2165910201
24
2-8760138340
74
25-9779868774
25
2-6658363315
75
18-9452546609
25
3-0054344565
75
27-1469962869
26
2-7724697847
76
19-7030648473
26
3-1406790071
76
28-3686111198
27
2-8833685761
77
20-4911874412
27
3-2820095624
77
29-6451986202
28
2-9987033192
78
21-3108349389
28
3-4296999927
78
30-9792325581
29
3-1186514519
79
22-1632683364
29
3-5840364924
79
32-3732980232
30
3'2433975IOO
80
23-0497990699
30
37453181345
80
33-8300964342
31
3'373 I 334io4
81
23-9717910327
31
3-9138574506
81
35-3524507738
32
3-5080587468
82
24-9306626740
32
4-0899810359
82
36-9433110586
33
3-6483810967
83
25-9278891809
33
4-2740301825
83
38-6057600562
34
3-7943163406
84
26-9650047482
34
4-4663615407
84
40-3430192587
35
3-9460889942
85
28-0436049381
35
4-6673478100
85
42-1584551254
36
4-1039325540
86
29-1653491356
36
4-8773784615
86
44-0555856060
37
4-2680898561
87
30-3319631010
37
5-0968604922
87
46-0380869583
38
4-4388134504
88
31-5452416251
38
5-3262192144
88
48-1098008714
39
4-6163659884
89
32-8070512901
39
5-5658990790
89
50-2747419106
40
4-8010206279
90
34-II933334I7
4O
5-8163645376
90
52-5371052966
41
4-9930614531
9 1
35-4841066753
41
6-0781009418
91
54-9012750350
42
5-1927839112
92
36-9034709424
42
6-3516154842
92
57-3718324115
43
5-4004952676
93
38-3796097801
43
6-6374381810
93
59-9535648701
44
5-6165150783
94
39-9147941713
44
6-9361228991
94
62-6514752892
45
5-8411756815
95
41-5113859381
45
7-2482484296
95
65-4707916772
46
6-0748227087
96
43-1718413756
46
7-5744196089
96
68-4169773027
47
6-3178156171
97
44-8987150307
47
7-9152684913
97
71-4957412813
48
6-5705282417
98
46*6946636319
48
8-2714555734
98
74-7130496390
49
6-83334937I4
99
48-5624501772
49
8*6436710742
99
78-0751368727
50
7-1066833463
100 50-5049481842
50
9-0326362725
100
81-5885180320
THE ENGINEER'S VALUING- ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
5 per cent.
Years
5 per cent.
Years
5i per cent.
Years
5| per cent.
I
I'OS
51
12-0407697750
I
1-055
51
15-3417690708
2
1-1025
52
12-6428082638
2
1-113025
52
16-1855663697
3
1-157625
53
13-2749486769
3
1-174241375
53
17-0757725200
4
1-21550625
54
13-9386961108
4
1-2388246506
54
18-0149400086
5
1-2762815625
55
14-6356309164
5
I -3069600064
55
19-0057617091
6
1-3400956406
56
15-3674124622
6
1-3788428068
56
20-0510786031
7
1*4071004227
57
16-1357830853
7
1-4546791611
57
21-1538879262
8
1-4774554438
58
16-9425722396
8
1-5346865150
58
22-3173517622
9
1-5513282160
59
177897008516
9
1-6190942733
59
23-5448061091
10
1-6288946268
60
18-6791858941
10
17081444584
60
24-8397704451
ii
I7io339358i
61
19-6131451888
ii
I '8020924036
61
26-2059578196
12
1-7958563260
62
20-5938024483
12
1-9012074858
62
27-6472854996
13
1-8856491423
63
2r62.34925707
13
2-0057738975
63
29-1678862021
14
1-9799315994
64
22703.6671992
H
2-1160914618
64
307721199432
15
2-0789281794
65
23-8399005592
15
2-2324764922
65
32-4645865401
16
2-1828745884
66
25-0318955872
16
2-3552626993
66
34-2501387998
17
2-2920183178
67
26-2834903665
17
2-4848021478
67
36-1338964338
18
2-4066192337
68
27-5976648848
18
2-6214662659
68
38-1212607377
*9
2-5269501954
69
28-9775481291
19
27656469105
69
40-2179300782
20
2-6532977051
70
30-4264255355
20
2-9177574906
70
42-4299162325
21
27859625904
71
31-9477468123
21
3-0782341526
71
4476356l6253
22
2-9252607199
72
33-545I34I529
22
3-2475370310
72
47-2255575147
23
3-0715237559
73
35-2223908606
23
3-4261515677
73
49-8229631780
24
3-2250999437
74
36-9835104036
24
3-6145899039
74
52-5632261528
25
3*3863549409
75
38-8326859238
25
3-8133923486
75
55-4542035912
26
3-5556726879
76
40-7743202199
26
4-0231289278
76
58-5041847888
27
37334563223
77
42*8130362310
27
4-2444010188
77
617219149521
28
3-9201291385
78
44-9536880425
28
4-4778430749
78
65-1166202745
29
4-1161355954
79
47-2013724446
29
47241244440
79
68-6980343896
30
4-3219423752
80
49-5614410669
30
4-9839512884
80
72-4764262810
31
4-5380394939
81
52-0395131202
31
5-2580686093
81
76-4626297265
32
4-7649414686
82
54-6414887762
32
5-5472623828
82
80-6680743614
33
5-0031885420
83
57-3735632I50
33
5-8523618138
83
85-1048184513
34
5-253347969I
84
60-2422413758
34
6-1742417136
84
897855834661
35
5-5160153676
85
63-2543534446
35
6-5138250078
85
94-7237905568
36
37
5-7918161360
6-0814069428
86
87
66-4170711168
69-7379246726
36
37
6-8720853833
7-2500500793
86
87
99-9315990374
105-42^469845
38
6-3854772899
88
73-2248209063
38
7-6488028337
88
111-2285940686
39
6-7047511544
89
76-8860619516
39
8-0694869895
89
117-3461667424
40
7-0399887121
90
80-7303650492
40
8-5133087740
90
123-8002059132
41
7-3919881477
91
847668833016
41
8-9815407565
9 1
130-6092172384
42
7-7615875551
92
89-0052274667
42
9'4755254982
92
1377927241865
43
8-1496669329
93
93-4554888400
43
9-9966794005
93
145-3713240168
44
8-5571502795
94
98-1282632820
44
10-5464967676
94
153-3667469377
45
8-9850077935
95
103-0346764461
45
11-1265540898
95
161-8019179138
46
9-43*2581832
96.
108-1864102685
46
117385145647
96
1707010233991
47
9-9059710923
97
H3'59573078l9
47
12-3841328658
97
180-0895796860
48
10-4012696469
98
119-2755173210
48
13-0662601734
98
189-9945065687
49
10-9213331293
99
125-2392931870
49
13-7838494830
99
200-4442044300
50
11-4673997858
100
I3I-50I2578464J50 | 14-5419612045
100
211-4686356737
TABLE I.
Amount of 1 in n years at the following rates per cent.
XI
Years
6 per cent.
Years
6 per cent.
Years
. 7 per cent.
Years
7 per cent.
!
I -06
51
I9-52536353I5
I
1-07
51
31-5190168175
2
1-1236
52-
20-6968853434
2
I-I449
52
337253479947
3
1-191016
53
2 1 -9386984640
3
1-225043
53
36-0861223543
4
i -26247696
54
23-2550203718
4
1-31079601
54
38-6121509191
5
1-3382255776
55
24-6503215941
5
1-4025517307
55
41-3150014834
6
1-4185191123
56
26-1293408898
6
1-5007303518
56
44-2070515873
7
1-5036305290
57
27-6971013432
7
1-6057814765
57
47-30I545I984
8
1-5938480745
58
29-3589274238
8
1-7181861798
58
50-6126533623
9
1-6894789590
59
31-1204630692
9
1-8384592124
59
54-I555390976
10
1-7908476965
60
32-9876908533
10
I-967I5I3573
60
57-9464268345
ii
1-8982985883
61
34-9669523045
ii
2-1048519523
61
62-0026767129
12
2-0121964718
62
37-0649694428
12
2-2521915890
62
66-3428640828
13
2-1329282601
63
39-2888676094
13
2-4098450002
63
70-9868645686
14
2-2609039558
64
41-6461996659
14
2-578534I502
64
75-9559450884
15
2-3965581931
65
44-1449716459
15
27590315407
65
81-2728612446
16
2-5403516847
66
46-7936699447
!6
2-9521637486
66
86-9619615317
17
2-6927727858
67
49-6012901413
17
#1588152110
67
93-0492988389
18
2-854339 1 529
68
52-5773675498
18
3-3799322757
68
99-5627497577
19
3-0255995021
69
557320096028
19
3-6165275350
69
106-5321422407
20
3-2071354722
70
59-0759301790
20
3-8696844625
70
II3-989392I975
21
3'3995 6 36oo5
71
62-6204859897
21
4-1405623749
71
121-9686496514
22
3-6035374166
72
66-3777151491
22
4-4304017411
72
130-5064551270
23
3-8197496616
73
70-3603780580
23
4-7405298630
73
139-6419069858
24
4-0489346413
74
74-5820007415
24
5-0723669534
74
149-4168404749
25
4-2918707197
75
79-0569207860
25
5-4274326401
75
159-8760193081
26
4-5493829629
76
83-8003360332
26
5-8073529249
76
171-0673406597
27
4-8223459407
77
88-8283561952
27
6-2138676297
77
183-0420545058
28
5-1116866971
78
94-1580575669
28
6-6488383637
78
I95-85499832I2
29
5-4183878990
79
99-8075410209
29
7-1142570492
79
209-5648482037
30
5-7434911729
80
1057959934821
30
7-6122550427
80
224-2343874780
31
6-0881006433
81
112-1437530911
3 1
8-1451128956
81
239-9307947085
32
6-4533866819
82
118-8723782765
32
87152707983
82
2567259503380
33
6-8405898828
83
126-0047209731
33
93253397542
83
274-6967668617
34
7-2510252758
84
133-5650042315
34
9-978II35370
84
293-9255405420
35
7-6860867923
85
141-5789044854
35
10-6765814846
85
314-5003283799
36
8u 472 5 1 9999
86
150-0736387545
36
11-4239421885
86
336-5I535I3666
37
8-6360871198
87
159-0780570798
37
12-2236181417
87
360-0714259622
38
9-1542523470
88
168-6227405046
38
13-0792714116
88
385-2764257796
39
9-7035074879
89
178-7401049348
39
13-9948204105
89
412-2457755842
40
10-2857179371
90
189-4645112309
40
I4-9744578392
90
441-1029798750
4i
10-9028610134
9 1
200-8323819048
41
16-0226698879
91
471-9801884663
42
11-5570326742
92
212-8823248191
42
17-1442567801
92
505-0188016589
43
12-2504546346
93
225-6552643082
43
18-3443547547
93
540-3701177751
44
12-9854819127
94
239-1945801667
44
I9-6284595875
94
578-1960260193
45
13-7646108274
95
253-5462549767
45
21-0024517587
95
618-6697478407
46
14-5904874771
96
2687590302753
46
22*4726233818
96
661-9766301895
47
15-4659167257
97
284-8845720918
47
24-0457070185
97
708 -3 1 49943028
48
16-3938717293
98
301-9776464174
48
257289065098
98
757-8970439040
49
17-3775040330
99 [320-0963052024
49
27-5299299655
99
810-9498369773
so
18-4210542750
100 339-3020835145
50
29-4570250630 100 867-7163255057
THE ENGINEER'S VALUING ASSISTANT.
Amount of ^1 in n years at the following rates per cent.
Years
8 per cent.
Years
8 per cent.
Years
9 per cent.
Years
per cent.
I
I -08
51
50-6537415143
I
1-09
51
81-0496968827
2
1-1664
52
54-7060408355
2
1-1881
52
88-3441696021
3
1-259712
53
59-0825241023
3
1-295029
53
96-2951448663
4
I -36048896
54
63-8091260305
4
1-41158161
54
104-9617079043
5
I -4693280768
55
68-9138561129
5
1-5386239549
55
114-4082616157
6
1-5868743229
56
74-4269646020
6
1-6771001108
56
124-7050051611
7
17138242688
57
80-3811217701
7
1-8280391208
57
135-9284556256
8
1-8509302103
58
86-8116115117
8
1-9925626417
58
148-1620166319
9
1-9990046271
59
937565404327
9
2-1718932794
59
161-4965981287
10
2-1589249973
60
101-2570636673
10
2-3673636746
6O
176-0312919603
ii
2-3316389971
6>1
109-3576287606
ii
2-5804264053
61
191-8741082367
12
2-5181701168
62
118-1062390615
12
2-8126647818
62
209-1427779780
13
2-7196237262
6 3
I27-554738I864
13
3-0658046121
63
227-9656279961
14
2-9371936243
6 4
1377599172413
14
3-3417270272
64
248-4825345157
15
3-1721691142
65
1487798466206
15
3-6424824597
65
270-8459626221
16
3-4259426433
66
160-6822343503
16
3-9703058811
66
295-2220992581
17
3-7000180548
67
I73-5368I30983
17
4-3276334104
67
321-7920881913
18
3-9960194992
68
187-4197581462
18
47171204173
68
3507533761286
19
4-3157010591
69
202-4133387979
19
5-1416612548
69
382-3211799801
20
4-6609571439
70
218-6064059017
20
5-6044107678
7O
416-7300861784
21
5-0338337I54
71
236-0949183738
21
6-1088077369
71
454-2357939344
22
5-4365404126
72
254-9825118437
22
6-6586004332
72
495-1170153885
23
5-8714636456
73
275-3811127912
23
7-2578744722
73
539-6775467735
24
6-3411807372
74
297-4116018145
24
7-9110831747
74
588-2485259831
25
6-8484751962
75
321-2045299597
25
8-6230806604
75
641-1908933216
26
7"3963532ii9
76
346-9008923565
26
9-399I579I98
76
698-8980737205
27
7-9880614689
77
374-6529637450
27
10-2450821326
77
7617989003553
28
8-6271063864
78
404-6252008446
28
11-1617395246
78
830-3608013873
29
9-3172748973
79
436-9952169122
29
12-1721820818
79
905-0932735122
30
10-0626568891
80
47I-954834265I
30
13-2676784691
80
986-5516681283
31
10-8676694402
81
509-7112210063
31
14-4617695314
81
1075-3413182598
32
11-7370829954
82
550-4881186869
32
157633287892
82
1172-1220369032
33
12-6760496351
83
594-5271681818
33
17-1820283802
83
1277-6130202245
34
13-6901336059
84
642-0893416363
34
187284109344
84 1392-5981920447
3 I
14-7853442943
85
693-4564889673
35
20-4139679185
85
1517-9320293287
36
15-9681718379
86
748-9330080846
36
22-2512250312
86
1654-5459119683
37
17-2456255849
87
808-8476487314
37
24-2538352840
87
1803-4550440455
38
18-6252756317
88
873-5554606299
38
26-4366804596
,00
oo
1965-7659980095
.39
20-1152976822
89
943-4398974803
39
28-8159817009
89
2142-6849378304
40
21-7245214968
9O
1018-9150892787
40
31-4094200540
90
2335-526582235I
41
23-4624832166
91
1100-4282964210
41
34-2362678589
9 1
2545-7239746463
42
2 5 '33948 1 8739
92
1188-4625601347
42
37"3 I 753i9 6 62
92
2774-8391323536
43
27-3666404238
93
1 283-539564945 5
43
40-6761098431
93
3024-5746542654
44
29-5559716577
94
1386-2227301411
44
44-3369597290
94
32967863731493
45
31-9204493903
95
1497-1205485524
45
48-3272861046
95
3593-497I467327
46
34-4740853415
96
1616-8901924366
46
52-6767418540
96
3916-9118899387
47
37-2320121689
97
1746-2414078316
47
57-4176486209
97
4269-4339600331
48
40-2105731424
98
1885-9407204581
48
62-5852369968
98
4653-6830164361
49
43-4274189938
99
2036-8159780947
49
68-2179083265
99
5072-5144879154
5O 46-9016125133 1OO
2199-7612563423
so
74-3575200758
100
5529-0407918277
TABLE I.
Amount of 1 in n years at the following rates per cent.
Xlll
Years
10 per cent.
rears 10 per cent.
Years
11 per cent.
Years
11 per cent.
I
no .
51 129-129938
I
I'll
51
204-866958
2
1*21
52 142-042932
2
I-232I
52
227-402323
3
i'33i
53
156-247225
3
1-367361
53
252-416579
4
1-4641
54
171-871948
4
1-518070
54
280-182402
5
1-61051
55
189-059142
5
1-685058
55
311-002466
6
1-771561
56
207-965057
6
1-870415
56
345-212738
7
1-948717
57
228761562
7
2-076160
57
383-I86I39
8
2-143589
58
251-637719
8
2-304538
58
425-336614
9
2-357948
59
276-801490
9
2-558037
59
472-123642
10
2-593742
60
304-481640
10
2-839421
60
524-057242
ii
2-853117
61
334-929803
ii
3-I5I757
61
581703539
12
3-138428
62
368-422784
12
3-498851
62
645-690928
13
3-452271
63
405-265062
13
3-883280
63
716716930
H
3-797498
64
445791568
H
4-310441
64
795-555793
15
4-177248
65
490-370725
15
4784589
65
883-066930
16
4-594973
66
539-407798
16
5-310894
66
980-204292
17
5-054470
67
593-348578
17
5-895093
67
1088-026764
18
5"5599 J 7
68
652-683435
18
6-543553
68
1207709708
J 9
6-115909
69
717-951779
19
7-263344
69
I340-557776
20
6-727500
70
789746957
20
8-062312
70
1488-019132
21
7-400250
71
868-721652
21
8-949166
71
1651701236
22
8-140275
72
955-5938i8
22
9-933574
72
I833-388372
23
8-954302
73
1051-153200
23
1 1 -026267
73
2035-061093
24
9-849733
74
1156-268519
24
12-239157
74
2258-917813
25
10-834706
75
1271-895371
25
13-585464
75
2507-398773
26
11-918177
76
1399-084909
26
15-079865
76
2783-212638
27
13-109994
77
I538-993399
27
16738650
77
3089-366028
28
14-420994
78
1692-892739
28
18-579901
78
3429-196291
29
15-863093
79
1862-182013
29
20-623691
79
3806-407883
30
17-449402
80
2048-400215
30
22-892297
80
4225-112750
31
19-194342
81
2253-240236
31
25-410449
81
4689-875153
32
21-113777
82
2478-564260
32
28-205599
82
5205761420
33
23-225154
83
2726-420686
33
31-308214
83
5778-395176
34
25-547670
84,
2999-062754
34
34752118
84
6414-018645
35
28-102437
85
3298-969030
35
38-574851
85
7119-560696
36
30-912681
86
3628-865933
36
42-818085
86
7902712373
37
34-003949
87
3991752526
37
47-528074
87
8772-010734
38
37-404343
88
4390-927778
38
52756162
88
9736-931915
39
41-144778
89
4830-020556
39
58-559340
89
10807-994425
40
45-259256
90
5313-022612
40
65-000867
90
11996-873812
41
49-785181
9 1
5844-324873
41
72-150963
91
13316-529932
42
54-763699
92
6428757360
42
80-087569
92
14781-348224
43
60-240069
93
707 1 -633096
43
88-897201
93
16407-296529
44
66-264076
94
7778-796406
44
98-675893
94
18212-099147
45
72-890484
95
8556-676047
45
109-530242
95
20215-430053
46
80-179532
96
9412-343651
46
121-578568
96
22439-127359
47
88-197485
97
I0 353"578oi6
47
134-952211
97
24907-431368
48
97-017234
98
11388-935818
48
149-796954
98
27647-248819
49 106718957
99
12527-829400
49
166-274619
99
30688-446189
50 117-390853 |XOO
13780-612340
50
184-564827
100
34064-175270
THE ENGINEEB'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
12 per cent.
Years
12 per cent.
Years
13 per cent.
Years
13 per cent.
I
1*12
51
323-682453
I
I-I3
51
509331595
2
1-2544
52
362-524347
2
1-2769
52
575-544703
3
1-404928
53
406-027269
3
1-442897
53
650-365514
4
I-5735I9
54
454750541
4
1-630474
54
734-9I303I
5
1762342
55
509-320606
5
1-842435 .
55
830-451725
6
1-973823
56
570-439078
6
2-081952
56
938-410449
7
2-210681
57
638-891768
7
2-352605
57
1060-403808
8
2-475963
58
715-558780
8
2-658444
58
1198-256303
9
2773079
59
801-425833
9
3-004042
59
1354-029622
10
3-105848
60
897-596933
10
3-394567
60
I530-053473
ii
3-478550
61
1005-308566
ii
3-835861
61
1728-960425
12
3-895976
62
1125-945593
12
4-334523
62
1953725280
13
4-363493
63
1261-059065
13
4-898011
63
2207-709566
H
4-887112
64
1412-386152
H
5-534753
64
2494-711810
15
5-473566
65
1581-872491
15
6-254270
65
2819-024345
16
6-130394
66
1771-697189
16
7-067326
66
3I85-4975IO
17
6-866041
67
1984-300852
17
7-986078
67
3599-612186
18
7-689966
68
2222-416954
18
9-024268
68
4067-561770
19
8-612762
69
2489-106989
19
10-197423
69
4596-344800
20
9-646293
70
2787799828
20
11-523088
70
5193-869624
2 T
10-803848
71
3122-335807
21
13-021089
71
5869-072675.
22
12-100310
72
3497-016104
22
14713831
72
6632-052123
23
13-552347
73
3916-658036
23
16-626629
73
7494-218899
24
15-178629
74
4386-657001
24
18788091
74
8468-467356
25
17-000064
75
4913-055841
25
21-230542
75
9569-368112
26
19-040072
76
5502-622542
26
23-9905I3
76
10813-385967
27
21-324881
77
6162-937247
27
27-109279
77
12219-126143
28
23-883866
78
6902-489716
28
30-633486
78
13807-612541
29
26-749930
79
7730788482
29
34-615839
79
15602*602172
30
29-959922
80
8658-483100
30
39-II5898
80
17630-940454
31
33-555113
8 1
9697-501072
31
44-200965
81
19922-962713
32
37-581726
82
10861*201201
32
49-947090
82
22512-947866
33
42-091533
83
.12164-545345
33
56-440212
83
25439-63I089
34
47-142517
84
13624-290786
34
63777439
84
28746*783130
35
52-799620
85
15259-205681
35
72-068506
85
32483*864937
36
59-135574
86
17090-310362
36
81-437412
86
36706767379
37
66-231843
87
19141-147606
37
92-024276
87
41478*647138
38
74-179664
88
21438-085318
38
104-987432
88
46870*871266
39
83-081224
89
24010-655557
39
117-505798
89
52964*084530
40
93-050970
90
26891-934223
40
132781552
90
59849*415520
41
104-217087
91
30118-966330
41
150-043153
91
67629*839537
42
116723137
92
33733-242290
42
169-548763
92
76421718677
43
130729914
93
37781-231365
43
191-590103
93
86356*542105
44
146-417503
94
42314-979128
44
216-496816
94
97582*892578
45
163-987604
95
47392-776624
45
244-641402
95
110268*668614
46
183-666116
96
53079-909819
46
276-444784
96
124603*595533
47
205-706050
97
59449-498997
47
312-382606
97
140802*062953
48
230-390776
98
66583-438876
48
352-992345
98
159106*331137
49
258-037669
99
74573H5 1 542
49
398-881350
99
179790*154184
50
289-002190
100
83522-265727
50
450735925
100
203162*874228
TABLE I.
Amount of ^1 in n years at the following rates per cent.
xv
Years
14 per cent.
rears
14 per cent.
Years
15 per cent.
Years
15 per cent.
!
1-14
51
798-265607
I
I-I5
51
1246-206058
2
1-2996
52
910-022792
2
1-3225
52
1433-136966
3
1-481544
53
1037-425983
3
1-520875
53
1648-107511
4
1-688960
54
1182-665620
4
I -749006
54
1895-323638
5
1-925415
55
1348-238807
5
2-011357
55
2179-622184
6
2-194973
56
1536-992240
6
2-313061
56
2506-565512
7
2-502269
57
1752-171154
7
2 "660020
57
2882-550338
8
2-852586
58
1997-475115
8
3-059023
58
3314-932889
9
3-251949
59
2277-121631
9
3-517876
59
3812-172822
10
3-707221
60
2595-918660
10
4-045558
60
4383-998746
ii
4-226232
61
2959^47272
ii
4-652391
61
5041-598558
12
4-817905
62
3373-655890
12
5-350250
62
5797-838341
13
5-492411
63
3845-967715
13
6-152788
63
6667-514092
14
6-261349
64
4384-403195
14
7-075706
64
7667-641206
15
7'i37938
65
4998-219642
15
8-137062
65
8817787387
16
8-137249
66
5697-970392
16
9-357621
66
10140-455495
17
9-276464
67
6495-686247
17
10-761264
67
11661-523819
18
10-575169
68
7405-082321
18
12-375454
68
13410752392
19
12-055693
69
8441793846
19
14-231772
69
15422-365251
20
13743490
70
9623-644985
20
16-366537
7O
17735-720039
21
15-667578
71
10970-955283
21
I8-82I5I8
71
20396-078045
22
17-861039
72
12506-889022
22
2 1 '644746
72
23455-489751
23
20-361585
73
14257-853485
2 3
24-891458
73
26973-813214
24
23-212207
74
16253-952973
24
28-625176
74
31019-885196
25
26-461916
75
18529-506390
25
32-918953
75
35672-867976
26
30-166584
76
21123-637284
26
37.856796
76
41023798172
27
34-389906
77
24080-946504
27
43 ! 5353I5
77
47177-367898
28
39-204493
78
27452-279015
28
50-065612
78
54253-973082
29
44-693122
79
31295-598077
29
57-575454
79
62392-069045
30
50-950159
80
35676-981807
30
66-2II772
80
71750-979401
31
58-083181
81
40671759260
31
76-143538
81
82513-511312
32
66-214826
82
46365-805557
32
87-562068
82
94890-538008
33
75-484902
83
52857-018335
33
100-699829
83
109124-118710
34
86-052788
84
60257-000902
34
115-804803
84
125492736516
35
98-100178
85
68692-981028
35
I33-I75523
85
144316-646994
36
111-834203
86
78309-998372
36
I53-I5I852
86
165964-144043
37
127-490992
87
89273-398144
37
176-124630
87
190858-765649
38
i45-33'973i
88
101771-673884
38
202-543324
88
219487-580496
39
165-687293
89
116019708227
39
232-924823
89
252410717571
40
188-883514
90
132262-467379
40
267-863546
90
290272-325206
41
215-327206
91
1 50779-2 1 28 1 2
41
308*043078
91
3338r3'I73987
42
245-473015
92
171888-302606
42
354-249540
92
383885-150085
43
279-839237
93
I95952-66497I
43
407-386971
93
441467-922598
44
319-016730
94
223386-038067
44
468-495017
94
507688-110988
45
363-679072
95
254660-083396
45
538769269
95
583841-327636
46
414-594142
96
290312-495072
46
619-584659
96
671417-526781
47
472-637322
97
330956-244382
47
712-522358
97
772130-155799
48
538-806547
98
377290-118595
48
819-400712
98
887949-679168
49
614-239464
99
430! 10-735 199
49
942-310819
99
1021142-131044
50
700-232988
100
490326-238126
50
1083-657442
100
1174313-450700
THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
16 per cent.
Years
16 per cent.
Years
17 per cent.
Years
17 per cent.
I
ri6
51
1938-01641
I
I-I7
51
3002-47188
2
i'3456
52
2248-09904
2
1-3689
52
3512-89210
3
i '5 6090
53
2607-79488
3
I -6oi6l
53
4110-08376
4
1-81064
54
3025-04207
4
1-87388
54
4808-79800
5
2-10034
55
3509-04880
5
2-19244
55
5626-29366
6
2-43640
56
4070-49660
6
2-56516
56
658276358
7
2-82621
57
472177606
7
3-00124
57
7701-83339
8
3-27841
58
5477-26023
8
3-5II45
58
9011-14507
9
3-80296
59
6353-62187
9
4-10840
59
I0543-03973
10
4-41144
60
7370-20I37
10
4-80682
60
I2335-35648
ii
5-11726
61
8549-43358
ii
5-62399
61
14432-36708
12
5-93603
62
9917-34296
12
6-58007
62
16885-86949
13
-6-88579
63
11504-11783
13
7-69868
63
19756-46730
H
7-98752
64
1334477668
H
9-00745
64
23115-06674
15
9-26552
65
15479*94095
15
10-53872
65
27044-62809
16
10-74800
66
1795673150
16
12-33030
66
31642-21486
17
12-46768
67
20829-80855
17
14-42646
67
37021-39139
18
14-46251
68
24162-57791
18
16-87895
68
43315-02793
19
1677652
69
28028-59038
19
1974838
69
50678-58267
20
19-46076
70
32513-16484
20
23-10560
90
59293-94173
21
22-57448
71
377I5-27I2I
21
27-03355
71
69373-91182
22
26-18640
72
4374971461
22
31-62925
72
81167-47683
23
30-37622
73
50749-66895
23
37-00623
73
94965-94789
24
35-23642
74
58869-61598
24
43-29729
74
111110-15904
25
40-87424
75
6828875453
25
50-65783
75
129998-88607
26
47-41412
76
79214-95526
26
59-26966
76
152098-69670
27
55-00038
77
91889-34810
27
69-34550
77
I77955-475I4
28
63-80044
78
106591-64379
28
81-13423
78
208207-90592
29
74-00851
79
123646-30680
29
94-92705
79
243603-24992
30
85-84988
80
143429-7-1589
30
111-06465
80
285015-80241
31
99-58586
81
166378-47043
31
129-94564
81
333468-48882
32
115-51959
82
192999-02570
32
152-03640
82
390158-13192
33
134-00273
83
223878-86981
33
177-88259
83
456485-01435
34
I55-443I7
84
259699-48898
34
208-12263
84
534087-46679
35
180-31407
85
301251-40722
35
243-50347
85
624882-33614
36
209-16432
86
349451-63238
36
284-89906
86
731112-33329
37
242-63062
87
405363-89356
37
333-33I9I
87
855401-42994
38
281-45151
88
470222-11653
38
389-99833
88
1000819-67303
39
326-48376
89
545457-65517
39
456-29805
89
1170959-01745
40
378-72116
90
632730-88000
40
533-8687I
90
1370022-05042
41
439-31654
91
733967-82080
41
624-62639
91
1602925-79899
42
509-60719
92
851402-67213
42
730-81288
92
1875423-18482
43
591-14434
93
987627-09967
43
855-05107
93
2194245-22623
44
68572744
94
1145647-43561
44
1000-40975
94
256726679769
45
795-44383
95
1328951-02531
45
1170-47941
95
3003702-15330
46
92271484
96
1541583-18936
46
1369-46091
96
3514331-51936
47
1070-34921
97
1788236-49966
47
1602-26927
97
4111767-87766
48
1241-60509
98
2074354-33961
48
1874-65504
98
4810768-41686
49
1440-26190
99
2406251-03394
49
2193-34640
99
5628599-04772
50
1670-70380
100
2791251-19938 |
50
2566-21528
100
6585460-88584
/7Y- V T
^^^-
Amount of 1 in n years at the following rates per cent.
TABLE I.
XVll
Years
18 per cent.
Years
18 per cent.
Years
19 per cent.
Year
19 per cent.
I
1-18
51
4634-28109
I
I-I9
51
7126-80754
2
1-3924
52
5468-45169
2
1-4161
52
8480-90098
3
1-64303
53
645277300
3
1-68516
53
10092-27216
4
1-93878
54
7614-27214
4
2-00534
54
12009-80387
5
2-28776
55
8984-84112
5
. 2-38635
55
14291-66661
6
2-69955
56
10602-11252
6
2-83976
56
17007-08327
7
3*18547
57
12510-49278
7
3'37932
57
20238-42909
8
375886
58
14762-38148
8
4-02139
58
24083-73061
9
4'43545
59
17419-61014
9
478545
59
28659-63943
10
5-23384
60
20555'13997
10
5-69468
60
34104-97092
n
6-17593
61
24255-06516
ii
6-7766 7
61
40584-91539
12
7-28759
62
28620-97689
12
8-06424
62
48296-04932
13
8-59936
63
3377275273
13
9-59645
63
57472-29869
14
10-14724
64
39851-84822
H
11-41977
64
68392-03544
15
11-97375
65
47025-18090
15
I3-58953
65
81386-52217
16
14-12902
66
55489-71346
16
16-17154
66
96849-96139
17
16-67225
67
65477-86188
17
19-24413
67
115251-45405
18
19-67325
68
77263-87702
18
22-90052
68
137149-23032
19
23-21444
69
91171-37489
19
27-25162
69
163207-58408
20
27-39303
70
107582-22237
20
32-42942
70
194217-02506
21
32-32378
71
126947-02239
21
38-59101
71
231118-25982
22
38-14206
72
149797-48643
22
45-9233I
72
27503072918
23
45-00763
73
176761-03398
23
54-64873
73
327286-56773
24
53-10901
74
208578-02010
24
65-03199
74
389471-01560
25
62-66863
75
246122-06372
25
7738807
75
463470-50856
26
73'94898
76
290424-03518
26
92-09181
76
551529-90518
27
87-25980
77
342700-36152
27
109-58925
77
656320-58717
28
102-96656
78
404386-42659
28
130-41121
78
781021-49873
29
121-50054
79
477175-98338
29
I55-I8934
79
929415-58349
30
143-37064
so
563067-66039
30
184-67531
80
1106004-54435
31
169-17735
81
664419-83926
31
219-76362
81
1316145*40778
32
199-62928
82
784015-41032
32
261-51871
82
1566213-03526
33
2 35"5 62 55
83
925138-18418
33
311-20726
83
1863793-51196
34
277-96381
84
1091663-05733
34
370-33664
84
2217914-27923
35
327-99729
85
1288162-40765
35
440-70061
85
2639317-99228
36
387-03680
86
1520031-64103
36
524-43372
86
3140788-41082
37
45670343
87
I793637-3364I
37
624-07613
87
3737538-20887
38
538-91004
oo
oo
2116492-05697
38
742-65059
QO
OO
4447670-46856
39
635-91385
89
2497460-62722
39
88375421
89
5292727-85759
40
750-37834
90
2947003-54012
4O
1051-66751
90
6298346-15053
41
885-44645
91
3477464-17734
41
1251-48433
91
7495031-91913
42
1044-82681
92
410340772926
42
1489-26636
92
8919087-98376
43
1232-89563
93
4842021-12053
43
1772-22696
93
0613714-70068
44
1454-81685
94
5713584-92223
44
2108-95009
94
2630320-49381
45
1716-68388
95
6742030-20823
45
2509-65060
95
5030081-38763
46
2025-68698
96
7955595-6457I
46
2986-48422
96
7885796-85128
47
2390-31063
97
9387602-86194
47
3553-9I622
97
21284098-25302
48
2820-56655
98
1077371-37708
48
4229-16030
98
25328076*92110
49
3328-26853
99
3071298-22496
49
5032-70076
90
30140411-53611
50
3927-35686
LOO
5424131-90545
SO
5988-9I390
00
3586708972797
THE ENGINEEK'S VALUING ASSISTANT.
Amount of 1 in n years at the following rates per cent.
Years
20 per cent.
Years
20 per cent.
Years
21 per cent.
Years
21 per cent.
I
I '20
51
10920-52578
I
I-2I
51
16674-54093
2
1-440
52
13104-63094
2
1-4641
52
20I76-I9453
3
17280
53
15725-55712
3
I77I56
53
244I3-I9538
4
2-07360
54
18870-66855
4
2-14359
54
29539-96641
5
2-48832
55
22644-80226
5
2-59374
55
35743-35935
6
2-98598
56
2717376271
6
3-I3843
56
43249-46482
7
3'583l8
57
32608-51525
7
3-79750
57
52331-85243
8
4-29982
58
39130-21830
8
4*59497
58
63321-54144
9
5-I5978
59
46956-26196
9
5-55992
59
76619-06514
10
6-19174
60
56347-5I435
10
672750
60
92709-06882
ii
7-43008
61
67617*01722
ii
8-14027
61
112177-97327
12
8-91610
62
81140-42067
12
9-84973
62
I35735-34766
13
10-69932
63
97368-50480
13
11-91818
63
164239-77066
H
12-83918
64
116842-20576
14
14-42099
64
198730-12250
15
15-40702
65
140210-64692
15
17-44940
65
240463-44823
16
18-48843
66
16825277630
16
21-11378
66
290960-77236
17
22-l86lI
67
201903-33156
17
25-54767
67
352062-53455
18
26-62333
68
242283-99787
18
30-91268
68
425995*66681
19
31-94800
69
29074079744
19
37-40434
69
51545475684
20
38-33760
7O
348888-95693
20
45-25926
70
623700-25577
21
46-00512
71
41866674832
21
54-76370
71
754677-30949
22
55-206I4
72
502400-09798
22
66-26408
72
9 I 3 1 59-54448
23
66-24737
73
602880-11758
23
80-17953
73
1 104923-04882
24
79-49685
74
723456-14109
24
97-01723
74
1336956-88907
25
95-39622
75
868147-36931
25
117-39085
75
1617717-83578
26
II4-47546
76
1041776-84318
26
142-04293
76
1957438-58129
27
I37-37055
77
1250132-21181
27
171-87195
77
2368500-68336
28
29
164-84466
197-81359
78
79
1500158-65417
1800190-38501
28
29
207-96506
251-63772
78
79
2865885-82686
3467721-85051
30
237-37631
so
2160228-46201
3O
304-48164
80
4i95943-439ii
31
284-85158
81
2592274-15441
31
368-42278
81
5077091-56133
32
341-82189
82
3110728-98529
32
44579 : 57
82
6143280-78921
33
410-18627
83
373287478235
33
539-40780
83
7433369-75494
34
492-22352
84
4479449-73882
34
652-68344
84
8994377-40348
35
590-66823
85
5375339-68659
35
789-74696
85
10883196-65821
36
708-80187
86
6450407-62391
36
955-59382
86
13168667-95643
'37
850-56225
87
7740489-14869
37
1156-26852
87
15934088-22728
38
1020-67470
88
9288586-97843
38
1399-08491
88
19280246-75501
39
1224-80964
89
11146304-37411
39
1692-89274
89
23329098-57356
40
1469-77157
9O
I3375565-24893
40
2048-40021
90
28228209-27401
41
1763-72588
9 1
16050678-29872
41
2478-56426
91
34156133-22154
42
2116-47106
92
19260813-95847
42
2999-06275
92
41328921-19807
43
2539-76527
93
23112976-75016
43
3628-86593
93
50007994-64967
44
3047-71832
94
27735572-10019
44
4390-92778
94
60509673-52610
45
3657-26199
95
33282686-52023
45
5313-02261
95
73216704-96658
46
4388-71439
96
39939223-82427
46
6428-75736
96
88592213-00956
47
5266-45726
97
47927068-58913
47
7778-79641
97
107196577-74156
48
6319-74872
98
57512482-30695
48
9412-34365
98
129707859-06729
49
7583-69846
99
69014978-76834
49
11388-93582
99
156946509-47142
50
9100-43815
100 82817974-52201
50
13780-61234 100
189905276-46042
TABLE I.
Amount of 1 in n years at the following rates per cent.
xix
Years
22 per cent.
Years
22 per cent.
Years
23 per cent.
Years
23 per cent.
I
1-22
51
2537I-80497
I
1-23
51
38473-41024
2
1-4884
52
30953-60207
2
1-5129
52
47322-29460
3
1-81585
53
37763-39452
3
1-86087
53
58206-42235
4
2-21553
54
46071-34132
4
2-28887
54
71593-89950
5
270271
55
56207-03641
5
2-81531
55
88060-49638
6
3-29730
56
68572-58441
6
3-46283
56
108314-41055
7
4-02271
57
83658-55299
7
4-25928
57
13322672497
8
4-90771
58
102060-43464
8
5-2389I
58
163868-87172
9
5-98740
59
124517-39026
9
6-44386
59
20I5587I22I
10
7-30463-
60
151911-21612
10
7-92595
60
247917-21602
ii
8-91165
61
I8533I-68367
ii
9-74891
61
304938-17571
12
IO-8722I
62
226104-65408
12
11-99116
62
375073-95612
13
13-26410
63
275847-67797
13
I4749I3
63
461340-96603
H
I6-I8220
64
336534-16713
14
18-14143
64
567449-38821
15
1974229
65
410571-68369
15
22-31396
65
69796274750
16
24-08559
66
500897-45435
16
27-44617
66
858494-17943
17
29-38442
67
611094-89431
17
3375859
67
1055947-84070
18
35-84899
68
74553577105
18
4I-5233I
68
1298815-84406
19
4373577
69
909553-64069
19
51-07368
69
1597543-48819
20
70
1109655-44164
20
62-82062
70
1964978-49048
21
65-09632
71
I353779-63880
21
77-26936
71
2416923-54329
22
79-41751
72
1651611-15933
22
95-04132
72
2972815-95824
23
96-88936
73
2014965-61439
23
116-90082
73
3656563-62864
24
118-20502
74
2458258-04955
24
143-78801
74
4497573^6322
25
144-21013
75
2999074-82045
25
176-85925
75
5532015-11376
26
175-93636
76
3658871-28095
26
217-53688
76
6804378-58993
27
214-64236
77
4463822-96276
27
267-57036
77
8369385-66561
28
261-86368
78
5445864-01457
28
329-11155
78
10294344-36870
29
319-47368
79
6643954-09778
29
404-80720
79
12662043-59351
30
389-75789
80
8105623-99929
30
497-91286
80
I55743I3-5954I
31
475-50463
81
9888861-27913
31
612-43282
81
1915640572236
32
580-11565
82
1206441076054
32
753-29237
82
23562379-03850
33
707-74109
83
14718581-12786
33
926-54961
83
28981726-21735
34
803-44413
84
17956668-97599
34
1139-65602
84
35647523-24734
35
1053-40184
85
21907136-15071
35
1401-77690
85
43846453-59423
36
1285-15025
86
26726706-10386
36
1724-18559
86
5393II37-9209I
37
1567-88330
87
32606581-44671
37
212074828
87
66335299^4272
38
1912-81763
88
39780029-36499
38
2608-52038
88
81592418-56054
39
2333-6375I
89
48531635-82529
39
3208-48007
89
100358674-82947
40
2847-03776
90
5920859570685
40
3946-43049
90
123441170-04024
41
3473-38607
91
7223448676236
41
4854-10950
91
151832639-14950
42
43
4237-53100
5169-78782
92
93
88126073-85007
107513810-09709
42
43
5970-55469
7343-78226
92
93
186754146-15388
22970759976928
44
6307-14114
94
131166848-31845
44
9032-85218
94
28254034771621
45
7694-71219
95
160023554-94851
45
11110-40819
95
347524627-69094
46
47
9387-54887
11452-80963
96
97
195228737-03718
238179059-18536
46
47
13665-80207
16808-93654
96
97
427455292-05986
525770009-23362
48
13972-42774
98
290578452-20614
48
20674-99195
98
646697111-35736
49
17046-36185
99
354505711-69149
49
25430-24010
99
795437446-96955
so
20796-56145
100
432496968-26362
50
31279-19532
100
97838805977254
THE ENGINEER'S VALUING- ASSISTANT.
Amount of 1 in n years at the following rates per cent.
1
Years 24 per cent.
Years 24 per cent.
Years
25 per cent.
Years
25 per cent.
I
1-24
51 | 58144-13892
I
1-25
51
87581-15402
2
1-5376
52 72098-73226
2
1-5625
52
109476-44253
3
I -90662
53 89402-42801
3
I-953I3
53
I36845-553I6
4
2-36421
54
110859-01073
4
2-44141
54
171056-94145
5
2-93163
55
137465-17330
5
3-05176
55
213821-17681
6
3-63522
56
170456-81489
6
3-81470
56
267276-47101
7
4-50767
57
211366-45047
7
476837
57
334095-58876
8
5'5895I
58
262094-39858
8
5-96046
58
417619-48595
9
6-93099
59
324997-05424
9
7-45058
59
522024-35744
10
8-59443
60
402996-34726
10
9-3I323
60
652530-44680
ii
10-65709
61
499715-47060
ii
11-64153
61
815663-05850
12
13-21479
62
619647-18355
12
14-55192
62
1019578-82312
13
16-38634
63
768362-50760
13
18-18989
63
1274473-52891
14
20-31906
64
952769-50942
14
2273737
64
1593091-91113
15
25-19563
65
1181434-19168
15
28-42171
65
1991364-88892
16
31-24259
66
1464978-39769
16
35-527I4
66
2489206-11114
17
38-74081
67
1816573-21313
17
44-40892
67
3111507-63893
18
48-03860
68
2252550-78428
18
55-5IH5
68
3889384-54866
19
59-56786
69
2793162-97251
19
69-38894
69
4861730-68583
20
73-86415
70
3463522-08591
20
86-73617
70
6077163-35729
21
91-59155
71
4294767-38653
21
I08-42022
71
7596454-19661
22
II3-57352
72
53255ii-5593o
22
135-52527
72
9495567-74576
23
140-83116
73
6603634-33353
23
169-40659
73
11869459-68220
24
174-63064
74
8188506-57358
24
21175824
74
14836824-60275
25
216-54199
75
10153748-15124
25
264-69780
75
18546030-75344
26
268-51207
76
12590647-70754
26
230-87225
76
23182538-44180
27
332'95497
77
15612403-15735
27
4I3-5903I
77
28978173-05225
28
412-86416
78
i9359379-9i5i2
28
516-98788
78
36222716-31531
2 9
511-95156
79
24005631-09474
29
646-23485
79
45278395-39414
30
634'8i993
so
29766982-55748
30
80779357
80
56597994-24267
31
787-17672
81
36911058-37128
31
1009-74196
81
70747492-80334
32
976-09913
82
45769712-38038
32
I262-I7745
82
88434366-00418
33
1210-36292
83
56754443-35168
33
I57772I8I
83
110542957-50522
34
1500-85002
84
70375509-75608
34
1972-15226
84
138178696-88152
35
1861-05403
85
87265632-09754
35
2465-19033
85
172723371-10191
36
2307-70699
86
108209383-80094
36
3081-48791
86
215904213-87738
37
2861-55667
87
134179635-91317
37
3851-85989
87
269880267-34673
38
3548-33027
88
166382748-53233
38
4814-82486
88
337350334-I834I
39
4399-92954
89
206314608-18009
39
6018-53108
89
421687917-92926
4O
5455-91262
90
255830114-14331
40
7523-16385
90
527109897-16158
41
6765-33165
91
317229341-53771
41
9403-95481
91
658887371-45197
42
8389-01125
92
393364383-50676
42
II754-9435I
92
823609214-31497
43
10402-37395
93
487771835-54838
43
14693-67939
93
1029511517-89371
44
12898-94370
94
604837076-07999
44
18367-09923
94
1286889397-36713
45
15994-69019
95
749997974-33919
45
22958-87404
95
160861174670892
46
19833-41583
96
929997488-18060
46
28698-59255
96
2010764683-38615
47
24593-43563
97
1153196885-34394
47
35873-24069
97
25I3455854-23268
48
30495-86018
98
1429964137-82648
48
44841-55086
98
3141819817-79085
49
37814-86662
99
I 773 1 55530-90484
49
56051-93857
99
3927274772-23857
59
46890-43461
100
2198712858-32200
so
70064-92322
100
4909093465-29821
TABLE II.
The sum to which 1 will amount in n years up to
one hundred, by half-yearly and quarterly payments, at
the rate of 3 per cent., the half-yearly and quarterly ratio
being 0*015 and 0*0075 respectively.
Calculated to 10 decimal places.
TABLE II.
XXlll
Amount of 1 in n years at the rate of 3 per cent. Payable by half-yearly
and quarterly instalments.
Years
Amount of i in n
years at 3 per cent,
'ayable half-yearly.
Katio = o'ois
Amount of i in n
rears at 3 per cent.
Payable quarterly.
Eatio = 0*0075
Fears
Years
Amount of i in n
years at 3 per cent.
Payable half-yearly.
Eatio = o'ois
Amount of i in n
years at 3 per cent.
Payable quarterly.'
Eatio = o'oojs
Years
o*
1-0075000000
oi
i
1-4858942602
i
i 'oi 50000000
1-0150562500
1-4948001774
1-4970384672
4
...
I'O22669I7I9
|
4"
...
1-5082662557
f
1
I-03022500OO
1-0303391907
1
14
I'5I7222l8oi
I-5I95782526
14
i
... ...
I -0380667346
i
4
i
...
1-5309750895
i
J
1-0456783750
1-0458522351
1-5399805128
1-5424574027
3
4
1-0536961269
&
|
I-5540258332
|
2
1-0613635506
1-0615988478
2
15
1-5630802205
1-5656810269
15
*
...
1-0695608392
i
i
...
1-5774236346
\
I '0772840039
1-0775825455
i
1-5865264238
1-5892543119
\
|
... ...
1-0856644146
3.
4
|
...
1-6011737192
^
3
1-0934432639
1-0938068977
3
16
1-6103243202
I-6l3l82522I
16
i
I-I020I04494
i
1
...
1-6252813911
i
1-1098449129
I-II02755278
1-6344791850
I-63747IOOI5
\
&
...
I-II86025942
...
1-6497520340
&
4
1-1264925866
1-1269921137
4
17
1-6589963727
I-662I25I743
17
i
...
I-I354445545
i
i
...
I-67459III3I
i
I'I433899754
1-1439603887
1-6838813183
1-6871505464
4
1-1525400916
|
4
...
1-6998041755
f
5
I'I6O5408250
1-1611841423
5
18
1-7091395381
I7I25527068
18
i
...
1-1698930234
i
^
1-7253968521
i
1-1779489374
I-I7866722IO
17347766312
17383373285
^
...
1-1875072252
|
|
...
17513748585
f
6
I-I956l8l7I5
1-1964135294
6
19
1-7607982806
17645101699
19
I
... ...
1-2053866309
i
i
... ...
17777439962
i
1-2135524440
1*2144270306
17872102548
1-7910770762
|
...
1-2235352333
^
4
...
I-8045IOI542
f
7
1-2317557307
1-2327117476
7
2O
1-8140184087
1-8180439804
20
1
1-2419570857
i
i
...
1-8316793102
j.
4
I-2502320667
1-2512717638
i
1-8412286848
1-8454169051
i
^
... ...
1-2606563021
3
4
|
...
I-85925753I9
3.
4
8
1-2689855477
I-270III2243
8
21
1-8688471151
1-8732019633
21
*
1-2796370585
i
i
...
1-8872509781
i
1-2880203309
1-2892343364
1-8968798218
1-9014053604
|
...
1-2989035940
|
|
1-9156659006
f
9
1-3073406358
1-3086453709
9
22
1-9253330191
I-9300333949
22
i
... ...
I-3I84602II2
i
i
4
...
1-9445086453
i
1-3269507454
1-3283486628
*
I
1-9542130144
1-9590924602
I
3
... ...
1-3383112778
!
3
4
...
1-9737856536
^
10
1-3468550065
1-3483486123
10
23
1-9835262096
1-9885890460
23
i
4
1-3584612269
i
i
...
2-0035034639
i
I
1-3670578316
1-3686496861
2-0132791028
2-0185297398
...
1-3789145588
i
|
...
2-0336687129
^
11
1-3875636991
1-3892564180
11
24
2-0434782893
2-0489212282
24
4
1-3996758411
i
4
i
... ...
2-0642881375
i
i
1-4083771546
1-4101734099
i
2-0741304637
2-0797702985
i
\
... ...
1-4207497105
4"
3.
...
2-0953685757
f
12
1-4295028119
1-4314053333
12
25
2-1052424206
2-1110838400
25
-
...
1-4421408733
i
i
...
2-1269169688
i
j
1 "4509453541
1-4529569299
2-1368210569
2-1428688461
I
1
1-4638541068
I
3
...
2-1589403625
f
13
1-4727095344
1-4748330126
13
26
2-1688733728
2-I75I324I52
26
XXIV
Amount o
THE ENGINEER'S VALUING ASSISTANT.
in n years at the rate of 3 per cent. Payable by half-yearly
and quarterly instalments.
Amount of i in n
Amount of i in n
Amount of i in n
Amount of i in n
Years
years at 3 per cent.
Payable half-yearly
years at 3 per cent.
Payable quarterly.
Years
Years
years nt 3 per cent
Payable half-yearly
years at 3 per cent
Payable quarterly
Year
Ratio = 0*015
Ratio = o'oo75
Ratio = 0*015
Ratio = 0-0075
i
2-1914459083
i
4
J.
4
3-2320167709
i
2-2014064734
2-2078817526
1
|
i
3-2420323025
3-2562568967
^
... ...
2-2244408657
4
1
4
...
3-2806788235
|
27
2-2344275705
2-2411241727
27
40
3-2906627870
3-3052839146
40
*
2-2579326035
i
|
...
3-3300735440
I
4
2-2679439840
2-2748670980
f
3-3400227288
3-3550490956
i
|
... ...
2-2919286013
4
|
... ...
3-3802119638
f
28
2-3019631438
2-3091180658
28
41
3-3901230697
3-4055635535
41
|
...
2-3264364513
i
i
...
3-4311052802
i
2-3364925909
2-3438847247
*
i
3-4409749158
3-4568385698
|
2-3614638601
J
3
4
3-4827648590
a
29
2-37I5399798
2-3791748391
29
42
3-4925894395
3-5088855955
42
i
2-3970186504
1
4
i
3-5352022375
1
4
2-4071130795
2-4149962902
*
3-5449783826
3-5617162542
|
2-4331087624
4
3
4
3-5884291261
|
30
2-4432197757
2-4513570781
30
43
3-598I530583
3-6153423446
43
1
... ...
2-4697422562
i
i
3-6424574122
i
%
2-4798680723
2-4882653231
3-6521253542
3-6697758428
f
...
2-5069273131
f
4
...
3-6972991616
^
31
2-5170660934
2-5257292679
31
44
3-7069072345
3-7250289053
44
I
... ...
2-5446722374
JL
4
i
...
37529666221
|
2-5548220848
2-5637572792
i
37625108430
37811138717
...
2-5829854588
|
3
4
... ...
3-8094722258
4
32
2-5931444161
2-6023578497
32
45
3-8189485057
3-8380432675
45
I
2-6218755336
i
1
4
... ...
3-8668285920
1
4
2-6320415823
2-6415396001
i
3-8762327333
3-8958298064
|
...
2-66I35II47I
|
1
...
3-9250485300
|
33
2-6715222061
2-6813112807
33
46
3-9343762243
3-9544863939
46
i
... ...
270I42III53
i
i
3-9841450419
i
$
27115950391
272l68l7737
3-99339I8676
4-0140261297
|
2-7420943870
f
^
...
4-0441313257
^
34
27522689647
27626600949
34
47
4-0532927457
4-0744623106
47
i
... ...
27833800456
i
i
... ...
4-1050207780
i
27935529992
2-8042553959
^
4-1140921368
4-1358084338
*
2-8252873114
^
...
4-1668269971
4
35
2-8354562942
2-8464769662
35
48
4-1758035189
4-1980781995
48
*
2-8678255435
i
i
...
4-2295637860
i
2-8779881386
2-889334235I
I
i
4-23844057I7
4-2612855144
2
... ...
2-9110042418
1
1
4-2932451558
|
36
2-9211579607
2-9328367736
36
49
4-3020171803
4-3254444944
49
i
... ...
2-9548330494
i
...
4-3578853282
i
2'964975330I
2-9769942973
|
i
4-3665474380
4-3905694681
|
2-9993217545
4
!
...
4-4234987391
^
37
3-0094499600
3-0218166677
37
50
4-4320456495
4-4566749797
50
I
3-0444802927
i
i
4-4901000420
i
J
3-0545917094
3-0673138949
4-4985263343
4-5237757923
i
...
3-0903187491
|
|
...
4-5577041108
1
38
3-1004105851
3-1134961397
38
51
4-5660042293
4-5918868916
51
i
... ...
3-1368473608
i
i
...
4-6263260433
f
if
3-1469167439
3-1603737160
4-6344942927
4-6610234886
1
...
3-1840765189
|
... ...
4-6959811648
|
39
3-1941204950
3-2079570928
39
52
4-7040117071
4-73I20I0235
52
TABLE II.
Amount of 1 in n years at the rate of 3 per cent. Payable by half-yearly
and quarterly instalments.
Years
Amount of i in n
years at 3 per cent.
Pa.\ able half-yearly.
Katio = 0*015
Amount of i in n
years at 3 per cent.
Payable quarterly.
Ratio = 0*0075
Years
Years
Amount of i in n
years at 3 per cent.
Payable half-yearly.
Ratio = 0*015
Amount of i in n
years at 3 per cent.
Payable quarterly.
Ratio = 00075
Years
i
4-7666850312
1
i
6*8230583759
i
47745718827
4-8024351689
6-8252639321
6*8742313137
|
|
...
4.8384534327
|
|
... ...
6*9257880485
3_
4
53
4-8461904610
4-8747418334
53
65
6-9276428911
6-97773H589
65
f
. .. ...
4-9II3023972
i
i
7*0300644449
i
4-9188833179
4-9481371652
7-0315575345
7*0827899282
|
... ...
4-9852481939
|
7*1359108527
^
54
4-9926665676
5-0226375554
5ft
66
7-1370308975
7-1894301840
66
i
5-0603073370
i
i
7-2433509104
*
5-0675565662
5-0982596421
7-2440863609
7-2976760423
|
... ...
5-1364965894
3.
4
|-
... ...
7-3524086126
^
55
5-1435699146
5-1750203138
55
67
7-3527476563
7-4075516772
67
i
4
5-2138329661
i
|
7-4631083147
JL
}
5-2207234634
5-2529367134
i
7-4630388712
7-5190816271
%
3.
4
5-2923337387
1
|
...
7-5754747393
|
56
5-2990343153
5-3320262418
56
68
7-5749844543
7-6322907999
68
i
...
5-3720164386
i
|
... ...
7-6895329809
i
S'SySSlQ^OO
5-4123065619
7-68860922II
7-7472044782
|
... ...
5-4528988611
3
$
^
... ...
7-8053085118
57
5-4591976275
5'4937956026
57
69
7-8039383594
7-8638483256
69
i
... ...
5"534999o696
|
1
... ...
7-9228271881
i
}
5-5410855919
5-5765115626
7-9209974348
7-9822483920
f
5-6183353993
3-
|
8-0421152549
&
58
5-6242018758
5-6604729148
58
70
8-0398123963
8-1024311193
7O
i
57029264617
.1
i
... ...
8-1631993527
i
5-7085649039
5-7456984101
8-1604095822
8-2244233479
5
...
57887911482
|
4"
...
8*2861065230
^
59
57941933775
5-8322070818
59
71
8-2828157260
8*3482523219
71
i
5-8759486349
i
i
... ...
8*4108642143
1
5-8811062781
5-9200182497
8*4070579619
8*4739456959
i
...
5-9644183866
|
3.
...
8-5375002886
f
60
5-9693228723
6-0091515245
60
72
8-533I6383I3
8*6015315408
72
1
6-0542201609
i
i
8*6660430274
i
6-0588627154
6-0996268121
8-66ll6l2888
87310383501
*
2
...
6-1453740132
3.
f
... ...
87965211377
1
61
6-1497456561
6-1914643183
61
73
8-7910787081
8-8624950462
73
1
4
6-2379003007
i
i
8-9289637591
i
6-2419918410
6-2846845529
8-9229448887
8-9959309873
f
3
...
6-3318196871
f
f
... ...
9-0634004697
I
62
6-3356217186
6-3793083347
62
74
9-0567890621
9'i3i3759732
7ft
1
4
...
6-4271531473
i
i
...
9-1998612930
i
6-4306560444
6-4753567959
9-1926408980
9-2688602527
...
6-5239219718
^
f
...
9-3383767046
%
63
6-5271158850
6-5728513866
63
75
9-3305305H5
9-4084145299
75
|
6-6221477720
i
i
... ...
9-4789776389
i
|
6-6250226233
6-6718138803
|
9-4704884691
9-5500699711
f
a
4
6-72 1 8 =524844
S
|-
... ...
9-6216954959
f
6ft
6-7243979627 | 67722663780
6ft
76
9*6125457962 9*6938582121
76
d
XXVI
THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 in n years at the rate of 3 per cent. Payable by half-yearly
and quarterly instalments.
Amount of i in rc Amount of i in n
Amount of i in n
Amount of i in n
Years
years at 3 per cent, years at 3 per cent.
Payable half-yearly. | Payable quarterly.
Years
Years
years at 3 per cent.
Payable half-yearly.
years at 3 per cent.
Payable quarterly.
Years
Ratio = 0-015
Ratio = 0*0075
Ratio = o'ois
Ratio = 0*0075
i
97665621487
i
i
13-9799091478
i
975 6 733983 I
9-8398113649
i
13-9472786641
14-0847584665
|
9-9136099501
4
|
14-1903941550
4
77
9-9030849929
9-9879620247
77
89
14-1564878441
I4-296822IIII
89
i
10-0628717399
i
i
14-4040482769
i
4
10-0516312677
10-1383432779
14-3688351617
14-5120786390
|
... ...
10-2143808525
|
|
...
14-6209192288
|
78
10-2024057368
10-2909887089
78
90
14-5843676891
I4730576I230
90
*
10-3681711242
i
i
4
... .
14-8410554440
i
I
10-3554418228
10-4459324077
14-8031332045
14-9523633598
\
i
... ...
10-5242769007
I
|
... ...
15-0645060850
i
79
10-5107734502
10-6032089775
79
91
15-0251802025
15-1774898806
91
i
...
10-6827330448
i
|
... ...
15-2913210547
i
10-6684350519
107628535427
15-2505579056
15-4060059626
i
|
... ...
10-8435749442
|
|
... ...
15-5215510074
3
4
80
10-8284615777
10-9249017563
80
92
15-4793162742
15-6379626399
92
i
... ...
11-0068385195
1
4
i
4
... ...
157552473597
i
10-9908885013
1 1 -0893898084
i
157115060183
15-8734117149
3.
...
11-1725602319
i
... ...
15-9924623028
^
81
11-1557518289
11-2563544337
81
93
15-9471786086
I6-II24057700
93
.1
... ...
11-3407770919
i
4
i
... ...
16-2332488133
i
1 1 '323088 1 063
11-4258329201
16-1863862877
16-3549981794
i
3.
... ...
11-5115266670
4
4
... ...
16-4776606658
4 a
82
11-4929344279
11-5978631170
82
94
16-4291820820
I6-60I243I208
94
i
...
1 1 -6848470904
i
|
... ...
16-7257524442
j.
4
11-6653284443
11-7724834436
16-6756198132
16-8511955875
|
11*8607770694
|
|
...
16-9775795544
|
83
11-8403083710
II-9497328974
83
95
16-9257541104
I7-I049II40II
95
JL
... ...
12-0393558942
i
i
... ...
17-2331982366
i
12-0179129965
12-1296510634
i
17-1796404221
17-3624472233
a
...
12-2206234463
3
4
|
... ...
17-4926655775
|
84
12-1981816915
12-3122781222
8ft
96
I7-4373350284
17-6238605693
96
i
12-4046202081
i
i
... ...
17-7560395236
1
4
12-3811544169
12-4976548597
I
17-6988950538
17-8892098200
i
|
... ...
12-5913872711
I
j|
...
18-0233788937
1
85
12-5668717331
12-6858226757
85
97
17-9643784796
18-1585542354
97
... ...
12-7809663457
i
i
... ...
18-2947433922
i
4
12-7553748091
12-8768235933
18-2338441568
18-4319539676
4"
... ...
12-9733997703
4
... ...
18-5701936224
^
86
12-9467054313
13-0707002685
86
98
18-5073518192
18-7094700745
98
i
...
13-1687395206
J.
i
... ...
I8-84979IIOOI '
13-1409060127
13-2674959995
I
18-7849620965
18-9911645333
|
...
1 3-367002 2 1 95
4
|
... ...
I 9'i3359 82 673 I
87
I3'3380I96029
13-4672547361
87
99
19-0667365279
19-2771002543 99
*
... ...
13-5682591466
i
i
... ...
19-4216785063 i \
13-5380898970
13-6700210902
i
I9'3527375758
19-5673410950 i
|
13-7725462484
2
4
|
19-7140961533 i f
83
13-7411612454
13-8758403453
88
1OO
19-6430286395
19-8619518744 |ioo
TABLE III.
Ike sum, to which 1 per annum will amount in
n years up to 100, at the rates of J, j, i, ij, 1^5 if? 2,
2i, 2l, 2|, 3, 31, 4, 41, 5, Si, 6, 7, 8, 9, and 10 per cent.
Calculated to 10 places of decimals to 7 per cent., and
to 6 places to 10 per cent.
TABLE III. xxix
Amount of 1 per annum in n years at the following rates per cent.
Years
| per cent.
Years
\ per cent.
Years
| per cent.
Years
| per cent.
I
i-
5^
57-9283888021
I
I*
51
61-8472142443
2
2-005
52
59-2180307461
2
2-0075
52
63-3110683512
3
3-015025
53
60-5141208998
3
3-02255625
53
647859013638
4
4-030100125
54
61-8166915043
4
4-0452254219
54
66*2717956241
5
5-0502506256
55
63-1257749619
5
5-0755646125
55
67-7688340912
6
6-0755018788
56
64-4414038367
6
6-1136313471
56
69-2771003469
7
7-1058793881
57
657636108559
7
7-1594835822
57
70-7966785995
8
8-1414087851
58
67*0924289101
8
8-2131797091
58
72-3276536890
9
9-1821158290
59
68-4278910547
9
9-2747785569
59
73-8701110917
10
10-2280264082
60
69-7700305100
10
10-3443393961
60
75-424I369249
ii
11-2791665402
61
71-1188806625
ii
11-4219219416
61
76-9898179518
12
123355623729
62
72-4744750658
12
12-5075863561
62
78-5672415865
13
13-3972401848
63
73-8368474412
13
I3-60I3932538
63
80-1564958984
H
14-4642263857
64
75-2060316784
H
14-7034037032
64
81-7576696176
15
I5-5365475I76
65
76-5820618368
15
15-8136792310
65
83-3708521398
16
16-6142302552
66
77-9649721460
16
16-9322818252
66
84-9961335308
17
17-6973014065
67
79-3547970067
17
18-0592739389
67
86-6336045323
18
18-7857879135
68
807515709917
18
19-1947184934
68
88-2833565663
19
19-8797168531
69
82-1553288467
19
20-3386788821
69
89-9454817406
20
20-979 ii 54374
70
83-5661054909
20
21-4912189738
70
91-6200728536
21
22-0840110146
71
84-9839360184
21
22-6524031161
71
93-3072234000
22
23-1944310696
72
86-4088556985
22
23-8222961394
72
95-0070275755
23
24-3104032250
73
87-8408999770
23
25-0009633605
73
967195802824
24
25-4319552411
74
89-2801044769
24
26-1884705857
74
98-4449771345
25
26-5591150173
75
90-7265049993
25
27-3848841151
75
100-1833144630
26
27-6919105924
76
92-1801375243
26
28-5902707459
76
101-9346893215
27
28-8303701454
77
93-6410382119
27
29-8046977765
77
103-6991994914
28
29-9745219961
78
95-1092434030
28
31-0282330098
78
105-4769434876
29
31-1243946061
79
96*5847896200
29
32-2609447574
79
107-2680205637
30
32-2800165791
80
98-0677135681
30
33-5029018431
80
109-0725307180
31
33-4414166620
81
99-5580521359
31
347541736069
81
110-8905746984
32
34-6086237453
82
101-0558423966
32
36-0148299090
82
112-7222540086
33
35-7816668640
83
102-5611216086
33
37-2849411333
83
114-5676709137
34
36-9605751984
84
104-0739272166
34
38-5645781918
84
116-4269284455
35
38-1453780744
85
105-5952968527
35
39-8538125282
85
118-3001304089
36
39-3361049647
86
107-1222683370
36
41-1527161216
86
120-1873813869
37
40-5327854896
87
108-6578796787
37
42-4613614925
87
122-0887867473
38
4i7354494i7o
88
110-2011690771
38
437798217037
88
124-0044526480
39
42-9441266641
89
1117521749224
39
45-1081703665
89
125-9344860428
40
44-1588472974
90
II3-3I0935797I
40
46-4464816442
90
127-8789946881
4i
4537964I5339
9 1
1 14-8774904760
4i
47-7948302566
91
129-8380871483
42
46-6065397416
92
116-4518779284
42
49-1532914835
92
131-8118728019
43
47-8395724403
93
118-0341373181
43
50-5219411696
93
133-8004618479
44
49-0787703025
94
119-6243080047
44
51-9008557284
94
135-8039653118
45
50-3241641540
95
I2I-2224295447
45
53-2901121464
95
137-8224950517
46
5I-5757849748
96
122-8285416924
46
54-6897879875
96
139-8561637645
47
52-8336638996
97
124-4426844009
47
56-0999613974
97
141-9050849928
48
54-0978322191
98
126-0648978229
48
57-5207111079
98
I43'969373 I 32
49
55-3683213802
99
127-6952223120
49
58-9521164412
99
146-0491434287
so
56-6451629871
ico 129-3336984235
50
60-3942573I45
100
1 48- I445I20044
XXX THE ENGINEERS VALUING ASSISTANT.
Amount of 1 per annum in n years at the following rates per cent.
Years
1 per cent.
Years
1 per cent.
Years
1| per cent.
Years
1^ per cent.
I
I-
51
66-1078140061
I
I-
51
707428122595
2
2'01
5 2
677688921462
2
2-0125
52
72-6270974128
3
3-0 01
53
69-4465810676
3
3-03765625
53
74-534936I304
4
4-060401
54
71-1410468783
4
4-0756269531
54
76-4666228320
5
5-10100501
55
72-8524573471
5
5-1265722900
55
78-4224556174
6
6*1520150601
56
74-5809819206
6 6-1906544437
56
80-4027363127
7
7-2135352107
57
76-3267917398
7
7-2680376242
57
82-4077705166
8
8-2856705628
58
78-0900596571
8
8-3588880945
58
84-4378676480
9
9-3685272684
59
79-870960253?
9
9-4633741957
59
86-4933409936
10
10-4622125411
60
81-6696698563
10
10-5816663731
60
88-5745077560
ii
11-5668346665
61
83-4863665548
ii
II7I39372028
61
90-6816891030
12
12-6825030132
62
85-3212302204
12
12-8603614178
62
92-8l52I02l68
13
13-8093280433
63
87-1744425226!
13
14-0211159356
63
94-9754003445
14
14-9474213238
64
89-0461869478
H
15-1963798848
64
97-1625928488
15
16-0968955370
65
90-9366488173
15
16-3863346333
65
99-3771252594
16
17-2578644924
66
92-8460153054
16
17-5911638162
66
101-6193393252
17
18-4304431373
67
94-7744754585
17
18-8110533639
67
103-8895810667
18
19-6147475687
68
967222202131
18
20-0461915310
68
106-1882008300
19
20-8108950443
69
98-6894424152
19
21-2967689251
69
108-5155533404
20
22-0190039948
70
100-6763368393
20
22-5629785367
70
IIO-87I9977572
21
23-2391940347
71
102-6831002077
21
23-8450157684
71
113-2578977291
22
24-4715859751
72
104-7099312098
22
25-1430784655
72
115-6736214508
23
25-7163018348
73
1067570305219
23
26-4573669463
73
118-1195417189
24
26-9734648532
74
108-8246008271
24
27-7880840331
74
120-5960359904
25
28-2431995017
75
110-9128468354
25
29-1354350836
75
123-1034864403
26
29-5256314967
76
113-0219753037
26
30-4996280221
76
125-6422800208
27
30-8208878117
77
115-1521950568
27
31-8808733724
77
I28-2I280852IO
28
32-1290966898
78
117-3037170074
28
33-2793842895
78
130-8154686275
29
33-4503876567
79
119-4767541774
29
34-6953765932
79
1334506619854
30
34-7848915333
80
121-6715217192
30
36-1290688006
80
136-1187952602
31
36-1327404486
81
123-8882369364
3 1
37-5806821606
81
I38-82028020IO
32
37-4940678531
82
126-1271193058
32 39-0504406876
82
I4I-5555337035
33
38-8690085316
83
128-3883904988
33
40-5385711962
83
144-3249778748
34
40-2576986169
84
130-6722744038
34
42-0453033361
84
147-1290400982
35
41-6602756031
85
132-9789971478
35
43-5708696278
85
149-9681530994
36
43-0768783591
86
135-3087871193
36
45-1155054982
86
152-8427550132
37
44-5076471427
87
137-6618749905
37
46-6794493169
87
i55753 2 89458
38
* 45-9527236141
88
140-0384847404
38
48-2629424334
88
158-7002055690
39
47-4122508503
89
142-4388786778
39
49-8662292138
89
161-6839581386
40
48-8863733588
90
144-8632674646
40
51-4895570789
90
164-7050076153
41
50-3752370923
91
I47-3IIOCOI393
4i
53-1331765424
91
167-7638202105
42
51-8789894633
92
149-7850191406
42
54-7973412492
92
170-8608679631
43
53-3977793579
93
152-2828693321
43
56-4823080148
93
1 73-9966288 1 27
44
54-9317571515
94
154-8056980254
44
58-1883368650
94
177-1715866728
45
56-4810747230
95
I57 ! 3537550056
45
59-9156910758
95
180-3862315062
46
58-0458854702
96
159-9272925557
46
61-6646372143
96
183-6410594001
47
59-6263443249
97
162-52656548.12
47
63-4354451794
97
186-9365726426
-48
61-2226077681
98
165-1518311361
48
65-2283882442
98
190-2732798006
49
62-8348338458
99
167-8033494474
49
67-0437430972
99
193-6516957981
.50
64-4631821843
ICO
170-4813829419
50
68-8817898859
100
197-0723419956
TABLE III. xxxi
Amount of 1 per annum in n years at the following rates per cent.
Years
1J per cent.
Years
1J per cent.
Years
If per cent.
Years
If per cent.
I
i-
51
75-7880704611
I
i
51
81-2830136099
2
2-015
52
77-9248915180
2
2-0175
52
837054663481
3
3-045225
53
80-0937648907
3
3-05280625
53
86-1703120092
4
4-090903375
54
82-2951713641
4
4-1062343594
54
88-6782924693
5
5-1522669256
55
84-5295989346
5
5-1780893907
55
91-2301625875
6
6-2295509295
56
86-7975429186
6
6-2687059550
56
93-8266904328
7
7-3229941935
57
89-0995060624
7
7-3784083092
57
96-4686575154
8
8-4328391064
58
91-4359986533
8
8-5075304546
58
99-1568590219
9
9*5593316922
59
93-8075386331
9
9-6564123376
59
101-8921040548
10
10-7027216683
60
96-2146517126
10
10-8253994517
60
104-6752158758
ii
11-8632624934
61
98-6578714883
ii
12-0418439421
61
107-5070321536
12
13-0412114308
62
101-1377395606
12
13-2251037111
62
110-3884052163
13
14-2368296022
63
103-6548056540
13
14-4565430261
63
113-3202023076
H
15-4503820463
64
106-2096277388
H
15-7095325290
64
116-3033058480
15
16-6821377770
65
108-8027721549
15
16-9844493483
65
119-3386137003
16
17-9323698436
66
111-4348137372
16
18-2816772119
66
122-427039440!
17
19-2013553913
67
114-1063359433
17
19-6016065631
67
125-5695126303
18
20-4893757221
68
116-8179309824
18
20-9446346780
68
128-7669791013
19
21-7967163580
69
119-5701999472
19
22-3111657848
69
132-0204012356
20
23-1236671033
TO
122-3637529464
20
23-7016111861
70
I35-3307582572
21
24-4705221099
71
125-1992092406
21
25-1163893818
71
138-6990465267
22
25*83757994i5
72
128-0771973792
22
26-5559261960
72
142-1262798409
23
27-2251436406
73
I30-9983553399
23
28-0206549044
73
145-6134897381
24
28-6335207953
74
I33-9633306700
24
29-5110163653
74
149-1617258086
25
30-0630236072
75
136-9727806300
25
31-0274591517
75
152-7720560102
26
31-5139689613
76
140-0273723395
26
32-5704396868
76
156-4455669904
27
32-9866784957
77
143-1277829246
27
34-1404223813
77
160-1833644137
28
34-4814786731
78
146-2746996684
28
35737879773
78
163-9865732910
29
35-9987008532
79
149-4688201635
29
37-3632926691
79
167-8563383235
30
37-5386813660
80
1527108524659
30
39-0171502908
80
1717938242442
31
39-1017615865
81
156-0015152529
31
40-6999504209
81
175-8002161684
32
40-6882880103
82
I59-34I53798I7
32
42-4121995532
82
179-8767199514
33
42-2986123305
83
162-7316610514
33
44-1544130454
83
184-0245624505
34
43-93309I5I54
84
166-1726359672
34
45-9271152737
84
188-2449923951
35
45-5920878882
85
169-6652255067
35
47-7308397910
85
192-5392797620
36
47-2759692065
86
173-2102038893
36
49-5661294873
86
196-9087171579
37
48-9851087446
87
176-8083569476
37
51-4335367534
87
201-3546197081
38
50-7198853757
88
180-4604823018
38
53-3336236466
88
205-8783255530
39
52-4806836564
89
184-1673895364
39
55-2669620604
89
210-4811962502
40
54-2678939112
90
187-9299003794
40
57-2341338964
90
215-1646171846
41
56-0819123199
91
191-7488488851
41
59-2357312396
91
219-9299979853
42
57-9231410047
92
195-6250816184
42
61-2723565363
92
2247787729500
43
597919881198
93
I99-5594578427
43
63-3446227757
93
229-7124014766
44
61-6888679416
94
203-5528497103
44
65-4531536743
94
234-7323685025
45
63-6142009607
95
207-6061424560
45
67-5985838636
95
239-8401849513
46
65-5684139751
96
2117202345928
46
69-7815590812
96
245-0373881879
47
67-5519401847
97
215-8960381117
47
72-0027363651
97
250-3255424812
48
69-5652192875
98 220-1344786834
48
74-2627842515
98
255-7062394746
49
71-6086975768
99 224-4364958636
49
76-56238297591 99
261-1810986654
50
73-6828280405
100 228-8030433016 |i so
78-9022246780 ,100
266-7517678920
xxxii THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 per annum in n years at the following rates per cent.
Years
2 per cent.
Years
2 per cent.
Years
2J per cent.
Years
2J per cent.
I
I-
51
87-2709894828
I
I-
51
93-7996641635
2
2 '02
52
90-0164092724
2
2-0225
52
96-9101566072
3
3-0604
53
92-8167374579
3
3-06800625
53
100-0906351308
4
4-121608
54
95-6730722070
4
4-1370363906
54
103-3426744213
5
5-20404016
55
98-5865336512
5
5-2301197094
55
106-6678845958
6
6-3081209632
56
101-5582643242
6
6-3477974029
56
110-0679119992
7
7-4342833825
57
104-5894296107
7
7-4906228444
57
113-5444400192
8
8-5829690501
58
107-6812182029
8
8-6591618584
58
117-0991899196
9
9-7546284311
59
110-8348425670
9
9-8539930003
59
120-7339216928
10
10-9497209997
6O
114-0515394183
10
11-0757078428
60
124-4504349309
ii
12-1687154197
61
II7'33 2 5702067
ii
12-3249112692
61
128-2505697168
12
13-4120897281
62
120-6792216108
12
13-6022217728
62
132-1362075354
13
14-6803315267
63
124-0928060430
13
14-9082717627
63
136-1092722050
H
I5-973938I53I
64
127-5746621639
14
16-2437078773
64
140-1717308296
15
17.2934169162
65
131-1261554073
15
17-6091913046
65
144-3255947733
16
18-6392852545
66
1347486785154
16
19-0053981089
66
148-5729206557
17
20-0120709596
67
138-4436520857
17
20-4330195664
67
152-9158113704
18
21-4123123788
68
142-2125251275
18
21-8927625066
68
157-3564171262
19
22-8405586264
69
146-0567756300
19
23'3853496630
69
161-8969365116
20
24-2973697989
70
149-9779111426
20
24-9115200304
70
166-5396175831
21
257833I7I949
71
153-9774693655
21
26-4720292311
71
171-2867589787
22
27-3989835388
72
158-0570187528
22
28-0676498888
72
176-1407110557
23
28-8449632096
73
162-2181591278
23
29-6991720113
73
181-1038770545
24
30-4218624738
74
166-4625223104
24
31-3674033816
74
186-1787142882
25
32-0302997232
75
170-7917727566
25
33-0731699577
75
191-3677353597
26
33-6709057177
76
175-2076082117
26
34-8173162817
76
196-6735094053
27
35-3443238320
77
179-7117603759
27 ! 36-6007058980
77
202-0986633669
28
37-0512103087
78
184-3059955835
28
38-4242217808
78
207-6458832927
29
38-7922345149
79
188-9921154951
29
40-2887667708
79
213-3179156667
30
40-5680792052
80
I9377i9578o5o
30
42-1952640232
80
219-1175687692
31
42-3794407893
81
198-6473969611
31
44-1446574637
81
225-0477140666
32
44-2270296051
82
203-6203449003
32
46-1379122566
82
231*1 1 12876331
33
46-1115701972
83
208-6927517984
33
48-1760152824
83
237-3112916048
34
48-0338016011
84
213-8666068343
34
50-2599756262
84
243-6507956659
35
49-994477633I
85
219-1439389710
35
52-3908250778
85
250-1329385684
36
51-9943671858
86
224-5268177504
36
54-5696186421
86
256-7609296862
37
54-0342545295
87
230-0173541054
37
567974350615
87
263-5380506041
38
56-1149396201
88
235-6177011875
38
59-0753773504
88
270-4676567427
39
58-2372384125
89
241-3300552113
39
61-4045733408
89
277-553I790I94
40
60-4019831808
9O
247-1566563155
40
63-7861762410
90
284-7981255474
41
62-6100228444
91
253-0997894418
41
66-2213652064
91
292-2060833722
42
64-8622233013
92
259-1617852306
42
68-7113459235
92
299-7807202481
43
67-1594677673
93
265-3450209353
43
71-2573512068
93
307-5257864536
44
69-5026571226
94
271-6519213540
44
73-8606416089
94
315-4451166489
45
71-8927102651
95
278-0849597810
45
76-5225060451
95
323-5426317735
46
74-3305644704
96
284-6466589766
46
79-2442624312
96
331-8223409884
47
76-8171757598
97
291-3395921562
47
82-0272583359
97
340-2883436606
48
793535192750
98
298-1663839993
48
84-8728716484
98
348-9448313930
49
81-9405896605
99 305-1297116793
49
877825112605
99 357-7960900993
50
84-5794014537 1001312-2323059129
50 907576177639
100:366-8465021265
TABLE III, xxxiii
Amount of 1 per annum in n years at the following rates per cent.
Years
2i per cent.
Years
2i percent.
Years
2 per cent.
Years
2J per cent.
I
I-
51
100-9214575078
I
r
51
108-6940225574
2
2'025
52
104-4444939455
2
2-0275
52
112-6831081777
3
3-075625
53
108-0556062941
3
3-08325625
53
116-7818936526
4
4-152515625
54
1117569964515
4
4-1680457969
54
120-9933957281
5
5-2563285156
55
115-5509213628
5
5-2826670563
55
125-3207141106
6
6-3877367285
56
119-4396943968
6
6-4279404003
56
129-7670337486
7
7-5474301467
57
123-4256867568
7
7-6047087613-
57
134-3356271767
8
8-7361159004
58
127-5113289257
8
8-8138382523
58
139-0298569241
9
9-9545I87979
59
131-6991121488
9
10-0562188042
59
I43-853I779855
10
11-2033817679
60
135-9915899525
10
11-3327648213
60
148-8091403842
ii
12-483466312 1
61
140-3913797014
ii
12-6444158539
61
I53-90I39I7448
12
137955529699
62
144-9011641939
12
13-9921372899
62
159-1336800177
13
15-1404417941
63
149-5236932987
13
15-3769210654
63
164-5098562182
14
16-5189528390
64
154-2617856312
H
16-7997863947
64
170-0338772642
'5
17-9319266599
65
159-1183302720
15
18-2617805205
65
1 75 7098088890
16
19-3802248264
66
164-0962885288
16
19-7639794849
66
181-5418286334
17
20-8647304471
67
169-1986957420
17
21-3074889207
67
187-5342289209
18
22-3863487083
68
174-4286631356
18
22-8934448660
68
193-6914202162
19
23-9460074260
69
179-7893797139
19
24-5230145998
69
200-0179342721
20
25-5446576116
70
185-2841142068
20
26-1973975013
70
206-5184274646
21
27-1832740519
71
190-9162170620
21
27-9178259326
71
213-1976842199
22
28-8628559032
72
196-6891224885
22
29-6855661458
72
220-0606205359
23
30-5844273008
73
202*6063505507
23
31-5019192148
73
227-1122876008
24
32-3490379833
74
208-6715093145
24
33-3682219932
74
234-3578755098
25
34-1577639329
75
214-8882970474
25
35-2858480980
75
241-8027170863
26
36-0117080312
76
221-2605044735
26
37-2562089207
76
249-4522918062
27
37-9I20007320
77
2277920170854
27
39-2807546660
77
257-3122298308
28
39-8598007503
78
234-4868175125
28
41-3609754193
78
265-3883161511
29
41-8562957690
79
241-3489879503
29
43-4984022433
79
273-6864948452
30
43-9027031633
80
248-3827126491
30
45-6946083050
8O
282-2128734535
31
46-0002707423
81
255-5922804653
31
47-9512100334
81
290-9737274734
32
48-1502775109
82
262-9820874770
32
50-2698683093
82
299-9755049789
33
50-3540344487
83
270-5566396639
33
52-6522896878
83
309-2248313659
34
52-6128853099
84
278-3205556555
34
55-1002276543
84
318-7285142284
35
54-9282074426
85
286-2785695469
35
57-6154839148
85
328-4935483697
36
57-3014126287
86
294-4355337855
36
60-1999097224
86
338-5271209499
37
597339479444
87
302-7964221302
37
62-8554072398
87
348-8366167760
38
62-2272966430
88"
311-3663326834
38
65-5839309389
88
359-4296237373
39
64-7829790591
89
320-1504910005
39
68-3874890397
89
370-3139383901
40
67-4025535356
90
329-1542532755
40
71-2681449883
90
381-4975716958
41
70-0876173740
9 1
338-3831096074
4i
74-2280189755
91
392-9887549174
42
72-8398078083
92
347-8426873476
42
77-2692894973
92
404-7959456777
'43
75-6608030035
93
357-53875453I3
43
80-3941949585
93
416-9278341838
44
78-5523230786
94
367-4772233946
44
83-6050353198
94
429-3933496238
45
81-5161311556
95
377-6641539794
45
86-9041737911
95
442-2016667385
46
84-5540344344
96
388-1057578289
46
90-2940385704
96
455-3622125738
47
87-6678852953
97
398-8084017747
47
93-7771246311
97
468-8846734196
48
90-8595824277
98
409-7786118190
48
97-3559955584
98
482-7790019386
49
so
94-1310719884
97-4843487881
99
100
421-0230771145
432-5486540424
49 101-0332854363
so 1104-8117007858
99
100
497-0554244919
5117244486654
xxxiv THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 per annum in n years at the following rates per cent.
Years
3 per cent.
Years
3 per cent.
Years
3| per cent.
Years
3J per cent.
I
!
51
117-1807733090
I
I'
51
136-5828370186
2
2-03
52
121-6961965083
2
2-035
52
142-3632363142
3
3-0909
53
126-3470824035
3
3-106225
53
148-3459495852
4
4-183627
54
131-1374948756
4
4-214942875
54
154-5380578206
5
5-30913581
55
136-0716197219
5
5-3624658746
55
160-9468898443
6
6-4684098843
56
141-1537683135
6
6-5501521813
56
167-5800309888
7
7-6624621808
57
146-3883813629
7
7-7794075076
57
174-4453320734
8
8-8923360463
58
151-7800328038
8
9-0516867704
58
181-5509186959
9
10-1591061276
59
I57-3334337879
9
10-3684958073
59
188-9052008503
10
11-4638793115
60
163-0534368016
10
H73I393l6o6
60
196-5168828800
ii
12-8077956908
6l
168-9450399056
ii
I3'i4i99i92i2
61
204-3949737808
12
14-1920295615
62
175-0133911028
12
14-6019616385
62
212-5487978630
13
15-6177904484
63
181-2637928359
13
16-1130302958
63
220-9880057882
H
17-0863241618
64
187-7017066209
14
17-6769863562
64
229-7225859908
15
18-5989138867
65
I94-3327578I96
15
19-2956808786
65
238-7628765004
16
20-1568813033
66
201-1627405541
16
20-9710297094
66
248-1195771780
17
217615877424
67
208-1976227708
17
22-7050157492
67
257-803762379I
18
23-4I44353747
68
2I5-44355I4539
18
24-4996913004
68
267-8268940623
19
25-1168684359
69
222-9068579975
19
26-3571804960
69
278-2008353545
20
26-8703744890
70
230-5940637374
20
28-2796818133
70
288-9378645919
21
28-6764857237
71
238-5118856496
21
30-2694706768
71
300-0506898525
22
30-5367802954
72
246-6672422190
22
32-3289021505
72
311-5524639973
23
32-4528837042
73
255-0672594856
23
34-4604137267
73
323-4568002372
24
34-4264702154
74
263-7192772702
24
36-6665282071
74
335-7777882455
25
36-4592643218
75
272-6308555883
25
38-9498566944
75
348-5300108340
26
38-5530422515
76
281-8097812559
26
41-3131016786
76
361-7285612132
27
40-7096335190
77
291-2640746936
27
43-7590602373
77
375*3890608856
28
43-9309225246
78
301-0019969344
28
46-2906273456
78
389-5276779855
29
45-2188502003
79
311-0320568424
29
48-9107993027
79
404-1611467150
30
47-5754I57063
so
321-3630185477
3O
51-6226772782
so
419-3067868500
31
50-0026781775
81
332-0039091041
31
54-4294709829
81
434-9825243897
32
52-5027585229
82
342-9640263773
32
57-3345024673
82
451-2069127433
33
55-0778412785
83
354-2529471686
33
60-3412100536
83
467-9991546893
34
57-7301765169
84
365-8805355836
34
63-4531524055
84
485-3791251034
35
60-4620818124
85
377-8569516512
35
66-6740127396
85
503-3673944820
36
63-2759442668
86
390-1926602007
36
70-0076031855
86
521-9852532888
37
66-1742225948
87
402-8984400067
37
73-4578692969
87
541-2547371539
38
69-1594492726
88
415-9853932069
38
77-0288947223
88
561-1986529543
39
72-2342327508
89
429-4649550031
39
80-7249060376
89
58r84o6o58o7<;
40
75-4012597333
9O
443-3489036532
40
84-5502777488
9O
603-2050270105
41
78-6632975253
91
457-6493707628
4i
88-5095374700
91
625-3172029562
42
82-0231964511
92
472-3788518857
42
92-6073712814
92 1648-2033050596
43
85-4838923446
93
487-5502174423
43
96-8486292763
93 671-890420736;
44
89-0484091150
94
503-1767239655
44
101-2383313009
94 696-40658 5462^
45
927198613884
95
519-2720256845
45
105-7816728964
95 721 -78081 5953^
46
96-5014572301
96
535-8501864550
46
110-4840314477
96 748-043 1445 1 if
47
100-3965009470
97
552-9256920487
47
115-3509725484
97 775-224654569^
48
104-4083959754
98
570-5134628101
48
120-3882565875
98 1803-357517479;
49
108-5406478546
99
588-6288666944
49
125-6018455681
99 1832-475030591;
SO
1 127968672903 100
607-2877326953 50
130-9979101629
ioo 862-611656662:
TABLE III. xxxv
. Amount of 1 per annum in n years at the following rates per cent.
Years
4 per cent.
Years
4 per cent.
Year
4J per cent.
Years
4i per cent.
I
j.
51
1597737670032
I
V
51
187-5356645512
2
2*04
52
167-164717683'
2
2-045
52
196-9747694560
3
3-I2I6
53
174-8513063906
3
3-137025
53
206-8386340816
4
4-246464
54
182-8453586462
4
4-278191125
54
217-1463726152
5
5-41632256
55
191-1591729921
5
5-4707097256
55
227-9179593829
6
6-6329754624
56
199-8055399118
6
6*7168916633
56
239-1742675552
7
7-8982944809
57
208-7977615082
7
8-0191517881
57
250-9371095951
8
9-2142262601
58
218-1496719686
8
9-3800136186
58
263-2292795269
9
10-5827953105
59
227-8756588473
9
10-8021142314
59
276-0745971056
10
I2-006IO7I230
60
237-9906852012
10
12-2882093718
60
289-4979539754
ii
13-4863514079
61
248-5103126092
ii
13-8411787936
61
303-5253619043
12
15-0258054642
62
259-4507251136
12
15-4640318393
62
318-1840031900
J3
16-6268376828
63
270-8287541182
13
17-1599132721
63
333-5022833335
*4
18-2919111901
64
282-6619042829
H
18-9321093693
64
349-5098860835
15
20-0235876377
65
294-9683804542
15
20-7840542909
65
366-2378309573
16
21-8245311432
66
3077671156724
16
22-7193367340
66
3837185333503
17
23-6975123889
67
321-0778002993
17
24-7417068870
67
401-9858673511
18
25-6454128845
68
334-9209123112
18
26-8550836970
68
421-0752313819
*9
27-6712293998
69
349-3177488037
19
29-0635624633
69
441-0236167941
2O
297780785858
70
364-2904587558
20
31-3714227742
70
461-8696795498
21
31-9692017189
71
379-8620771061
21
337831367990
71
483-6538151296
22
34-2479697876
72
396-0565601903
22
36-3033779550
72
506-4182368104
2 3
36-6178885791
73
412-8988225979
23
38-9370299629
73
530-2070574669
24
39-0826041223
74
430-4147755018
24
41-6891963113
74
555-0663750529
25
41-6459082872
75
448-6313665219
25
44-5652101453
75
581-0443619302
26
44-3117446187
76
467-5766211828
26
47-5706446018
76
608-1913582171
27
47-0842144034
77
487-2796860301
27
50-7113236089
77
636-5599693369
28
49-9675829795
78
507-7708734713
28
53-993333I7I3
78
666-2051679570
29
52-9662862987
79
529-0817084102
29
57-4230331640
79
697-1844005151
30
56-0849377507
so
551-2449767466
30
61-0070696564
80
729-5576985383
31
59-3283352607
81
574-2947758164
31
64-7523877909
81
763-3877949725
32
62-7014686711
82
598-2665668491
32
68-6662452415
82
798-7402457462
33
66-2095274180
83
623-1972295231
33
72-7562262774
83
835-6835568048
34
69-8579085147
84
649-1251187040
34
77-0302564599
84
874-2893168610
35
73-6522248553
85
676-0901234521
35
81-4966180005
85
914-6323361199
36
77-5983I38495
86
704-1337283902
36
86-1639658106
86
956-7907912453
37
81-7022464035
87
733-2990775258
37
91-0413442720
87
000-8463768513
38
85-9703362596
88
763-6310406269
38
96-1382047643
88
046-8844638096
39
90-4091497100
89
795-1762822519
39
01-4644239787
89
094-9942646810
40
95-0255156984
9O
827-9833335420
40
07-0303230577
90
145-2690965917
41
99-8265363263
9 1
862-1026668837
41
12-8466875953
91
197-8061118883
42
04-8195977794
92
897-5867735591
42
18-9247885371
92
252-7073869233
43
10-0123816905
93
934-4902445014
43
25-2764040213
93
310-0792193348
44
115-4128769582
94
972-8698542815 ;
44
31-9138422022
94
370-0327842049
45
121-0293920365
95
012-7846484527
45
38-8499651013
95
432-6842594941
46
126-8705677179
96
054-2960343908
46
46-0982135309
96
498-1550511713
47 132-9453904267
97
[097-4678757665
47
53-6726331398
97
566-5720284740
48 139-2632060437
98
[142-3665907971
48
161-5879016311
98
638-0677697553
49 I45-8337342855
50 152-6670836569
99
00
[189-0612544290
[237-6237046062
49
50
169-8593572045
178-5030282787
99
00
712-7808193943
790-8559562671
xxxvi THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 per annum in n years at the following rates per cent.
Years
5 per cent.
Years
5 per cent.
Years
5i per cent.
Years
5$ per cent.
I
I' .
51
220-8153955009
I
I-
51
260-7594376502
2
2-05
52
232-8561652759
2
2-055
52
276-1012067210
3
3-I525
53
245-4989735397
3
3-168025
53
292-2867730906
4
43IOI25
54
2587739222167
4
4-342266375
54
309-3625456106
5
5-52563125
55
272-7126183276
5
5-5810910256
55
327-3774856192
6
6-8019128125
56
287-3482492439
6
6-8880510320
56
346-3832473282
7
8-1420084531
57
302-7156617061
7
8-2668938388
57
366-4343259313
8
9-5491088758
58
318-8514447914
8
9-7215729999
58
387-5882138575
9
11*0265643196
59
3357940I703IO
9
11-2562595149
59
409-9055656197
10
12-5778925355
60
353-5837I78826
10
I2-8753537882
60
433'45037I7288
ii
14*2067871623
61
372-2629037767
ii
14-5834982466
61
458-2901421738
12
15-9171265204
62
391-8760489655
12
16-3855906502
62
484-4960999934
13
177129828465
63
412-4698514138
13
18-2867981359
63
512-1433854930
14
19-5986319888
64
434-0933439845
14
20-2925720334
64
541-3112716952
15
21-5785635882
65
456-7980111837
15
22-4086634952
65
572-0833916384
16
23-6574917676
66
480-6379117429
16
24-6411399875
66
604-5479781785
17
25-8403663560
67
505-6698073301
17
26-9964026868
67
638-7981169783
18
28-1323846738
68
531-9532976966
18
29-4812048345
68
674-9320134121
19
30-5390039075
69
559-5509625814
19
32-1026711004
69
713-0532741498
20
33-0659541029
70
588-5285107105
20
34-8683180110
70
753-2712042280
21
357192518080
71
618-9549362460
21
37-7860755016
71
795-7011204606
22
38-5052143984
72
650-9026830583
22
40-8643096542
72
840-4646820859
23
41-4304751184
73
684-4478172112
23
44-1118466851
73
887-6902396006
24
44-5019988743
74
719-6702080718
24
47-5379982528
74
937-5132027787
25
477270988180
75
756-6537184754
25
51-1525881567
75
990-0764289315
26
5I-II34537589
76
795-4864043992
26
54-9659805053
76
1045-5306325227
27
54-6691264468
77
836-2607246191
27
58-9891094331
77
1104-0348173115
28
58-4025827692
78
879-0737608501
28
63-2335104519
78
1165-7567322636
29
62-3227119076
79
924-0274488926
29
677H3535268
79
I230-873352538I
30
66-4388475030
so
971-2288123372
30
72-4354779708
80
1299-5713869277
31
70-7607898782
81
1020-7902624041
31
77-4194292592
81
1372-0478132087
32
75-2988293721
82
1072-8297755243
32
82-6774978684
82
1448-5104429352
33
80-0637708407
83
1127-4712643005
33
88-2247602512
83
1529-1785172966
34
85-0669593827
84
1184-8448275156
34
94-0771220650
84
1614-2833357480
35
90-3203073518
85
1245-0870688914
35
100-2513637786
85
1704-0689192141
36
95-8363227194
86
1308-3414223359
36
106-7651887864
86
1798-7927097709
37
101-6281388554
87
I374-7584934527
37
113-6372741696
87
1898-7263088083
38
107-7095457982
88
1444-4964181254
38
120-8873242490
88
2004-1562557927
39
114-0950230881
89
1517-7212390316
39
128-5361270827
89
2115-3848498613
40
120-7997742425
90
I 594-6073009832
40
136-6056140722
90
2232-7310166037
41
127-8397629546
91
1675-3376660324
41
145-1189228462
91
2356-5312225169
42
I 35' 2 3i75 II02 4
9 2
1760-1045493340
42
154-1004636027
92
2487-1404397553
43
1 42 -99333865 7 5
93
1849-1097768007
43
163-5759891009
93
2624-9331639419
44
151-1430055904 94
1942-5652656408
44
173-5726685014
94
2770-3044879587
45
159-7001558699 95
2040-6935289228
45
184-1191652690
95
2923-6712347964
46
168-6851636634 96
21437282053689
46
195-2457193588
96
3085-4731527102
47
178-1194218465 97
2251-9416156374
47
206-9842339235
97
3256*1741761092
48 ; 1 88-0253929389! 98
2365-5103464193
48
219-3683667893
98
3436-2637557952
49 198-4266625858! 99
2484-7858637402
49
232-4336269627
99
3626-2582623640
50 209-3479957151 100 2610-0251569272
50
246-2174764457
LOO (3826-7024667940
TABLE III. xxxvii
Amount of 1 per annum in n years at the following rates per cent.
Years
6 per cent.
Years
6 per cent.
Years
7 per cent.
Years
7 per cent.
I
r
51
3087560588582
I
!'
51
435-985954535I
2
2-06
52
328-2814223897
2
2-07
52
467-5049713526
3
3-1836
53
348-9783077331
3
3-2149
53
501-2303193473
4
4-374616
54
370-9170061970
4
4-439943
54
537-3164417016
5
5-63709296
55
394-1720265689
5
5-7507390!
55
575-9285926207
6
6-9753185376
56
418-8223481630
6
7-1532907407
56
617-2435941042
7
8-3938376499
57
444-9516890528
7
8-6540210925
57
661-4506456914
8
9-8974679088
58
472-6487903960
8
10*2598025690
58
7087521908898
9
11-4913159834
59
502-0077178197
9
11-9779887489
59
759-3648442521
10
13-1807949424
60
533-1281808889
10
13-8164479613
60
813-5203833498
ii
14-9716426389
61
566-1158717422
ii
I57835993I86
61
871-4668101843
12
16-8699411973
62
601-0828240468
12
17-8884512709
62
933-4694868972
13
18-8821376691
63
638-1477934896
13
20-1406428598
63
999-8123509800
H
21-0150659292
64
677-4366610990
H
22-5504878600
64
1070-7992155486
15
23*2759698850
65
719-0828607649
15
25-1290220102
65
1146-7551606370
16
25-6725280781
66
763-2278324108
16
27-8880535509
66
1228-0280218815
17
28-2128797628
67
810-0215023555
17
30-8402172995
67
1314-9899834132
18
30-9056525485
68
859-6227924968
18
33-9990325104
68
1408-0392822522
19
337599917014
69
912-2001600466
19
37-3789647862
69
1507-6020320098
20
36-7855912035
70
967-9321696494
20
40-9954923212
70
1614-1341742505
21
39-9927266757
71
1027-0080998284
21
44-8651767837
71
1728-1235664480
22
43-3922902763
72
1089-6285858181
22
49-0057391585
72
1850-0922160994
23
46-9958276929
73
1156-0063009672
23
53-4361408996
73
1980-5986712264
24
50-8155773544
74
1226-3666790252
24
58-1766707626
74
2120-2405782122
25
54-8645119957
75
1300-9486797667
25
63-2490377160
75
2269-6574186871
26
59-1563827154
76
1380-0056005527
26
68-6764703561
76
2429-5334379952
27
63-7057656784
77
1463-8059365859
27
74-4832832810
77
2600-6007786548
28
68-5281116191
78
1552-6342927810
28
80-6976909107
78
2783-6428331606
29
73-6397983 1 62
79
16467923503479
29
87-3465292745
79
2979-4978314819
30
79-0581862152
80
1746-5998913688
30
94-4607863237
80
3189-0626796856
31
84-8016773881
81
1852-3958848509
31
102-0730413663
81
3413-2970672636
32
90-8897780314
82
1964-5396379420
32
110-2181542620
82
3653-2278619721
33
97-3431647133
83
2083-4120162185
33
118-9334250603
83
3909-9538123101
34
104-1837545961
84
2209-4167371916
34
128-2587648145
84
4184-6505791718
35
111-4347798719
85
2342-9817414231
35
138-2368783515
85
4478-5761197139
36
119-1208666642
86
2484-5606459085
36
148-9134598361
86
4793-0764480938
37
127-2681186640
87
2634-6342846630
37
160-3374020247
87.
5129-5917994604
38
135-9042057839
88
27937123417428
38
172-5610201664
QQ
oo
5489-6632254226
39
145-0584581309
89
2962-3350822473
39
185-6402915780
89
5874-9396512022
40
154-7619656188
90
3141-0751871822
40
199-6351119885
9O
6287-1854267864
41
165-0476835559
91
3330-5396984I3I
4i
214-6095698277
91
6728-2884066614
42
175-9505445692
92
3531-3720803179
42
230-6322397156
92
7200-2685951277
43
187-5075772434
93
3744-2544051369
43
247-7764964957
93
7705-2873967866
44
199-7580318780
94
3969-9096694452
44
266-1208512504
94
8245-6575145617
45
212-7435137907
95
4209-1042496119
45
2857493108380
95
8823-8535405810
46
226-5081246181
96
4462-6505045886
46
306-7517625966
96
9442-5232884217
47
241-0986120952
97 4731-4095348639
47
329-2243859784
97
10104-4999186112
48
256-5645288209
98 5016-2941069558
48
353-2700929969
98
10812-8149129140
49
272-9584005502
99 5318-2717533731
49
378-9989995066
99
11570-7119568180
50 290-3359045832
100 5638-3680585755
50
406-5289294721
100
I238r66l7937952
xxxviii THE ENGINEER'S VALUING ASSISTANT.
Amount of 1 per annum in n years at the following rates per cent.
Years
8 per cent.
Years
8 per cent.
Years
9 per cent.
Years
9 per cent.
I
I-
51
620-671769
j
r
51
889-441076
2
2'08
52
671-325510
2
2-09
52
970-490773
3
3-2464
53
726-031551
3
3-2781
53
1058-834943
4
4'5o6lI2
54
785-114075
4
4-573129
54
1155-130088
5
5-86660I
55
848-923201
5
5-984711
55
1260-091796
6
7'335929
56
917-837058
6
7-523335
56
1374-500057
7
8-992803
57
992-264022
7
9-200435
57
1499-205063
8
10-636628
58
1072*645144
8
1 1 -028474
58
I635-I335I8
9
12-487558
59
1159-456755
9
13-021036
59
1783-295535
10
14-486562
60
1253-213296
10
15-192930
60
1944792133
ii
16-645487
61
1354-470360
ii
17-560293
61
2120-823425
12
18-977126
62
1463-827988
12
20-140720
62
2312-697533
13
21-495297
63
1581-934227
13
22-953385
63
2521-840331
H
24-214920
64
1709-488966
H
26-019189
64
2749-805939
15
27-152114
65
1847-248083
15
29-360916
65
2998-288474
16
30-324283
66
1996-027929
16
33-003399
66
3269-134436
17
33-750226
67
2156710164
17
36-973705
67
3564'356535
18
37-450244
68
2330-246977
18
41-301338
68
3886-148624
19
41-446263
69
2517-666735
19
46-018458
69
4236*902000
20
45761964
70
2720-080074
20
51-160120
70
4619-223180
21
50-422921
71
2938-686480
21
56764530
71
5035-953266
22
55-456755
72
3174781398
22
62-873338
72
5490-189060
23
60-893296
73
3429763910
23
69-531939
73
5985-306075
24
66-764759
74
3705-145023
24
76789813
74
6524-983622
25
73-105940
75
4002-556624
25
84700896
75
7113-232148
26
79-954415
76
4323761154
26
93-323977
76
7754-42304I
27
87-350768
77
4670-662047
27
102723135
77
8453-321115
28
95-338830
78
5045-315011
28
112-968217
78
9215-120015
29
103-965936
79
5449-9402II
29
124-135356
79
10045-480817
3O
113-283211
80
5886-935428
30
136-307539
80
10950-574090
31
123-345868
81
6358-890263
31
149-575217
81
11937-125758;
32
I34-2I3537
82
6868-601484
32
164-036987
82
13012-467077
33
145-950620
83
7419-089602
33
179-800315
83
14184-589114
34
158-626670
84
8013-616770
34
196-982344
84
15462-202134
35
172-316804
85
8655-706112
35
215710755
85
168^4-800326
36
187-102148
86
9349-162601
36
236-124723
86
18372732355
37
203-070320
87
10098-095609
37
258-375948
87
20027-278267
38
220-315945
88
10906-943258
38
282-629783
88
21830733311
39
238-941221
89
11780-498719
39
309-066463
89
23796-499309
40
259-056519
9O
12723-938616
40
337-882445
90
25939-184247
4i
280-781040
91
13742-853705
41
369-291865
91
28274-710829
42
304-243523
92
14843-282002
42
403-528133
92
30820-434804
43
329-583005
93
16031-744562
43
440-845665
93
33595-273936
44
356-949646
94
17315-284127
44
481-521775
94
36619-848591
45
386-505617
95
18701-506857
45
525-858734
95
39916-634964
46
418-426067
96
20198-627405
46
574-186021
96
43510-132110
47
452-900152
97
21815-517598
47
626-862762
97
47427-044000
48
490-132164
98
23561 759oo6
48
684-280411
98
51696-477960
49
530342737
99
25447-699726
49
746-865648
99
56350-160977
50
573770156
LOO
27484-515704
50
815-083556
LOO 61422-675465
TABLE III. xxxix
Amount of 1 per annum in n years at the following rates per cent.
Years
10 per cent.
Years
10 per cent.
Years
10 per cent.
Years
10 per cent.
T
I"
26
109-181765
51
1281-299382
7 6
13980-849085
2
2TO
27
1 2 1 -099942
52
1410*429320
77
15379*933994
3
3'3I
28
134-209936
53
1552-472252
78
16918-927393
4
4-641
2 9
148*630930
54
1708719477
79
18611-820133
5
6-I05I
30
164-494023
55
1880-591425
80
20474-002146
6
77I56I
56
2069-650567
7
9-487171
31
181-943425
57
2277-615624
81
22522-402360
8
II-435888
32
201-137767
58
2506-377186
82
24775-642596
9
I3-579477
33
222-251544
59
2758-014905
83
27254-206856
10
15*937425
34
245-476699
60
3034-816395
84
29980-627542
35
271-024368
85
32979-690296
ii
18-531167
36
299-126805
61
3339-298035
86
36278-659326
12
21-384284
37
330-039486
62
3674-227838
87
39907-525258
13
24-5227I2
38
364-043434
63
4042-650622
88
43899-277784
H
27-974983
39
401-447778
64
4447-915685
89
48290-205562
15
31772482
40
442-592556
65
4893-707253
90
53I20-226ll8
16
35-949730
66
5384-077978
17
40-544703
41
487-851811
67
5923-485776
91
58433-248730
18
45'599!73
42
537-636992
68
6516-834354
92
64277-573603
19
51-159090
43
592-400692
69
7169-517789
93
70706-330964
20
57-274999
44
652-640761
70
7887-469568
94
77777-964060
45
718-904837
95
85556*760466
21
64-002499
46
79I79532I
71
8677-216525
96
94113-436513
22
71-402749
47
871-974853
72
9545-938177
97
103525-780164
23
79-543024
48
960-172338
73
10501-531995
98
113879-358180
24
88-497327
49
1057-189572
74
11552-685195
99
125268-293998
25
98-347059
so
1163-908529
75
12708-953714
100
137796-123398
TABLE IV.
Present value of 1, due n years hence, to one
hundred years, at the rates of 3, 3^, 4, 4^, 5, 6, 7, 8,
9, and 10 per cent, and at the rates of 1 1, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, and 25 _p^ 007i. to 50 years.
Calculated to 8 decimal places for each percentage.
TABLE IV. xliii
Present value of 1 due n years hence at the following rates per cent.
Years
3 per cent.
Years
3 per cent.
Fears
3 a per cent.
Years
3 per cent.
I
97087379
5 1
22146318
I
96618357
51
17299843
2
94259591
5?
.21501280
2
'933 5 i 7o
52
16714824
3
91514166
53
20875029
3
90194270
53
16149589
4
88848705
54
20267019
4
87144223
54
15603467
5
86260878
55
19676717
5
84197317
55
15075814
6
83748426
56
19103609
6
81350064
56
14566004
7
81309151
57
18547193
7
78599096
57
14073433
8
78940923
58
18006984
8
75941156
58
13597520
9
76641673
59
17482508
9
73373097
59
I3I3770I
10
74409391
60
16973309
3.0
70891881
6O
12693431
ii
72242126
61
16478941
II
68494571
61
12264184
12
70137988
62
15998972
12
66178330
62
11849453
13
68095134
63
15532982
13
63940415
63
11448747
H
66111781
64
15080565
H
61778179
64
11061591
15
64186195
65
14641325
15
59689062
65
10687528
16
62316694
66
14214879
16
57670591
66
10326114
i/
60501645
67
13800853
17
55720378
67
09976922
18
58739461
68
13398887
18
53836114
68
09639538
19
57028603
69
13008628
19
52015569
69
09313563
20
55367575
70
12629736
20
50256588
7O
08998612
21
53754928
71
I226l88o
21
48557090
71
08694311
22
52189250
72
11904737
22
46915063
72
08400300
23
50669175
73
II557998
23
45328563
73
08116232
24
49193374
74
II22I357
24
43795713
74
07841770
25
47760556
75
10894521
25
42314699
75
07576590
26
46369473
76
10577205
26
40883767
76
07320376
27
45018906
77
10269131
27
39501224
77
07072827
28
43707675
78
09970030
28
38165434
78
06833650
29
42434636
79
09679641
29
36874815
79
06602560
30
41198676
80
09397710
30
35627841
80
06379285
31
39998714
81
09123990
31
34423035
81
06163561
32
35833703
82
08858243
32
33258971
82
05955131
33
37702625
83
08600236
33
32134271
83
05753750
34
36604490
84
08349743
34
31047605
84
05559178
35
35538340
85
08106547
35
29997686
85
05371187
36
34503243
86
07870434
36
28983272
86
05189553
37
33498294
87
07641198
37
28003161
87
05014060
33
32522615
88
07418639
38
27056194
88
04844503
39
31575355
89
07202562
39
26141250
89
04680679
40
30655684
90
06992779
&o
25257247
90
04522395
4i
29762800
91
06789105
4i
24403137
91
04369464
42
28895922
92
06591364
42
23577910
92
04221704
43
28054294
93
06399383
43
22780590
93
04078941
44
27237178
94 -06212993
44
22010231
94
03941006
45
26443862
95 j -06032032
45
21265924
95
03807735
46
25673652
96 -05856342
46
20546787
96
03678971
47
24925877
97 -05685769
47
19851968
97
03554562
48
24199880
98 -05520164
48
19180645
98
03434358
49
23495029
99
05359383
49
18532024
99
03318221
59
22810708
100
05203284 so-
17905337
100
03206DII
THE ENGINEER'S VALUING ASSISTANT.
/Present value of 1 due n years hence at the following rates per cent.
Years
4 per cent.
Years
4 per cent.
Years
4J per cent.
Years
4| per cent.
!
96153846
51
13530059
I
95693780
51
10594225
2
92455621
52
13009672
2
91572995
52
10138014
3
88899636
53
12509300
3
87629660
53
09701449
4
85480419
54
12028173
4
83856134
54
09283683
5
82192/11
55
11565551
5
80245105
55
08883907
6
79031453
56
III20722
6
76789574
56
08501347
7
7599I78I
57
10693002
7
73482846
57
08135260
8
73069020
58
10281733
8
70318513
58
07784938
9
70258674
59
09886282
9
67290443
59
07449701
10
67556417
60
09506040
10
64392768
60
07128901
ii
64958093
61
09140423
ii
61619874
61
06821915
12
62459705
62
08788868
12
58966386
62
06528148
13
60057409
63
08450835
13
56427164
63
06247032
H
57747508
64
08125803
14
53997286
64
05978021
15
55526450
65
07813272
15
51672044
65
05720594
16
53390818
66
07512760
16
49446932
66
05474253
17
51337325
67
07223809
17
47317639
67
05238519
18
49362812
68
06945970
18
45280037
68
05012937
19
47464242
69
06678818
19
43330179
69
04797069
20
45638695
7O
06421940
20
41464286
70
04590497
21
43883360
71
06174942
21
39678743
71
04392820
22
42195539
72
05937445
22
37970089
72
04203655
23
40572633
73
05709081
23
36335013
73
04022637
24
39012147
74
05489501
24
34770347
74
03849413
25
37511680
75
05278367
25
33273060
75
03683649
26
36068923
76
05075353
26
31840248
76
03525023
27
34681657
77
04880147
27
30469137
77
03373228
28
'33347747
78
04692449
28
29157069
78
03227969
2 9
32065141
79
04511970
29
27901502
79
03088966
3O
30831867
80
04338433
3O
2670000!
so
02955947
31
29646026
81
04171570
31
25550241
81
02828658
32
28505794
82
04011125
32
24449991
82
02706850
33
27409417
83
03856851
33
23397121
83
02590287
34
26355209
84
03708510
34
22389589
84
02478744
35
25341547
85
03565875
35
21425444
85
02372003
36
24366872
86
03428726
36
20502817
86
02269860
37
23429685
87
03296852
37
19619921
87
02172115
38
22528543
88
03170050
38
18775044
88
02078579
39
21662061
89
03048125
39
17966549
89
01989070
40
20828904
90
02930890
40
17192870
90
01903417
41
20027792
91
02818163
41
16452507
91
01821451
42
19257493
92
02709772
42
15744026
92
01743016
43
18516820
93
02605550
43
15066054
93
01667958
44
17804635
94
02505337
44
14417276
94
01596132
45
17119841
95
02408978
45
I379 6 437
95
01527399
46
16461386
96
02316325
46
13202332
96
01461626
47
15828256
97
02227235
47
12633810
97
01398685
48
15219476
98
02141572
48
12089771
98
01338454
49
14634112
99
02059204
49
11569158
99
01280817
so
14071262
ICO
01980004
SO
11070965
100
01225663
TABLE IV. Xlv
Present value of 1 due n years hence at the following rates per cent.
fears
5 per cent.
Years
5 per cent.
Years
6 per cent.
Years
6 per cent.
I
95238095
51
08305117
I
94339623
51
05121544
2
90702948
52
07909635
2
88999644
52
04831645
3
86383760
53
07532986
3
83961928
53
04558156
4
82270247
54
07174272
4
79209466
54
04300147
5
78352616
55
06832640
5
74725817
55
04056742
6
74621546
56
06507276
6
70496054
56
03827115
7
71068133
57
06197406
7
66505711
57
03610486
8
67683936
58
05902291
8
62741237
58
03406119
9
64460892
59
05621230
9
59189846
59
03213320
10
61391325
60
05353552
10
55839478
60
03031434
ii
58467929
61
05098621
ii
52678753
61
02859843
12
55683742
62
04855830
12
49696936
62
02697965
13
53032135
63
04624600
13
46883902
63
02545250
H
50506795
64
04404381
H
44230096
64
02401 179
IS
48101710
65
04194648
15
41726506
65
02265264
16
45811152
66
03994903
16
39364628
66
02137041
17
43629669
67
03804670
17
37136442
67
02016077
18
41552065
63
03623495
18
35034379
68
01901959
19
'3957339 6
69
03450948
19
33051301
69
01794301
20
37688948
70
03286617
20
31180473
70
01692737
21
35894236
71
03130111
21
29415540
71
01596921
22
34184987
72
02981058
22
27750510
72
01506530
23
32557I3I
73
02839103
23
26179726
73
01421254
24
31006791
74
02703908
24
24697855
74
01340806
25
29530277
75
02575150
25
23299863
75
01264911
26
28124073
76
02452524
26
21981003
76
01193313
27
26784832
77
02335737
27
20736795
77
01125767
28
25509364
78
02224512
28
19563014
78
01062044
29
24294632
79
02118582
29
18455674
79
01001928
30
23137745
80
02017698
3O
I74IIOI3
80
00945215
31
22035947
81
01921617
31
16425484
81
00891713
32
20986617
82
018301 1 1
32
15495740
82
00841238
33
19987254
83
01742963
33
14618622
83
0079362 1
34
19035480
84
01659965
34
I379H53
84
00748699
35
18129029
85
01580919
35
13010522
85
00706320
36
17265741
86
01505637
36
12274077
86
00666340
37
16443563
87
01433940
37
II5793I8
87
00628622
38
15660536
88
01365657
38
10923885
OQ
OO
00593040
39
I49H797
89
01300626
39
10305552
89
00559472
40
14204568
90
01238691
40
09722219
90
00527803
41
13528160
91
01179706
4i
09171905
91
00497928
42
12883962
92
01123530
42
08652740
92
00469743
43
12270440
93
01070028
43
08162962
93
00443154
44
11686133
94
01019074
44
07700908
94
00418070
45
11129651
95
00970547
45
07265007
95
00394405
46
10599668
96
00924331
46
06853781
96
00372081
47
10094921
97
008803 1 5
47
06465831
97
00351019
48
09614211
98
00838395
48
06099840
98
00331150
49
09156391
99
00798471
49
05754566
99
003 1 2406
5J
08720373
100
00760449
53
05428836
100
00294723
xlvi THE ENGINEER'S VALUING ASSISTANT.
Present value of 1 due n years hence at the following rates per cent.
fears
7 per cent.
Yars
' 7 P3r cent.
Years
8 per cent.
Year
8 per cent.
~T
"93457944
51
03172688
!
92592593
51
01974188
2
87343873
52
02965129
2
85733882
52
01827952
3
81629/88
53
02771148
3
79383224
53
01692548
4
76289521
54
02589858
4
73502985
54
01567174
71298618
55
02420428
5
68058320
55
01451087
6
66634222
56
02262083
6
63016963
56
or 343 5 99
7
62274974
57
*O2 1 14096
7
58349040
57
01244073
8
58200910
58
01975791
8
54026888
58
01151920
9
'54393374
59
01846533
9
50024897
59
01066592
10
50834929
60
01725732
10
46319349
60
00987585
ii
47509280
61
01612834
ii
42888286
61
00914431
12
44401196
62
01507321
12
39711376
62
00846696
13
41496445
63
01408711
13
36769792
63
00783977
14
38781724
64
01316553
1.4
34046104
64
00725905
15
36244602
65
01230423
15
31524171
65
00672134
16
338/3460
66
01149928
16
29189047
66
00622346
17
31657439
67
01074699
17
27026895
67
00576247
18
29586392
68
01004392
18
25024903
68
00533562
19
27650833
69
00938684
19
23171206
69
00494039
20
25841900
70
00877275
20
21454821
70
00457443
21
24151309
71
00819883
21
19865575
71
00423558
22
22571317
72
00766246
22
18394051
72
'00392184
23
21094688
73
00716117
23
17031528
73
00363133
24
19714662
74
00669269
24
15769934
74
00336234
25
18424918
75
00625485
25
14601790
75
00311328
26
' T72I9549
76
00584565
26
I3520I76
76
00288267
27
16093037
77
00546323
27
I25I8682
77
00266914
28
15040221
78
00510582
28
II59I372
78
00247142
29
14056282
79
OD|77I79
29
10732752
79
00228835
3O
I3I367I2
so
0044.5962
30
09937733
so
00211885
31
I227730I
81
00416787
31
09201605
Si
00196190
32
II474II3
82
00389520
32
08520005
82
00181657
33
10723470
83
00364038
33
07888893
83
00168201
34
I002I934
84
00340222
34
07304531
84
00155742
35
09366294
85
00317965
35
06763454
85
00144205
36
08753546
86
00297163
36
06262458
86
00133523
37
08180884
87
00277723
37
05798572
87
00123633
38
07645686
88
00259554
38
05369048
88
00114475
39
40
07145501
06578038
89
90
00242574
00226704
39
40
04971341
04603093
89
90
00105995
00098144
41
06241157
91
002II873
41
04262123
9 1
00090874
42
05832857
92
00198012
42
03946411
92
00084142
43
05451268
93
00185058
43
03654084
93
00077910
44
05094643
94
00172952
44
033834II
94
00072138
4 1
04761349
95
00161637
45
03132788
95
00063795
46
04449859
96
OOI5IO53
46
02900730
96
00061847
47
04158747
97
00141180
47
02685861
97
00057265
48
03886679
98
00131944
48
02486908
98
00053024
49
03632410
99
OOI233I2
49
02302693
99
00049096
53
03394776
193
00115245
53
02132123 aoo
00045459
TABLE IV. xlvii
Present ralue of 1 due n years hence at the following rates per cent.
Years
per cent.
Years
9 per cent.
Years
10 per cent.
Years
10 per cent.
I
91743119
51
01233811
I
90909091
51
00774414
2
84167999
5 2
01131937
2
82644628
52
00704013
3
77218348
53
01038474
3
75131480
53
00640011
4
70842521
54
00952728
4
68301346
54
00581829
5
64993139
55
00874063
5
62092132
55
00528935
6
59626733
56
00801892
6
56447393
56
00480850
7
54703424
57
00735681
7
51315812
57
00437136
8
50186628
58
00674937
8
46650738
58
00397397
9
46042778
59
00619208
9
42409762
59
00361270
10
42241081
60
00568081
10
38554329
60
00328427
ii
38753285
61
00521175
ii
35049390
61
00298570
12
"35553473
62
00478142
12
31863082
62
00271427
13
32617865
63
00438663
13
28966438
63
00246752
H
29924647
64
00402443
H
26333125
64
00224320
15
27453804
65
00369214
15
23939205
65
00203927
16
25186976
66
00338728
16
21762914
66
00185388
17
23107318
67
00310760
17
19784467
67
00168535
18
21199374
68
00285101
18
17985879
68
00153214
19
19448967
69
00261560
19
16350799
69
00139285
20
17843089
7O
00239963
20
14864363
7O
00126623
21
16369806
71
O0220I50
21
I35I3057
71
OOII5II2
22
15018171
72
00201972
22
12284597
72
00104647
23
13778139
73
00185296
23
11167816
73
00095134
24
12640494
74
00169996
24
10152560
74
00086485
25
11596784
75
00155960
25
09229600
75
00078623
26
10639251
76
00143082
26
08390545
76
00071475
27
09760781
77
00131268
27
07627768
77
00064978
28
08954845
78
00120430
28
06934335
78
00059070
2 9
08215454
79
00110486
29
06303941
79
00053700
30
07537114
80
00101363
3O
05730855
80
00048819
31
06914783
8!
00092994
31
05209868
81
0004438 1
32
06343838
82
00085315
32
04736244
82
00040346
33
05820035
83
00078271
33
04305676 .
83
00036678
34
05339481
84
0007 1 808
34
03914251
84
00033344
35
04898607
85
00065879
35
03558410
85
00030313
36
04494135
86
00060440
36
03234918
86
00027557
37
04123059
87
00055449
37
02940835
87
00025052
38
03782623
88
00050871
38
02673486
88
00022774
39
03470296
89
00046670
39
02430442
89
00020704
to
03183758
90
00042817
40
02209493
90
00018822
4i
02920879
9 1
00039282
41
02008630
91
OOOI7III
42
02679706
9 2
00036038
42
01826027
92
00015555
43
02458446
93
00033063
43
01660025
93
00014141
44
02255455
94
00030333
44
01509113
94
00012855
45
02069224
95
00027828
45
01371921
95
OOOII687
46
01898371
96
00025530
46
OI2472OI
96
00010624
47
01741625
97
00023422
47
01133819
97
00009658
48
01597821
98
00021488
48
01030745
98
00008780
49
01465891
99
00019714
49
00937041
99
00007982
so
01344854
100
00018086
50
00851855 '100
00007257
Iviii THE ENGINEER'S VALUING ASSISTANT.
Present value of 1 due n years hence at the following rates per cent.
Years
11 per cent.
12 per cent.
13 per cent.
14 per cent.
15 per cent.
Years
I
90090090
89285714
88495575
87719211
86956530
I
2
81162243
79719388
78314668
76946753
75614367
2
3
73119138
7II78025
'69305016
67497152
65751623
3
4
65873097
63551808
6I33I873
59208028
57175325
4
5
59345U3
56742686
54275994
51936866
49717674
5
6
53464084
50663112
48031853
45558655
43232760
6
7
48165841
45234922
42506064
39963732
37593704
7
8
43392650
40388323
37615986
35055905
32690177
8
9
39092477
36061003
33288483
30750794
28426241
9
10
35218448
32197324
29458835
26974381
24718571
10
ii
31728331
28747610
26069765
23661738
21494322
n
12
28584082
25667509
23070589
20755910
18690715
12
13
25751426
22917419
20416450
18206939
16252796
13
14
23199482
20461981
18067655
15970999
14132866
H
15
20900435
18269626
15989075
14009648
12289449
15
16
18829220
16312166
14149624
12289165
10686477
16
17
16963262
14564434
12521791
10779969
09292589
17
18
I52822I8
13003959
II08I23I
09456113
08080512
18
19
13767764
11610678
09806399
08294836
07026532
19
20
12403391
10366677
08678229
07276172
06II0028
20
21
III74226
09255961
07679849
06382607
05313068
21
22
10066870
08264251
06796327
05598778
04620059
22
23
09069252
07378796
06014448
04911209
04017443
23
24
08170498
06588210
05322521
04308078
03493428
24
25
07360809
05882331
04710195
03779016
03037764
25
26
06631359
05252081
04168314
03314926
02641534
26
27
05974197
04689358
03688774
02907830
02296986
27
28
05382160
04186927
03264402
02550728
01997379
28
29
04848793
03738327
02888851
02237481
01736851
29
30
04368282
03337792
02556505
01962702
01510305
30
31
03935389
02980172
02262394
01721669
01313309
31
32
03545395
02660868
02002II9
01510236
OII42008
32
33
03194050
02375775
'01771786
01324768
00903344
33
34
02877522
02I2I227
01567953
01162077
00863522
34
35
02592363
01893953
01387569
01019366
00750889
35
36
02335462
01691029
01227937
00894181
00652947
36
37
O2IO4O2O
01509848
01086670
00784369
00567798
37
38
01895513
01348078
00961655
00688043
00493722
38
39
01707670
01203641
00851022
00603547
00429323
39
40
01538441
01074680
00753117
00529427
00373324
40
4i
01385983
00959536
00666475
00464410
00324630
4i
42
01248633
00856728
0058980!
00407377
00282287
42
43
01124895
00764936
00521948
00357348
00245467
43
44
01013419
00682978
00461901
00313463
00213449
44
45
00912990
00609802
00408762
00274968
00185608
45
46
00822513
00544466
00361736
00241200
00161398
46
47
00741003
00486131
00320120
002II579
00140346
47
48
00667670
00434045
00283292
00185595
OOI22O4O
48
49
00601415
00387540
00250701
00162803
OOI06I22
49
50
00541815
00346018
00221859
00142810
00092280 so
TABLE IV.
xlix
Present value of 1 due n years hence at the following rates per cent.
Years
16 per cent.
17 per cent.
18 per cent.
19 per cent.
20 per cent.
Years
I
86206897
85470085
84745763
84033613
83333333
I
2
74316290
73051355
71818443
70616482
69444444
2
3
64065767
62437056
60863087
5934I58I
57870370
3
4
55229110
53365005
51578888
49866875
48225309
4
5
47611302
45611115
43710922
41904937
40187757
5
6
41044225
38983859
37043154
35214233
33489798
6
7
35382952
33319538
31392503
29591792
27908165
7
8
30502546
28478237
26603816
24867052
23256804
8
9
26295298
24340374
22545607
20896683
19380670
9
10
22668360
20803738
19106447
17560238
16150558
10
ii
19541690
17780973
16191904
14756502
13458799
ii
12
16846284
15197413
13721953
12400422
11215665
12
13
14522659
12989242
11628773
10420523
09346388
13
M
12519534
11101916
09854893
08756742
07788657
14
15
1079270!
09488817
08351604
07358606
06490547
15
16
09304053
oSlIOIOO
07077628
06183703
05408789
16
17
08020735
06931709
05997992
05196389
04507324
17
18
06914427
05924538
05083044
04366713
03756104
18
19
05960713
05063708
04307664
03669507
03130086
J 9
20
05138546
04327955
03650563
03083619
02608405
20
21
04429781
03699107
03093698
02591277
02173671
21
22
03818776
03161630
02621778
02177544
01811393
22
23
03292049
02702248
02219846
01829869
01509494
23
24
02837973
02309614
01882920
01537705
01257912
24
25
02446528
01974029
01595695
01292189
01048260
25
26
02109076
01687204
01352284
01085873
00873550
26
27
01818169
01442055
01 146003
00912498
00727958
27
28
01567387
01232525
00971189
00766805
00606632
28
29
01351196
01053440
00823042
00644374
00505526
29
30
01164824
00900376
00697493
00541491
0042 1 272
30
31
01004159
00769553
00591096
00455034
00351060
31
32
00865654
00657737
00500929
00382382
00292550
32 .
33
00746253
00562169
00424516
00321329
00243792
33
34
00643322
00480486
00359759
00270025
00203160
34
35
00554588
00410672
00304880 -00226911
00169300
35
36
00478093
00351002
00258373 -00190682
00141083
36
37
00412149
00300001
00218960 -00160237
00117569
37
38
00355301
0025641 1
00185560 -00134653
00097974
38
39
00306294
00299155
00157254 -00113154
00081645
39
40
00264047
00187312
00133266 '00095087
00068038 40
41
00227626
00160096 -00112937
00079905
00056698
4i
42
00196230 -00136834 -00095710
00067147
00047248
42
43
00169163 -00116952 -OOoSlIIO -00056426
00039374
43
44
00145831 -00099959 -00068737 -00047417
00032811
44
45
00125716 -00085435 -00058252
00039846
00027343
45
46
00108376
0007302 1
00049366
00033484
00022786
46
47
00093427
00062411
00043662
00028138
00018988
47
48
00080541
00053343
00035454
00023645
00015823
48
49
00069432
00045592
00030046
00019870
00013186
49
50
00059855
00038968
00025462
00016698
00010988
50
1 THE ENGINEER'S VALUING ASSISTANT.
Present value of 1 due n years hence at the following rates per cent.
Years
21 per cent.
22 p?r cent.
23 per cent.
24 per cent.
25 per cent.
Years
I
2
82644628
68301346
56447393
81967213
67186240
55070689
81300813
66098222
53738392
80645161
"65036420
52448726
80000000
'64000000
51199869
I
2
3
4
46650738
45139909
43689749
42297360
40959937
4
i
38554329
31863082
36999925
30327808
-',5520122
28878148
34II0774
27508689
32768000
26214400
6
8
26333125
21762914
24858859
20376114
23478169
19087942
22184426
17890666
20971520
16777216
8
9
17985879
16701733
15518652
14427957
I342I773
9
10
14864363
13689945
12616790
II635449
I07374I8
10
II
12284597
II22I266
10257553
09383427
08589935
ii
12
10152560
09197759
08339474
07567280
06871948
12
I 3
08390545
07 5 39 i 47
06780060
06102645
05497558
13
14
06934335
06179629
05512244
04921488
04398047
14
15
05730855
05065269
04481499
03968942
03518437
15
16
04736244
04151860
03643495
03200759
02814750
16
17
039I425I
03403164
02962191
02581258
02251800
17
18
03234918
02789479
02408286
02081659
01801440
18
19
02673486
02286458
01957956
01678758
01441152
19
20
02209493
01874146
01591834
01353837
01152922
2O
21
01826027
01536185
01294174
01091804
00922337
21
22
01509113
01259168
01052174
00880487
00737870
22
23
OI24720I
01032105
00855426
00710070
00590296
23
24
01030745
00845988
00695468
00572637
00472237
24
25
00851855
00693433
00565421
00461804
00377789
25
26
00704013
00568387
00459692
00372423
00302231
26
27
00581829
00465891
00373733
00300341
00241785
27
28
00480850
00381878
00303848
002422IO
00193428
28
29
00397397
00313015
00247031
OOI9533I
00154743
29
30
00328427
00256570
00200838
00157525
00123794
30
31
00271427
00210303
00163283
00127036
00099035
31
32
00224260
00172379
00132751
00102449
00079228
32
33
00185388
00141295
00107927
OO08262O
00063383
33
34
00153214
00115815
00087746
00066629
00050706
34
35
00126228
00094931
00071338
00053733
00040565
35
36
00104647
00077812
00057998
00043333
00032452
36
37
00086485
00063780
00047153
00034946
00025961
37
38
00071475
00052279
00038336
00028l82
00020769
38
39
00059070
00042852
00031167
00022728
00016615
39
40
00048819
00035124
00025339
00018329
00013292
40
41
00040346
00028793
0002o6oi
00014781
00010634
41
42
00033344
00023599
00016749
OOOH920
00008507
42
43
00027557
00019345
00013617
00009613
00006806
43
44
00022774
00015855
OOOIIO7I
00007753
00005445
44
45
OOOI8822
00012996
0000900!
00006252
00004356
45
46
00015555
00010652
00007318
00005042
00003484
46
47
.00012855
00008731
00005949
00004066
00002788
47
48
00010624
00007157
00004837
00003279
00002230
48
49
00008780
00005866
00003932
00002644
00001784
49
50
00007257
00004808
00003197
00002133 -00001427
50
TABLE V.
FOR THE
EEDEMPTION OF CAPITAL,
OR THE
Fund necessary to be annually invested to produce 1
in n years, at the several rates of i^, 2, 2^, 3, 3^,
3j, 4, 4^, 4^, and 5 ^er cewi., calculated to 10 decimal
places, and to 100 2/ea?^s /or eacA, percentage. And for
rates of 10, 12, 15, 18, cuicZ 20 >cr ce;i^., to 10 decimal
places, and for 50 years for each percentage. Also, for
rates of interest of 3, 3 J, 3^, 3}, 4, 4^, 41, 4}, and 5 per
cent, per annum, payments being made half-yearly and
quarterly ; calculated to 6 decimal places and to 100 years
for each percentage.
TABLE V. liii
Eedemption Fund necessary to produce 1 in n years at the following rates per cent.
Years
1| per cent.
Years
1 per cent.
Years
2 per cent.
Years
2 per cent.
I
I -0000000000
51
0131946887
I
I -0000000000
51
0114585615
2
4962779156
52
0128328700
2
4950495049
52
0111090856
3
3183829602
S3
0124853664
3
3267546725
53
0107739189
4
2444447860
54
0121513812
4
2426237526
54
0104522618
5
1940893230
55
0118301756
5
1921583941
55
0101433732
6
1605252147
56
0115202954
6
1585258123
56
0098465645
7
1365561645 .
57
0112234068
7
1345119561
57
0095611957
8
1185840245
58
0109366116
8
1165097991
58
0092866706
9
1046098234
59
0106601241
9
1025154374
59
0090224335
10
0934341779
60
0103934274
10
0913265279
60
0087679658
ii
0842938442
61
0101360387
ii
0821779428
61
0081744379
12
0766799929
62
0098875059
12
0745595966
62
0082864306
13
0702403574
63
0096474061
13
0681183527
63
0080584849
14
0647233186
64
0094153423
H
0626019702
64
0078385471
15
0599443556
65
0091909423
15
0578254723
65
0076262436
16
0557650778
66
0089738563
16
0536501259
66
0074212231
17
0520796569
67
0087637552
17
0499698408
67
0072231553
18
0488057818
68
0085603297
18
0467021021
68
0070317294
19
0458784701
69
0083632878
19
0437817663
69
0068466526
20
0432457359
7O
0081723548
20
0411567181
7O
0066676485
21
0408654950
71
0079872709
21
0387847689
71
0064944567
22
0387033152
72
0078077911
22
0366314005
72
0063268307
23
0367307520
73
0076336836
23
0346680976
73
0061645379
24
0349241020
74
0074647293
24
0328710973
74
0060073582
25
0332634539
75
0073007206
25
0312204384
75
0058550830
26
0317319599
76
0071414609
26
0296992308
76
0057075147
27
0303152680
77
0069867637
27
0282930862
77
0055644661
28
0290010765
78
0068364523
28
0269896716
78
0054257595
29
0277787802
79
0066903586
29
0257783552
79
0052912260
30
0266391883
80
0065483231
30
0246499223
80
0051607055
31
0255742954
81
0064101941
31
0235963472
81
0050340453
32
0245770970
82
0062758275
32
0226106073
82
0049111006
33
0236414375
83
0061450857
33
0216865311
83
0047917333
34
0227618855
84
0060178380
34
0208186728
84
0046758118.
35
0219336303
85
0058939597
35
0200022092
85
0045632109
36
0211523955
86
0057733319
36
0192328526
86
0044538110
37
0204143673
87
0056558413
37
0185067789
87
0043474981
38
0197161329
88
0055413794
38
0178205663
88
0042441633
39
0190546298
89
0054298429
39
0171711439
89
0041437027
40
0184271017
90
0053211330
40
0165557478
9O
0040460169
4i
0178310610
91
0052151552
4i
0159718836
91
0039510108
42
0172642571
92
0051 118190
42
0154172945
92
0038585936
43
0167246488
93
0050110379
43
0148899334
93
0037686782
44
0162103801
94
0049127291
44
0143879391
94
0036811814,
45
0157197604
95
0048168132
45
0139096161
95
0035960233
46
0152512458
96
0047232141
46
0134534159
96
0035131275
47
0148034238
97
0046318590
47
0130172220
97
0034324205
48
0143749996
98
0045426778
48
0126018355
98
003353832 1
49
0139647841
99
0044556033
49
0122039639
99
0032772947
50
0135716832 100
0043705712
50
0118232097
100
0032027435
liv THE ENGINEEB'S VALUING ASSISTANT.
Redemption Fund necessary to produce 1 in n yenrs^at the following rates per cent.
Years
2i per cent.
Years
2J per cent.
Years
3 per cent.
Years
3 per cent.
I
I -0000000000
51
0099086955
I
I '0000000000
51
0085338232
2
49382/1604
52
0095744635
2
4926108374
52
0082171837
3
3251371672
53
0092544943
3
3235303633
53
0079147059
4
2408178777
54
0089479856
4
2390270452
54
0076255841
5
1902468603
55
0086541932
5
1883545714
55
0073490710
6
1565499709
56
0083724260
6
1545975005
56
0070844726
7
1324954297
57
0081020412
7
1305063538
57
0068311432
8
1144673456
58
0078424404
8
1124563888
58
0065884819
9
1004568897
59
0075930656
9
0984338570
59
0063559281
10
0892587631
60
0073533959
10
0872305066
60
0061329587
ii
0801059558
61
0071229444
ii
0780774478
61
0059190847
12
0724871271
62
0069012558
12
0704620855
62
0057138575
13
0660482710
63
0066879033
13
0640295440
63
0055168216
H
0605365249
64
0064824869
H
0585263390
64
0053276021
15
0557664561
65
0062846310
15
0537665805
65
0051458128
16
0515989886
66
0060939830
16
0496108493
66
0049710995
17
0479277699
67
0059102110
17
0459525294
67
0048031288
18
0446700805
68
0057330027
18
0427086959
68
0046415871
19
0417606151
69
0055620638
19
0398138806
69
0044861787
20
039I47I287
70
0053971168
20
0372157076
70
0043366251
21
0367873272
71
0052378997
21
0348717765
71
0041926632
22
0346466060
72
0050841652
22
0327473948
72
0040540446
23
0326963781
73
0049356794
23
0308139027
73
0039205345
24
0309128203
74
O0479222IO
24
0290474159
74
0037919109
25
0292759209
75
0046535805
25
0274278710
75
0036679633
26
0277687466
76
o45 i 95 594
26
0259382903
76
0035484929
27
0263768721
77
0043899655
27
0245642103
77
0034333105
28
0250879326
78
0042646320
28
0232932334
78
0033222371
29
0238912684
79
0041433776
29
022II467II
79
0032151027
30
0227776407
80
004026045 1
3O
O2IOI92593
80
0031117457
31
02 1 7390024
81
0039124812
31
0199989288
81
0030I20I27
32
0207683122
82
0038025403
32
0190466183
82
0029157577
33
0198593818
83
0036960837
33
Ol8l56l2I9.
83
0028228417
34
0190067507
84
0035929793
34
0173219634
84
0027331326
35
0182055822
85
0034931011
35
0165392916
85
0026465042
36
0174515767
86
0033963292
36
0158037942
86
0025628365
37
0167408991
87
0033025489
37
OI5III6244
87
0024820151
38
0160701179
88
0032116510
38
OI4459340I
88
0024039306
39
OI5436I533
89
0031235310
39
0138438516
89
0023284787
40
0148362331
90
0030380892
40
0132623779
90
0022555599
41
0142678555
91
0029552302
4i
OI27I24089
91
0021850789
42
0137287567
92
0028748628
42
OI2I9I673I
92
OO2 1 1 69449
43
0132168832
93
0027968996
43
OIl698lI03
93
0020510708
44
0127303682
94
0027212571
44
0112298469
94
0019873733
45
OI22675I05
95
0026478552
45
OI0785I757
95
0019257729
46
0118267567
96
0025766173
46
0103625378
96
0018661933
47
0114066855
97
0025074697
47
0099605065
97
0018085613
48
0110059938
98
002440342 1
48
0095777738
98
0017528070
49
0106234846
99
0023751667
49
0092131383
99
0016988633
SO
0102580569
100
0023118786
50
0088654944
LOO
0016466659
TABLE V. lv
Kedemption Fund necessary to produce 1 in n years at the following rates per cent.
Years
3J per cent.
Years
3i per cent.
Years
3| per cent.
Years
3J per cent.
I
I '0000000000
51
0079081725
I
I 'OOOOOOOOOO
51
0073215641
2
4920045476
52
0076010287
2
4914004914
52
0070242854
3
3227307792
53
0073079716
3
3219341806
53
0067409979
4
2381372828
54
0070281934
4
2372511395
54
0064708979
5
1874155909
55
0067609454
5
1864813732
55
0062132297
6
1536299447
56
0065055321
6
1526682087
56
0059672981
7
1295220120
57
0062613065
7
1285444938
57
0057324549
8
1114626472
58
0060276663
8
1104766465
58
0055080966
9
0974355561
59
0058040498
9
096446005 1
59
0052936605
10
0862310733
60
0055899327
10
0852413679
60
0050886213
ii
0770793519
61
0053848252
ii
0760919658
61
0048924882
12
0694671846
62
0051882685
12
0684839493
62
0047048020
13
0630392523
63
0049998334
13
0620615726
63
0045251325
H
0575417594
64
0048191173
14
0565707287
64
0043530765
15
0527885769
65
0046457423
IS
0518250694
65
0041882558
16
0486401341
66
0044793534
16
0476848306
66
0040303148
17
0449896669
67
0043196168
17
0440431317
67
0038789193
18
0417541470
68
0041662182
18
0408168408
68
0037337550
19
0388680383
69
0040188617
19
0379403252
69
0035945255
20
0362788848
70
0038772683
20
0353610768
70
0034609517
21
0339442356
71
0037411746
21
0330365869
71
0033327702
22
0318293586
72
0036103320
22
0309320742
72
0032097323
23
0299055555
73
0034845054
23
0290188043
73
0030916030
24
0281489054
74
0033634725
24
0272728303
74
0029781601
25
0265393258
75
0032470228
25
0256740354
75
0028691934
26
0250598100
76
0031349574
26
0242053963
76
0027645039
27
0236958807
77
'0030270874
27
0228524103
77
0026639029
28
0224351188
78
0029232333
28
0216026452
78
0025672117
29
0212668234
79
0028232256
29
0204453825
79
0024832606
30
0201817174
80
0027269026
30
0193713316
80
0023848887
31
0191717180
81
0026341111
31
0183723998
81
0022989429
32
0182297550
82
0025447051
32
0174415048
82
0022l6278l
33
0173496132
83
0024585460
33
0165724220
83
0021367560
34
0165258003
84
0023755019
34
0157596583
84
0020602452
35
0157534809
85
0022954470
35
0149983473
85
0019866205
36
0150283131
86
0022l826l6
36
0142841628
86
0019157629
37
0143464505
87
0021438315
37
0136132454
87
0018475589
38
0137044457
00
OO
0020720479
38
0129821414
88
0017819002
39
0130992039
89
0020028067
39
0123877506
89
0017186838
40
0125279401
90
0019360090
40
0118272823
90
0016578111
41
0119881387
91
0018715599
4i
0112982174
91
0015991884
42
0114775251
92
0018093692
42
0107982765
92
0015427259
43
0109940346
93
0017493500
43
0103253914
93
0014883379
44
0105357906
94
0016914200
44
0098776816
94
0014359428
45
0101010826
95
0016354999
45
0094534334
95
0013854621
46
0096883484
96
0015815142
46
0090510817
96
0013368213
47
0092961589
97
0015293902
47
0086691944
97
0012899487
48
0089232032
98
0014790587
48
0083064580
98
0012447758
49
0085682777
99
0014304533
49
0079616665
99
OOI20I2372
50
0082302744
100
0013835101
50
0076337096 100
0011592702
Ivi THE ENGINEER'S VALUING ASSISTANT.
Redemption Fund necessary to produce 1 in n years at the following rates per cent.
Years
4 per cent.
Years
4 per cent.
Years
4} per cent.
Years
4i per cent.
I
I'OOOOOOOOOO
51
0062588497
I
I 'OOOOOOOOOO
51
0057793980
2
4901960784
52
0059821236
2
4895858012
52
0055132157
3
3203485392
53
0057191451
3
3195596844
53
0052606425
4
2354900454
54
0054691025
4
2346150491
54
0050208438
5
1846271135
55
0052312426
5
1837070439
55
0047930729
6
1507619025
56
0050048662
6
I498I73286
56
0045766300
7
I266096I2I
57
0047893234
7
1256522089
57
0043708645
8
1085278320
'58
0045840087
8
1075649275
58
0041751705
9
0944929927
59
0043883581
9
0935294356
59
0030889840
10
0832909443
60
0042018451
10
0823301166
60
0038117785
ii
0741490393
61
0040239779
ii
0731933807
61
0036430616
12
0665521727
62
0038542964
12
0656034888
62
0034823743
13
0601437278
63
003692370!
13
0592033981
63
0033292857
14
0546689731
64
0035377955
H
0537380572
64
0031833933
15
0499411004
65
0033901939
15
0490204277
65
0030443184
16
0458199992
66
0032492100
16
O449IO2239
66
0029117068
17
0421985221
67
0031145099
17
0413001642
67
0027852249
18
' 389933282
68
0029857795
18
0379785883
68
0026645598
!9
0361386184
69
0028527231
19
0352642692
69
0025494164
20
0335817503
70
0027450623
20
0327198351
70
0024395176
21
0312801054
71
0026325344
21
0304308333
71
0023346017
22
0291988111
72
0025248919
22
0283623442
72
0022344222
23
0273090568
73
0024219008
23
0264855182
73
0021387467
24
0255868313
74
0023233403
24
0247763107
74
0020473553
25
0240119628
75
0022290015
25
0232145232
75
0019600406
26
0225673805
76
0021386869
26
0217830598
76
0018766066
27
0212385106
77
0020522095
27
0204673559
77
0017968678
28
0200129752
78
0019693922
28
0192549241
78
0017206554
29
0188799342
79
0018900672
29
0181349985
79
0016477824
3O
0178300991
80
0018140755
3O
0170983084
30
0015781123
31
0168553524
81
OOI74I266I
31
0161365371
81
0015114887
32
0159485897
82
0016714957
32
0152427549
82
0014477702
33
0151035665
83
0016046284
33
0144106446
83
0013868224
34
0143147715
84
0015405351
34
0136346858
84
0013285180
35
0135773224
85
0014790927
35
0129099878
85
0012727359
36
0128868780
86
0014201848
36
OI22322OI5
86
0012193611
37
0122395655
87
0013637001
37
OII5974477
87
0016828445
38
0116319191
88
0013095329
38
OII0022538
88
ooi 1194021
39
0110608274
89
0012575828
39
0104435029
89
0010726152
40
0105234893
90
0012077538
ao
0099183887
9O
0010278300
4i
0100173765
91
OOII599547
4i
0094243778 ;
91
0009849569
42
0095402007
92
ooi 1 140984
42
0089591781 92
00094391 10
43
0090898859
93
OOI070I020
43
0085207094 93
0009046112
44
0086645444
94
0010278867
44
0081070805
94
0008669802
45 -0082624558
95
0009873767
45
"0077165675
95
0008309447
46 -0078820488
96
0009485002
46
0073544897
96
0007964344
47
0075218855
97
0009111884
47
0069987268
97
0007633827
48
0071806476
98
0008753757
48
0066686377 98
0007317257
49 -0068571240
99
0008409996
49
0063561161 99
0007014029
5O -0065502004
100
O00808000O
so
0060600458 100
0006723562
TABLE V. Ivii
Redemption Fund necessary to produce 1 in n years at the following rates per cent.
Years
4 per cent.
Years
4J per cent.
Years
5 per cent.
Years
5 per cent.
(I
I 'OOOOOOOOOO
51
0053323191
I
I -0000000000
51
0045286697
2
4889975550
52
0050767923
2
4878048780
52
0042944966
3
3107733582
53
0048346867
3
3172085646
53
0040733368
4
2337436479
54
0046051886
4
2320118326
54
0038643770
5
1827916395
55
0043875437
5
1809747981
55
0036668637
6
1488783875
56
0041810518
6
1470174681
56
0034800978
7
1247014680
57
0039850622
7
1228198184
57
0033034300
8
1066096533
58
0037989695
8
1047218136
58
0031362568
9
0925744700
59
0036222094
9
0906900800
59
0029780161
10
0813788217
6O
0034542558
1.0
0795045750
60
0028281845
ii
0722481817
61
0032946176
ii
0703888915
61
0026862736
12
0646661886
62
0031428356
1 2
0628254100
62
0025518273
13
0582753528
63
0029984802
13
0564557652
63
0024244196
14
0528203160
64
0028611494
14
0510239695
64
0023036520
15
0481138081
65
0027304661
15
0463422876
65
0021891514
16
0440153695
66
0026060769
16
0422699080
66
0020805683
17
0404175833
67
0024876496
17
0386991417
67
0019775751
18
0372368975
68
0023748725
18
0355462223
68
0018798643
19
0344073443
69
0022674523
19
0327450104
69
0017871473
20
0318761443
7Q
0021651129
20
0302425872
70
0016991530
21
0296005669
71
0020675946
21
0279961071
71
0016156265
22
0275456461
72
0019746524
22
0259705086
72
0015363280
23
0256824930
73
0018860556
23
0241368219
73
0014610318
24
0239870299
74
0018015863
24
0224709007
74
0013895254
25
0224390280
75
0017210390
25
0209524573
75
0013216085
26
0210213675
76
0016442194
26
0195643207
76
0012570925
27
0197194616
77
0015709439
27
0182918599
77
0011957993
28
0185208051
78
'0015010391
28
0171225304
78
0011375610
29
0174146147
79
0014343408
29
0160455149
79
0011061609
30
'0163915429
80
0013706935
30
0150514351
80
0010296235
31
0154434459
81
0013099502
31
0141321204
8l
0009796332
32
0145631962
82
0012519715
32
0132804189
82
0009321143
33
0137445281
83
0011966252
33
0124900437
83
0008869406
34
0129819119
84
0011437861
34
0117554454
84
0008439924
35
0122704478
85
0010933355
35
0110717072
85
0008031567
36
0116057796
86
0010451606
36
0104344571
86
0007643265
37
0109840206
87
0009915434
37
0098397945
87
0007274005
38
0104016920
88
0009452152
38
0092842282
88
0006922828
39
0098556712
89
0009132468
39
0087646242
89
0006588825
40
0093431466
90
0008731573
40
0082781611
90
0006271136
4i
0088615804
91
0008348597
4i
0078222924
91
0005968946
42
0084086759
9 2
0007982710
42
0073947131
92
0005681481
43
0079823492
93
0007633126
43
0069933328
93
0005408008
44
0075807056
94
0007299095
44
0066162506
94
0005147832
45
0072020184
95
0006979905
45
0062617347
95
0004900295
46
0068447107
96
0006674877
46
0059282036
96
0004664770
47
0065073395
97
0006383364
47
0056142109
97
0004440666
48
0061885821
98
0006104754
48
0053184306
98
0004227418
49
0058872235
99
0005838459
49
0050396453
99
0004024492
50
0056021459
100
0005583922
50
0047767355
100
0003831381
Iviii THE ENGINEER'S VALUING ASSISTANT.
Redemption Fund necessary to produce 1 in n years at the following rates per cent.
Years
10 per cent.
12 per cent.
15 per cent.
18 per cent.
20 per cent.
Year
I
I "OOOOOOOOOO
I -oooooooooo
I -0000000000
I -0000000000
I -0000000000
I
2
4761904761
4716981132
4651162790
4587155063
4545454545
2
3
3021148036
2963489805
2879769618
2799238607
2747252747
3
4
2154708037
2092344363
2002653515
1917387036
1862891207
4
5
1637974807
1574097319
1483155524
I3977784I8
1343797033
5
6
1296073803
1262257184
1142369065
I059IOI292
1007057459
6
7
1054054997
0991177359
0903603634
0823619993
0774239263
7
8
0874440175
0813028414
0728500896
0652443589
0606094224
8
9
0736405391
0676788887
0599574015
0523948239
0480794617
9
10
0627453949
-0569841642
0492520625
0425146413
0385227569
10
n
0539631420
0484154043
0410689830
0347763862
0311037942
ii
12
0467633151
0414368076
0344807761
0286278089
0252649649
12
*3
0407785238
0356771951
0291104565
0236862073
0206200011
13
14
0357462232
0308712461
0246884898
0196780583
0168930552
14
15
0314737769
0268242396
0210170526
0164027825
0138821198
15
16
0278l66207
0233900180
0179476914
OI37I00839
0114361350
16
17
0246641344
0204567275
0153668623
0114852711
0094401469
17
18
0219302222
0179373114
0131862873
0096894570
0078053857
18
19
0195468682
0157630049
0113863504
0081028390
0063624532
J 9
20
0174596248
0138787800
0097614704
0068I998I2
0053865307
20
21
0156243898
0122400915
0084167914
0057464327
0044439388
21
22
0140050629
0108105088
0072657713
0048462577
0036896187
22
23
OI257l8l27
0095599650
0062783947
0040901996
0030652575
23
24
0112997764
0084634417
0054298296
0034542973
0025478730
24
25
OIOI680722
0074999698
0046994023
0029l8826l
0021187290
25
26
0091590386
0066518581
0040698058
0024674779
0017624956
26
27
0082576423
0059040937
0035264815
0020867195
0014665923
27
28
00745IOI32
0052438691
0030571309
0017652846
0012206684
28
2 9
0067280747
0046602068
0026513265
0014937692
0010161900
29
30
0060792483
0041436576
0022801982
0012643056
0008461085
30
31
0054962193
0036860570
0019961796
0010702987
0007045936
31
32
00494Hl67
0032803263
0017328006
0009062108
0005868168
32
33
0044994063
0029203096
0015045161
0007673859
0004875834
33
34
0040737064
0026006383
0013065655
0006499044
0004071466
34
35
003689705 1
0023166193
0011348546
0005504633
0003391738
35
36
0033430638
0020641406
0009858572
0004662768
0002825649
36
37
0030299405
0018395924
0008565329
0003989937
0002354154
37
38
0027469250
0016397998
0007442569
0003346284
0001961410
38
39
0024909840
0014619665
0006467613
0002835030
0001634241
39
40
0022594144
0013036256
0005620850
000240I99I
0001361682
40
41
0020498028
0011625982
0004885308
0002035I7I
0001134606
4i
42
OOI85999II
0010369577
0004246290
0001724424
0000945416
42
43
0016880466
0009249987
0003691063
0001461163
0000787784
43
44
0015322365
0008252102
0003208590
OOOI238I20
0000656444
44
45
OOI39I0047
0007362523
0002789300
OOOI049I44
0000547007
45
46
*OOI2629527
0006569363
0002424890
0000889026
0000455818
46
47
OOIl86822I
0005862064
0002108156
0000758355
0000379834
47
48
OOI04I4797
0005231248
0001832843
0000638396
0000316518
48
49
0009459041
0004668576
0001593523
0000540984
0000263758
49
SO
0008591740
0004166635
0001385480
0000458440
oooo2i97<)4
50
N.B. Tho above Table for rates of interest of 10, 12, 15, 18, and 20 per cent, was employed
in calculating the Old Present Value Table of i per annum given in Table XII., but it is
evident that it could not be applied practically for the Redemption of Capital.
TABLE
lix
Redemption Fund necessary to produce 1 in n years, payments being made
Ilalf-ytarly and Quarterly, at tLe ioJlcwirg rates per cent.
ij
3 per cent.
Years'
Duration
3 per cent.
ll
3} per cent.
Years'
Duration
3J per cent.
Bedtrapt
Payments
Half-
yearly
ion Fund,
leingmade
Quarterly
Redempt
Payments
Half-
yearly
ion FuEd.
being made
Quarterly
Kedempi
Payments
Hall-
yearly
ion Fund,
being made
Quarterly
liedempl
Payments
Ealf-
y early
itn Fund,
being made
Quarterly
i
992556
988820
51
008413
008352
I
991941
987895 51
007781
007718
2
488890
487022
52
008099 -008040
2
487976
485954 52
007478
007416
3
321050
319806
53
007800 -007743
3
320046
318699 53
C07I88
007128
4
237168
236235
54
007514 -007458
4
236125
235H5 54
'006911
006853
5
186868
I86I23
55
007240 '007186
5
185807
185000 55
006647
006590
6
153360
152739
56
006978 -006925
6
152291
151619 56
006395 ' Co6 339
7
129447
128915
57
006728 -006676
7
128375
127800 57
006154 -006 ico
8
III530
111065
58
006488 "006437
8
110461
109958 58
005923 -005870
9
097612
097199
59
006258 -006208
9
096546
096100 59
005702
005651
10
086492
086I2I
60
006037 -005989
10
085432
085031 6O
005490
005441
ii
077407
077070
61
005826
005779
ii
076354
075990
61
005288
005240
12
069848
069540
62
005623 -005577
12
068804
068471
62
005094
005047
J3
063464
063 1 80
63
005428 -005383
13
062428
062122
63
004908
004862
058002
057739
64
005241 -005197
14
056976
056692
64
004730
004685
15
053278
053033
65
005061 [-005019
15
052262
051997
65
004558
004515
16
049154
048925
66
004888
004847
16
048147
047900
66
004394
004352
17
045524
045309
67
004722
004682
17
044527
044295
67
004237
004195
18
042305
O42IO2
68 -004563
004523
18
041319
041 ico
68
004085
004045
19
039432
039241
69 -004409
004371
19
038457
038250
69
003940
003901
20
036854
036673
70
004262
004224
20
035889
035694
70
003800
003762
21 -034529
034356
71
004119
004083
21
033575
033389
71
003666
003629
22
032421
032257
72
003982
003947
22
031478
031302
72
003537
003501
23
030503
030346
73
003851
003816
23
029571
029403
73
003413
003378
24
028750
028601
74
003724
003689
24
027829
027669
74
'03294
003259
25
027143
O27OOI
75
003601
003568
25
026234
026080
75
003179
003146
26
025666
025529
76 -003483 -003451
26
024767
024620
76
003069
003036
27
024303
024172
77 '003370 -003338
27
023415
023275
77
002963
002931
28
29
023042
021873
022916
021752
78 -003260 -003229
79 -003154 -003124
28
29
022166
021008
022031
020878
78
79
002860
002762
002829
C0273I
30
020787
020670
80
003052
003023
30
-019933
019808
80
002667
002637
31
019775
019663
8 1 -002954
002925
31
018932
018812
-8 1
002576
002547
32
018831
018722
82 -002859 '002831
32
-017999
017883
82
002488
OO24(:O
33
017948
017843
83 ,-002767
002740
33
017127
017015
83
002403
002375
34
OI7I2I
017020
84
002679
002652
34
016311
016203
84
002321
002294
35
'016345 '016247
85
002594 -002567
35
015546
015442 85
002243
002216
36
015616 -015521
86 -002511 -002485
36
014828
014727 86
002167
002I4I
37
014930 -014838
87 -002432 .-002406
37
014153
014055
87
002094
002069
38
014283 -014195
88 -002355 '002330
38
013517
013423 88
002023
001999
39
013673 -013587
89 '-002280-002256
39
012918
012827 89
001955 001931
40
013097 -013014
90 -002208 '-002185
40
012352
-012264 9
001889 '001866
41
012552 -012471
91 -002139 '002116
41
011818
011732
91
001826
001803
42
012036 -011958
92 -002072 -002050
42
011312
011229 9 2
001765 -001743
43
011547 : -oi 147 1
93 -002C07 -001985
43
010834
010753
93
001706 (001685
44 -011083 "011009
94 -001944 -001923
44
010380 i
010302
94
001649 '001628
45 -010642 ; -01057 1
95 -001884 -001863
45
009950
009875
95
001594
001574
46
-010224 -OIOI54
96 -001825 -001805
46
009542 :
009468
96
001541
COI52I
47
009826 -009758
97 1-001768 -001748
47
009154;
009083
97
001490
001471
48 -009446 -009381
98 ^001714 -001694
48
008785
008716
98
001441
001422
49 ^009085 -009021
99 |-ooi66i -001641
49
008434
008367
99
001393
001375
50 j-008741
008679
100/001609 '-001591
5O
008100*
008034
100
001347
001329
Ix THE ENGINEER'S VALUING ASSISTANT.
Redemption Fund necessary to produce 1 in n years, payments being made
Half-yearly and Quarterly, at the following rates per cent.
Years'
Duration
3i per cent.
||
!J
3S per cent.
g
gj
3| per cent.
1 Years'
Duration
3| per cent.
Redemption Fund.
Payments being made
|"**
Redempt
Payments
Half-
yearly
ion Fund,
oeing made
Quarterly
Redempt
Payments
Half-
yearly
ion Fund,
oeing made
Quarterly
Redempt
Payments
Half-
yearly
ion Fund,
being made
Quarterly
I
991326
986970
51
007189
007123
i
990712
986047
51
006636
006568
2
487065
484888
52
006896
006832
2
486155
483823
52.
006353
006287
3
319045
317594
53
OQ66l6
006554
3
318047
316493
53
006084
006019
4
235086
233999
54
006350
006289
4
23405 I
232887
54
005827
005765
5
184751
183882
55
006096
006037
5
183699
182769
55
005583
005523
6
I5I228
150504
56
005853
005796
6
I50I70
149396
56
005350
005292
7
I273II
126692
57
005621
'005566
7
126254
I2559I
57
005 1 29
005072
8
109399
108858
58
005400
005346
8
108346
107767
58
004917
004862
9
095490
095010
59
005 1 89
005136
9
094443
093929
59
004715
004661
10
084382
083951
60
004986
004935
10
083343
082882
60
004522
004470
ii
075313
074922
61
004793
004743
ii
074282
073864
61
004338
004288
12
067771
067414
62
004608
004560
12
066751
066368
62
004163
004113
13
061405
061076
63
004431
004384
13
060396
060044
63
003995
003947
14
055963
055658
64
004262
004216
H
054964
054639
64
003834
003788
15
051260
050976
65
004099
004055
15
050272
049969
65
003680
003635
16
047156
046891
66
003944
003900
16
046181
045898
66
003534
003490
17
43547
043298
67
003795
003752
17
042584
042319
67
003393
003351
18
040350
040116
68
003652
003611
18
039399
039150
68
003259
003217
J9
037500
037279
69
003515
003475
19
036561
036326
69
003130
003090
20
034944
034735
70
003383
003344
20
034018
033796
70
003007
002968
21
032641
032443
71
003257
003219
21
031728
031517
71
002888
002851
22
030556
030368
72
003136
003099
22
029656
029455
72
002775
002739
23
028661
028481
73
OO3O2O
002984
23
027773
027582
73
002667
002631
24
026931
026760
74
002908
002874
24
026056
025874
74
002563
002522
25
025348
025184
75'
002801
002767
25
024486
024312
75
002463
002430
26
023893
023737
76
002698
002665
26
023044
022878
76
002368
002335
27
022553
022403
77
002599
002567
27
02I7I7
021558
77
OO2276
002244
28
021316
021172
78
002505
002473
28
020492
020340
78
002188
002157
29
020170
020032
79
002413
002383
29
019359
OI92I3
79
002104
002074
30
019107
018974
80
002325
002296
30
018308
Ol8l68
80
002023
001994
31
Ol8ll8
017990
8l
002241
002212
31
017332
017197
81
001946
001917
32
017196
017074
82
002l6o
002132
32
016423
016293
82
001871 -001844
33
016336
016218
83
OO2O82
002055
33
015575
015450
83
OOlSoo -001773
34
015532
015418
84
002007
001980
34
014783
014663
84
OOI73I
001705
35
014779
014668
85
001935
001909
35
014042
013926
85
001665
001640
36
014072
013966
86
001865
001840
36
013348
013236
86
001602
001577
37
013408
013306
87
001798
001774
37
012696
012588
87
OOI54I
001517
38
012784
012685
88
001734
OOI7IO
38
012084
011980
88
001482
001459
39
012196
OI2IOO
89
001672
001649
39
011508
OII407
89
001426
001404
40
011642
OII549
90
00l6l2
001590
&o
010965
010868
90
001372
OOI35I
4i
011119
OIIO29
91
001555
001533
4i
010454
010360
91
OOI32I
001299
42
010625
010537
92
001500
001478
42
009971
009880
92
OOI27I
001250
43
010157
010073
93
001446
001425
43
009515
009427
93
001223
OOI2O3
44
009715
009633
94
001395
001375 j
44
009084
008999
94
OOII77
OOII57
45
009295
009216
95
001346
001326 j
45
008676
008594
95
OOII33
OOIII4
46
008898
OOS82I
96
001298
001279
46
008290
0082TO
96
OOIO9O
001072
47
008520
008446
97
001252
001233
47
007924
007846
97
001049
OOI03I
48
008162
008090
98
001208
001190
48
007576
007501
98
OOIOIO
000993
49
007822
007751
99
OOII65
001148
49
007247
007174
99
000972
000955
50
007498 [
007430
VJOJI24 OOII07
50
006933
006863
100
000936
OO0920
TABLE V.
Ixi
Redemption Fund necessary to produce 1 in n years, payments being made
Half-yearly and Quarterly, at the following rates per cent.
Years'
Duration
4 per cent.
Years'
Duration
4 per cent.
Years'
Duration
4J per cent.
Years'
Duration
4j per cent.
Redempt
Payments '
Half-
yearly
ion Fund.
Xiiugniade
Quarterly
llcuempt
Payments t
Half-
yearly
on Fund,
eiug made
Quarterly
Redemi t
Payments I
Half-
yearly
ton Fund,
eing made
Quarterly
Redcnirt
Payments
Half-
yearly
icn Fund,
seing made
Quarterly
I
990099
985124
51 -006199
006049
I
989487
984203
51 -005636
005565
2
485248
482761
52
005846
005779
2
484342
481701
52 -005375
005306
3
317052
315395
53
005588
005522
3
316059
314300
53
005127
005060
4
233020
231778
54
005342
005278
4
231992
230674
54
00489 1
004827
5
182653
I8l66l
55
005108
005046
5
I8l6l2
180559
55
004668
004605
6
I49II9
148294
56
004885
004825
6
148074
147198
56
004456
004395
7
125204
124498
57
004673
004615
7
I24l6l
I234II
57
004254
004195
8
107300
106684
58
004472
004416
8
106263
105608
58
004062
004CC5
9
093404
092857
59
004279
004225
9
092375
091795
59
003879
003824
10
082313
O8l822
60
004096
004043
10
081294
080773
eo
003706 -003653
ii
073263
072818
61
003922
003870
n
072254
071782
61
003540 -0034^0
12
065742
065335.
62
003755
003705
12
064746
064314
62 -003383 -003333
13
059399
059024
63
003596
003548
13
058414
058018
63 -003233 -003185
H
053979
053633
64
003444
003398
H
053008
052641
64
003090
005044
15
049300
048978
65
003300
003254
15
048342
048001
65
C02954
002900
16
045221
044921
66
003161
003118
16
044277
043959
66
002824 '02781
17
041637
041356
67
003029
002987
17
040707
040409
67
C0270I -002658
18
038466
038201
68
002903
002862
18
037550
037270
68
002583 -002542
19
035641
035391
69 1-002783
002743
19
034739
034475
69
002470 -002431
20
033II2
032875
70
002667
002629
032224
031975
70
002363
002324
21
030835
030641
71
002557
002520
21
029961
029725
71
002260
CO2223
22
028776
028564
72
002452
002415
22
027917
027693
72
002162
002127
23
026907
026705
73
002351
002316
23
026062
025850
73
C02069
002034
24
025204
0250II
74 j-oo2255
'OO222O
24
024373
024171
74 -001980.
001946
2 5
023646 [-023463
75 -002162
002 1 29
25
022830
022637
75 -001895
001862
26
022218
O22O43
76 -002074
C02042
26
02I4I6
021232
76 -001813
001782
27
020905
020737
77 -001989
COI95S
27
020II7
019941
77 ' -co 1 736
001705
28
019693 -019533
78 1-001908
001878
28
018920
018751
78 'co 1 66 1
001632
29
018573 -018420
79 -001831
001802
29
017814
017653
79 -001590
001562
30
017536 I-OI7388
eo
COI757
001728
3O
016790
016636
8O -001522
001495
3 1
016573-016431
81
001686
001658
31
015841
015693
81 -001458
001431
32
015677
015541
82
00l6l8
COIC9I
32
014959
014817
82 -001396
001370
33
014842
'OI47I2
33
001552 -001526
33
014138
014002
83 -001336
001311
34
014064
013938
84
001490-001465
34
013373
013241
84 -001280
001255
35
013335
OI32I4
85
001430 -001405
35
012658
012532
85 -001225
001202
36
012654
012537
86
COI372
001349
36 -011990
OII868
86 -001174
001 It, I
37
OI20I5
OII902
87
001317
001294
37
011364
OII247
87 -co 1 1 24
OCII02
38
011415
011306
88
001265
001242
38
010777
010664
88 -001077 -ooio' 5
39
010852
010747
89
OOI2I4
COIJ92
39 -010226
010118
9 j"COIO3I -OOIG] I
OI032I
010220
90
COII66
OOII45
40 -009709
009604
9O
000988 -00090 8
41
009822
009724
9 1
OOIII9
OOIO99
41 -009223
009122
91 -000946
0009: 7
42
009352
009257
92
001074
001055
42 -008764
008667
92 |-ccccc6
cc 08: 8
43
008908
008816
93
001032
'OOIOI2
43 -0083331-008239
93 -c col 68
cco8 ; r o
44
008488
008400
94
000991
000972
44
007926 -007835
94 -000832
-co 08] 4
45
008092
008007
95
00095 I
000933
45
C0754I
007454
95 -CC0797
0007' o
46
C077I7
007635
96
000913
000896
46
007178
007093
96 -000763
0007/7
47
007362
007283
97
000877
000860
47 1-006835
006753
97 -000731
000716
48
49
007026 -006949
006708 | -0066^3
98 -000842
99 -000809
000826
000793
48 -006510
49 -006203
006431
006127
98 -CC070I
99 -000672
000686
000657
SO '006406 '006333
ICO
000777
000762
so 1*005912
.005838
ICO, -00064 3
000629
Ixii
THE ENGINEER'S VALUING ASSISTANT.
Redemption Fund necessary to produce 1 in n years, payments being made
Half-yearly and Quarterly, at the following rates per cent.
Years'
Duration
4i per cent.
Years'
Duration
4| per cent.
Years'
Duration
4| per cent.
Years'
Duration
4| rer cent.
Ecdcmjt
Payments
Half-
yearly
icn Fund,
being made
Quarterly
Redempt
Payments 1
Half-
yearly
ion Fund.
3eing made
Quarterly
Eedcmpt
Payments
Half-
yearly
ion Fund,
leingmade
Quarterly
Rcdempt
Payments
Half-
yearly
ion Fund,
being made
Quarterly
j
988875
983282
51
005187
005II5
I
988264
982363
5i
004770
004696
2
483438
480643
52
004937
004867
2
482536
479587
52
004530
004459
3
315070
313208
53
004699
004632
3
314084
3I2II9
53
004303
004235
4
230969
229575
54
004475
004409
4
229950
228479
54
004089
0040: 4
5
180575
I7946I
55
004261
004198
5
'179544
178369
55
003886
003823
6
147035
146108
56
004059
003998
6
146002
145024
56
003694
003633
7
123125
122332
57
003867
003809
7
122095
I2I260
57
003512
003453
8
105233 -104541
58
003685
003628
8
104212
103483
58
003340
003283
9
091354-090741
59
003512
003457
9
090343
089697
59
003 1 76
003122
10
080284-079734
60
003348
003295
10
079284
078705
60
00302 1
002969
ii
071256 -070758
61
003192
003141
ii
070269
069745
61
002874
002824
12
063761 . -063305
62
003044
002994
12
062787
062308
62
002735
002686
13
057443 ; -05 7024
63
002903
002855
13
056484
056044
63
002603
002556
H
052051 1*051664
64
002768
002722
14
051 107
050700
64
002477
002432
IS
047399 -047039
65
002641
002596
15
046470
046092
65
002358
002314
16
043348 : -0430 1 3
66
OO252O
002476
16
042435
042083
66
002245
002202
17
039793 ''039479
67
002404
002362
17
038895
038566
67
002137
002096
18
036650 1-036356
68
002294
002254
18
035768
035459
68
002035
001996
19
033855 1-033578
69
002189
002 1 5 1
19
032989
032698
69
001938
OOI9CO
20
031355 ;'03io93
70
OO2O9O
002052
20
030504
030230
70
001845
001809
2 1
029107 ,-028860
71
001995
001958
21
028260
028014
71
001758
001722
22
027078 ,-026843
72
001904
001869
22
026259
026014
72
001674
001640
23
025238 -025016
73
OOT8l8
001784
23
024436
024203
73
001595
001562
24 -023565 -023353
74
001736
02 1 703
24
022778
022556
74
001519
001488
25
022037 -021835
75
001657
001626
25
021265
021055
75
001448
OOI4I7
26
020638
020445
76
001583
001552
26
019882
019681
76
001379
001350
27
019353
019169
77
OOI5T2
001482
27
018613
018422
77
001314
001286
28
018171
017995
78
001444
OOI4I5
28
017446
017263
78 -001252
001225
29
017080
016911
79
001379
OOI35I
29
016370
016195
79 -001194
ooi 167
30
016071
OI59IO
80
OOI3I7
OOI29I
30
015376
015209
80
001138
OOI I 12
31
015136
014982
81
001258
001233
31
014457
014297
81
001084
OOIO6O
32
014268
OI4I20
82
'CO 1 2 O2
OOII77
32
013604
013451
82
OOIO33
ooioio
33
013461
013320
83
OOII48
ooi 124
33
012812
012665
83
000985
000962
34
012710
012574
84
001097
001074
34
012075
011934
84
000939
0009 1 7
35
012009
011878
85
001048
001026
35
011388
OII253
85
000895
000874
36
011355
OII229
86
'OOIOO2
000980
36
010748
Olo6l8
86
000853
000833
37
010742
OI062I
87
000957
000936
37
010150
010025
87
000813
000794
38
010169
OIOO53
po
oo
000915
000894
38
009590
009470
88
000776
000757
39
009632
009520
89
000874
000855
39
009066
008951
89
000739
000721
40
009128
009020
9O
000835
0008 1 7
40
008576
008465
90
000705
000688
41
008654
008550
91
000798
000780
41
008 1 1 5
008009
91
000672
000655
42
008208
008108
92 -000763
000745 '
42
007683
007580
92
000641
000625
43
007789
007693
93 -000729
0007 I 2
43
007276
007178
93
0006II
000596
44
007395
007302
94 -000697
00068I
44
006894
006799
94
000583 '000568
45
007023
006933
95 -000666
000650
45
006535
006443
95
000556 -000541
46
006672
006585
96 -000637
000622
46
006196
006108
96
000530 -000516
47
006340
006257
97 ,-000609
000594
47
005877
005792
97
000505 j'OOO492
48
006027
005947
98 -000582
000568
48
005575
005494
98
000482 -000469
49 "005732
005654
99 -000556
000543
49
005291
005213
99
000460 ,'000447
SO 1-005452 -005377 i ioo;ooo532
000519 so
005023
004947
lOO,-ooo438 -000426
TABLE V.
Ixiii
Redemption Fund necessary to produce 1 in n years, payments being made
Half-yearly and Quarterly, at the following rates per cent.
Years'
Duration
5 per cent.
Years'
Duration
5 per cent.
Years'
Duration
5 per cent.
Years'
Duration
5 per cent.
Uedempt
Payments I
Half-
yearly
on Fund,
eing made
Quarterly
Redempt
Payments 1
Half-
yearly
on Fund.
>eing made
Quarterly
Redempt
Payments 1
Half-
yearly
ion Fund.
)eing made
Quarterly
Redempt
Payments
Half-
yearly
ion Fund,
rein g made
Quarterly
I
987654
981444
26
019149
018941
51
004381
004308
76
'OOI2OO
OOII72
2
481636
478533
27
017896
017697
52
004153
004082
77
OOII4I
OOIII4
3
313100
3H033
28
016745
016555
53
003937
003869
78
OOIO85
001059
4
228935
227387
29
015685
015504
54
003733
003668
79
001032
001007
5
178518
177282
55
003540
003478
6
144974
143947
3O
014707
014534
56
003358
003298
80
00098 1
000957
7
I2I073
I20I95
31
013803
013637
57
003186
003128
81
000933
000910
8
103198
102432
32
012965
012807
58
003023
002967
82
000887
000865
9
089340
088661
33
OI2I88
012037
59
002869
0028 1 5
83
000844
OOO822
10
078294
077686
34
011466
OII32I
60
002724
002672
84
OOO8O2
000782
35
010794
010655
85
000763
000743
ii
069293
068742
36
'OIOl68
010035
61
002586
002536
86
000726
000707
12
061826
061323
37
009584
009457
62
002455
002407
87
000690
000672
13
055538
055076
38
009039
008916
63
002331
002285
88
000657
000639
H
050176
049750
39
008529
008412
64
002214
002169
89
000625
000608
15
045555
045160
40
008052
007939
65
002103
002060
90
000594
000578
16
041537
041168
66
001997
001956
17
038014
037969
41
007605
007497
67
001897
001858
9 1
'000565
000549
1-8
034903
034580
42
007 1 86
007082
68
001803
001764
92
000538
000523
19
032140
031836
43
006793
006692
69
OOI7I3
001676
93
0005 I I
000497
20
029673
029386
44
006423
006327
70
001628
001592
94
000487
000473
45
006076
005984
95
000463
000450
21
027458
027187
46
005750
005661
71
001547
001513
96
OOO44O
000428
22
025461
025205
47
005443
005357
72
001470
001437
97
000419
000407
23
023654
02341 1
48
005153
005071
73
001397
001366
98
000399
000387
24
022012
021782
49
004881
004801
74
001328
001298
99
000379
000368
25
020516
020297
50
004624
004548
75
001263
001233
100
000361
000350
TABLE VI.
FOE
YALUING MINERAL AND OTHER PROPERTIES,
OB
The present value (or years' purchase) of 1 per annum in
n years, allowing interest to a present purchaser upon his
purchase money, or capital invested, at the rates of 3 J, 4,
4i> 5, 5i, 6, 7, 8, 9, 10, u, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, and 25 per cent, per annum, and redeeming
the capital so invested by an Annual Redemption Fund,
at the rate of 2^ per cent, per annum.
Calculated to 8 places of decimals, and to 100 years for
each percentage.
TABLE VI.
ixvii
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2 per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
3| per cent.
Years
3| per cent.
Years
4 per cent.
Years
4 per cent.
I
0*96618357
51
22-26740253
I
0*96153846
51
20-03658861
2
1-89097701
52
22-43436985
2
1*87326550
52
20*17167569
3
277671979
53
22-59657501
3
273869682
53
20-30271581
4
3-62558079
54
2275417147
4
3-56102684
54
20-42984993
5
4*43957354
55
22*90730687
5
4*34316454
55
20-55321308
6
5-22056984
56
23*05612326
6
5*08776468
56
20-67293462
7
5-97031216
57
23*20075737
7
579725504
57
20-78913857
8
6-69042456
58
23-34134075
8
6*47386019
58
20-90194379
9
7-38242257
59
23-47800014
9
7-11962227
59
20*81146433
10
8-04772215
60
23-61085761
10
773641938
60
21*11780963
ii
8^68764777
61
2374003086
n
8*32598178
61
21*22108482
12
9-30343965
62
23-86563316
12
8-88990612
62
21*32139072
13
9-89626037
63
23-98777393
13
9-42966812
63
21*41882435
14
10*46720091
64
24-10655857
14
9-94663383
64
21-51347888
15
1 1-01728593
65
24*22208884
15
10*44206960
65
21-60544393
16
11-54747897
66
24-33446278
16
10*91715111
66
21-69480559
17
12-05868675
67
24-44377517
17
11-37297126
67
2178164679
18
12-55176339
68
24-55011744
18
11-81054741
68
21*86604730
19
13-02751416
69
24-6535779I
19
12-23082775
69
21*94808392
20
13-48669891
70
2475424187
20
12-63469713
70
22*02783063
21
13-93003527
71
24*85219178
21
13-02298226
71
22*10535871
22
14-35820146
72
24*94750720
'22
1 3*39645636
72
22*18073675
23
14-77183903
73
25*04026512
23
1375584350
73
22-25403095
24
I5-I7I55533
74
25' 1 35 3996
24
14*10182243
74
22*32530510
25
i5'55792567
75
25-21840367
25
14-43503005
75
22*39462074
26
I5-93I49544
76
25-30392583
26
14*75606456
76
22*46203721
27
16-29278205
77
25'387I7376
27
15*06548845
77
22*52761178
28
16-64227669
78
25*46821272
28
I536383I05
78
22*59139983
29
16-98044595
79
25-547I0557
29
15-65159098
79
22*65345459
30
17-30773337
80
25-62391340
3O
15*92923832
80
2271382764
31
17-62456084
81
25-69869536
31
16*19721669
81
2277256882
32
17-93132983
82
2577150857
32
16*45594495
82
22-82972616
33
18-22842269
83
25*84240844
33
16*70581904
83
22*88534613
34
18-51620375
84
25*91144861
34
16-94721347
84
22*93947365
35
18-79502035
85
25-97868115
35
17*18048273
85
22*99215220
36
19-06520381
86
26*04415633
36
17*40596268
86
23*04342368
37
19-32707041
87
26*10792307
37
17-62397170
87
23*09332881
38
19-58092210
88
26*17002861
38
17*83481179
88
23*14190680
39
19-82704736
89
26-23051889
39
18-03876966
89
23*18919571
40
20-06572202
90
26*28943832
40
18*23611768
90
23*23523253
4i
20-29720981
9 1
26*34683006
41
18*42711474
91
23*28005217
42
20-52176308
92
26*40273591
42
1 8 '6 1 200708
9 2
23*32368980
43
20-73962342
93
26-45719651
43
1879102908
93
23*36917861
44
20-95102212
94
26-51025117
44
18*96440389
94
23'40755090
45
21-15618084
95
26-56193812
45
19*13234417
95
23-44783801
46
21-35531202
96
26-61229435
46
19*29505267
96
23*48707021
47
21-54861933
97
26-66135594
47
19*45272274
97
23-52527702
48
21-73629820
98
2670915766
48
19-60553899
98
23-56248679
49
21-91853623
99
26-7557335I
49
1975367772
99
23-59872722
50
22-09551334
100
26*80111636
50
19-89730725 ;ioo
23-63402508
Ixviii
THE ENGINEER'S VALUING ASSISTANT.
.Present Value of 1 per Annum in n years ; Redemption of Capital being at 2 J per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
4i per csnt.
Years
4i per cent.
Years.
5 per cent.
Years
5 per cent.
I
0-95693779
51
18-21205168
I
0-95238095
51
16*69206768
2
1-85588269
52
18-32358823
2
1-83881952
52
1678571558
3
2-70170112
53
18-43165277
3
2-66569161
53
16*87635701
4
3-49873146
54
l8'53637330
4
3-43857815
54
16*96410810
5
4-25085376
55
18-62787228
5
4-16238530
55
17-04907945
6
4-96154872
56
1873626655
6
4-84144343
56
17-13137638
7
5-63394788
57
18-83166781
7
5-47958928
57
17-21109929
8
6-27087631
58
18-92418277
8
6-08023432
58
17-28834387
9
6-87488920
59
19-01391350
9
6*64642212
59
17-36320145
10
7-44830339
60
19-10095769
10
7-18087665
60
I7-43575920
n
7-99322457
61
19-18540887
ii
7-68604322
61
17.50610040
12
8-51157080
62
19-26735653
12
8-16412323
62
I7-57430457
13
9-00509293
63
19-34688653
13
8*61710383
63
17-64044782
14
9'47539253
64
19-42408108
H
9-04678341
64
1770460288
15
9^2393738
65
19-49901911
15
945479348
65
1776683941
16
10-35207526
66
19-57177619
16
9-84261767
66
17*82722400
17
1076104593
67
19-64242497
17
IO'2Il6o8oi
67
17-88582053
18
11-15199177
68
1971103516
18
10-56299936
68
17-94269018
19
11-52596716
69
1977767371
J 9
10-89792172
69
17-99789158
20
1 1 '88394679
70
19-84240495
20
II-2I74II20
70
18*05148098
21
12-22683311
71
19-90529075
21
11*52241960
71
18*10351236
22
12*55546282
72
19-96639050
22
11-81382275
72
18*15403749
23
12-87061282
73
20-02576138
23
12*09242802
73
18*20310609
24
13-17300551
74
20-08345842
24
12-35898089
74
18-25076593
25
I3-4633I338
75
20-13953456
2 5
12*61417072
75
18*29706290
26
1374216331
76
20-19404074
26
12-85863594
76
18*34204111
27
14-01014041
77
20-24702607
27
13-09296875
77
18-38574298
28
14-26779137
78
20-29853790
28
I3'3i77i9 l8
78
18*42820937
2 9
14-51562764
79
20-34862170
29
I3-53339876
79
18*46947945
3O
1475412820
80
20-39732142
30
13-74048390
80
18*50959103
31
14-98374210
81
20-44467947
31
13-93941882
8l
18*54858055
32
15-20489072
82
20-49073663
32
14-13061819
82
18*58648299
33
15-41796996
83
20-5355323I
33
14-31446964
83
18-62333211
34
15-62335205
84
20-57910452
34
14-49133585
84
18-65916045
35
15*82138737
85
20-62149001
35
14-66155654
85
18-69399940
36
16*01240598
86
20-66272415
36
14-82545033
86
1872787914
37
16-19671910
87
2070284121
37
14-98331628
87
1876082890
38
16*37462043
88
2074187420
38
i5"!3543538
88
1879287677
39
16*54638731
89
2077985508
39
15-28207191
89
18-82404993
4O
1671228198
90
20*81681467
40
15-42347469
90
18*85437457
41
16-87255244
91
20-85278281
41
15-55987814
91
18*88387599
42
17-02743351
92
20-88778832
42
15-69150336
9 2
18*91257863
43
17-17714768
93
20-92185912
43
15*81855905
93
18-94050612
44
17*32190580
94
20-95502216
44
15-94124232
94
18-96768125
4 I
17-46190800
95
20-98730354
45
16-05973953
95
18*99412609
46
I7-59734425
96
21-01872846
46
16*17422704
96
19-01986190
47
17-72839498
97
21-04932143
47
16-28487178
97
19-04490934
48
17-85523177
98
21-07910600
48
16-39183198
98
19*06928826
49
17-97801787
99
21-10810515
49
16-49525768
99
19-09301799
50
18-09690851 100
21-13634101
SO
16-59529118
100
19-11611716
TABLE VI.
Ixix
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2-J per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
5i per cent.
Years
5i per cent.
Years
6 per cent.
Yeara
6 per cent.
I
0-94786729
51
15-40625632
I
0-94339622
51
14-30437219
12
1-82206726
52
15-48599780
' 2
1-80561748
52
14-37,308963
3
2-63062938
53
15-56311369
3
2'59647753
53
14-43949609
4
3-38045830
54
15-63770916
4
3-32427051
54
14-50368696
5
4-07752417
55
15-70988414
5
3-99605413
55
14-56575270
6
472701554
56
1577973360
6
4-61787178
56
14-62577911
7
5-33346334
57
15-84734790
7
5-19492853
57
14-68384768
8
5-90084182
58
15-91281296
8
573173161
58
14-74003580
9
6-43265153
59
15-97621063
9
6-23220356
59
1479441702
10
6-93198790
60
16-03761889
10
6-69977413
60
14-84706133
ii
7-40159821
61
16-09711210
ii
7-I3745532
61
14-89803537
12
7-84392921
62
16-15476111
12
7-54790311
62
14-94740253
13
8-26116715
63
16-21063363
13
7-93346860
63
14-99522328
14
8-65527158
64
16-26479426
H
8-29624050
64
15-04155525
15
9-02800393
65
16-31730474
15
8-63808079
65
15-08645345
16
9-38095204
66
16-36822402
16
8-96065468
66
15-12997030
17
97I555I02
67
16-41760854
17
9-26545597
67
15-17215595
18
10-03310116
68
16-46551225
18
9-55382852
68
15-21305826
J 9
10-33478341
69
16-51198683
: 9
9-82698462
69
15-25272302
20
10-62167284
70
16-55708174
20
10-08602078
70
15-29119400
21
10-89475019
71
16-60084440
21
IO'33I931 14
71
15-32851310
22
II-I549II99
72
16-64332019
22
10-56561923
72
15-36472039
23
11-40297948
73
16-68455267
23
1078790801
73
I5'39985427
24
11-63970635
74
1672458362
24
10-99954876
74
I5'43395I5S
25
11-86578550
75
1676345312
25
II-20I22862
75
15-46704749
26
12-08185506
76
16-80119964
26
H'39357731
76
I5'499I7590
27
12-28850378
77
16-83786014
27
II'577I73IO
77
1 5*5 303692 1
28
12-48627562
78
16-87347017
28
1175254786
78
15-56065862
29
12-67567400
79
16-90806377
2 9
11-92019168
79
15-59007395
30
12-85716552
80
16-94167377
30
12-08055692
8O
15-61864392
31
13-03118321
81
16-97433175
31
12-23406172
8l
15-64639615
32
13-19812955
82
17-00606802
32
12-38109319
82
I5-673357I3
33
i3'35 8 379 8
83
17-03691178
33
I2-5220I028
83
15-69955234
34
13-51228085
84
17-06689115
34
12-65714627
8 4
1572500630
35
13-66016047
85
17-09603323
35
1278681102
85
1574974261
36
13-80232212
86
17-12436404
36
12-91129300
86
1577378395
37
1 3^93905028
87
17-15190877
37
13-03086114
87
1579715221
33
14-07061124
88
17-17869160
38
13-14576640
88
15-81986840
39
14-19725458
89
17-20473589
39
13-25624328
89
15-84195282
40
14-31921448
90
17-23006415
40
13-36251116
90
15-86342500
41
14-43671083
91
17-25469809
41
13-46477548
91
15-88430376
42
14-54995038
92
17-27865867
42
13-56322885
92
15-90460727
43
14-65912762
93
17-30196614
43
13-65805203
93
i5-924353o6
44
14-76442586
94
17-32464001
44
1374941479
94
1 5 '94355 799
45
14-86601767
95
17-34669914
45
I3'8374768o
95
15-96223840
46
14-96406603
96
17-36816171
46
13-92238834
96
15-98040999
47
15-05872477
97
17-38904537
47
14-00429096
97
15-99808799
48
15-15013929
98
17-40936707
48
14-08331813
98
16-01528701
49
15-23844712
99
17-42914326
49
I4-I5959586
99
16-03202128
50
15*32377836
100
17-44838984
50
14-23324305
100
16-04830447
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2J per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
7 per cent.
Years
7 per cent.
Years
8 per cent.
Years
8 per cent.
~7~
0*93457943
51
12-51428263
I
0-92592592
51
II-I2239472
2
I773593I7
52
12-56684564
2
1-74268503
52
11-16389606
3
2-53076674
53
12-61758098
3
2-46829983
53
11-20391760
4
3-21731815
54
12-66656764
4
3-11703327
54
11-24252554
5
3-84250553
55
1271388033
5
370032951
55
11-27978231
6
4-41403720
56
1275958971
6
4-22743658
56
11-31574684
7
4-93838306
57
12-80376268
7
470598357
57
11-35047482
8
5-42101366
58
12*84646261
8
5-14225150
58
11-38401888
9
5-86658598
59
12-88774960
9
5-54148972
59
11-41642884
10
6-27908933
60
12*92768066
10
5-90811360
60
II-44775I86
ii
6-66196084
61
12-96630993
ii
6-24586384
61
11-47803265
12
7-01817785
62
13-00368882
12
6-55793062
62
II-5073I357
13
7-35033229
63
13-03986622
13
6-84705127
63
11-53563487
14
7-66069114
64
13-07488865
H
7-11558793
64
11-56303474
15
7-95124575
65
13-10880038
15
7-36558962
65
11-58954948
16
8-22375261
66
13-14164354
16
7-59884259
66
11-61521357
17
8-47976690
67
I3I734583I
17
7-81691106
67
11-64005988
18
8-72067060
68
13-20428300
18
8-02117073
68
11-66411963
19
8-94769592
69
13-23415415
19
8-21283630
69
11-68742262
20
9-16194509
70
13-26310663
20
8-39298446
70
1170999722
21
9-36440705
71
13-29117378
21
8-56257287
71
11-73187049
22
9-55597165
72
1 3'3! 838740
22
8-72245621
72
II75306824
23
973744175
73
I3-3447779 2
23
8-87339963
73
1177361513
24
9-90954367
74
I3-37037444
24
9-01609027
74
H79353469
25
10-07293602
75
13-39520480
25
9-15114686
75
11-81284943
26
10-22821745
76
13-41929566
26
9-27912805
76
11-83158084
2?
io-37593334
77
13-44267254
27
9-40053961
77
11-84974951
28
10-51658158
78
I3-46535993
28
9-51584045
78
11-86737515
29
10-65061765
79
13-48738124
29
9-62544798
79
11-88447657
3O
10-77845904
80
13-50875896
30
972974271
80
11-90107185
31
10-90048915
81
13-52951469
31
9-82907220
81
11-91717830
32
11-01706064
82
13-54966910
32
9-92375458
82
11-93281249
33
11-12849855
83
13-56924208
33
10-01408162
83
11-94799035
34
11-23510287
84
13-58825270
34
10-10032137
84
11-96272711
35
11-33715095
85
13-60671934
35
10-18272055
85
11-97703747
36
11-43489961
86
13-62465958
36
10-26150663
86
1 1 -99093545
37
11-52858698
87
13-64209042
37
10-33688966
87
12-00443460
38
11-61843418
88
13-65902812
38
10-40906394
88
12-01754788
39
1 1 70464682
89
13-67548840
39
10-47820941
89
12-03028779
40
1178741634
90
13-69148633
40
10-54449304
90
12-04266632
41
11-86692119
91
1370703646
41
10-60806990
91
12-05469502
42
11-94332795
92
1372215276
42
10-66908423
92
12-06638498
43
12-01679228
93
1373684876
43
10-72767041
93
12-07774693
44
12-08745980
94
*375II3742
44
1078395373
94
12-08879114
45
12-15546689
95
1376503129
45
10-83805117
95
12-09952754
46
12-22094142
96
13-77854242
46
10-89007209
96
12-10996566
47
12-28400338
97
1379168249
47
10-94011882
97
I2-I20II474
48
12-34476553
98
13-80446269
48
10-98828724
98
12-12998363
49
12-40333390
99
13-81689391
49
11-03466728
99
12-13958090
50
12-45980826 100
13-82898660
50
II-07934332
100
12-14891480
TABLE VI.
Ixxi
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2-^ per
cent, -with interest allowed to a Purchaser at the following rates per cent.
Years
9 per cent.
Fears
9 per cent.
Years
1
10 per cent.
Years
10 per cent.
I
0-91743119
51
10-00913879
!
0-90909091
51
9-09846119
2
171283569
52
10-04273551
2
1-68399168
52
9-12621397
3
2-40884238
53
10-07511052
3
2-35218202
53
9-15294155
4
3-02281124
54
10-10631994
4
2-93411838
54
9-17869196
5
3-56828262
55
10-13641658
5
3-44534304
55
9-20351043
6
4-05597290
56
10-16545022
6
3-89787610
56
9-22743946
7
4-49447434
57
10-19346782
7
4-30115982
57
9-25051913
8
4-89075650
58
10-22051367
8
4-66271450
58
9-27278719
9
5-25053203
59
10-24662965
9
4-98860379
59
9-29427928
10
5-57852784
60
10-27185534
10
5-28377119
60
9-31502904
n
5-87868893
61
10*29622821
ii
5-55228724
61
9-33506828
12
6-15433369
62
10-31978370
12
5.79753409
62
9-35442706
J 3
6-40827350
63
10-34255544
13
6-02234515
63
9373I3387
H
6-64290610
64
10-36457529
14
6-22911204
64
9-39121567
15
6-86028889
65
10-38587353
15
6-41986744
65
9-40869805
16
7-06219734
66
10-40647883
16
6-59635008
66
9-42560522
17
7-25017160
67
10-42641852
17
6-76005594
67
9-44196023
18
7-42555433
68
10-44571853
18
6-91227928
68
9-45778493
19
7-58952134
69
10-48440355
19
7-05414546
69
9-47310013
20
774310672
7O
10*48249710
2O
7-18663769
7O
9-48792557
21
7-88722361
71
10-50002156
21
7-31061876
71
9-50228010
22
8-02268134
72
10-51699826
22
7-42684892
72
9-51618161
23
8-15019983
73
10-53344755
23
7-53600071
73
9-52964717
24
8-27042159
74
10-54938886
24
7-63867128
74
9-54269306
25
8-38392185
75
10-56484070
25
773539259
75
9-55533480
26
8-49121714
76
10-57982079
26
7-82664013
76
9-56758721
27
8-59277262
77
10-59434604
27
7-91284025
77
9-57946443
28
8-68900829
78
10-60843265
28
7-99437627
78
9-59098000
29
878030436
79
10-62209606
29
8-07159385
79
9-60214680
30
8-86700585
80
10-63535108
3O
8-14480547
80
9-61297720
3 1
8-94942660
81
10-64821190
3 1
8-21429435
81
9-62348304
32
9-02785264
82
10*66069210
32
8-28031776
82
9-63367560
33
9-10254530
83
10*67280467
33
8-34310994
83
9-64356574
34
9-I7374377
84
10-68456211
34
8-40288466
84
9-65316382
35
9-24166739
85
10-69597637
35
8-45983736
85
9-66247981
36
9-30651770
86
1070705892
36
8-51414709
86
9-67152323
37
9-36848020
87
1071782081
37
8-56597823
87
9-68030325
38
9-42772592
88
10-72827258
38
8-61548190
88
9-68882864
39
9-48441278
89
1073842443
39
8-66279732
89
9-69710783
40
9-53868687
90
1074828609
40
8-70805296
90
970514892
41
9-59068349
91
1075786696
4i
875136753
91
971295968
42
9-64052816
92
1076717607
42
879285089
92
9-72054759
43
9-68833750
93
1077622210
43
8-83260492
93
9-72791985
44
973421995
94
1078501340
44
8-87072415
94
973508335
45
9-77827655
95
1079355801
45
8-90729647
95
974204476
46
9-82060150
96
10-80186368
46
8-94240367
96
9-74881046
47
9-86128277
97
10-80993787
47
8-97612199
97
975538664
48
9-90040256
98
10-81778775
48
9-00852257
98
976177919
49
9-93803786
99
10-82542025
49
9-03967185
99
9-76799386
50
9-97426073
100
10-83284205
SO
9-06963199
ipo
977403615,
Ixxii
THE ENGINEEB'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Eedemption of Capital being at 2^ per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
11 per cent.
Years
11 per cent.
Years
12 per cent.
Years
12 per cent.
I
0-90090090
51
8-33967875
I
0-89285714
51
7-69771412
2
1-65610305
52
8-36298969
2
1*62912309
52
771757006
3
2-29812591
53
8-38542820
3
2-24649855
53
7-73667489
4
2-85048187
54
8*44703602
4
277148130
54
7-75506492
5
3-33059270
55
8-42785217
5
3-22323971
55
777277425
6
375164175
56
8-44791337
6
3-61598302
56
7-78983487
7
4-12378906
57
8-46725416
7
3-96046772
57
7-80627686
8
4-45499098
58
8-48590709
8
4-26498623
58
7-82212853
9
475156694
59
8-50390280
9
4-53603424
59
7-83741652
10
5-01859986
60
8*52127024
10
4-77877239
60
7-85216596
ii
5-26022447
61
8-53803672
ii
4-9973525I
61
7-86640055
12
5-47983858
62
8-55422804
12
5-19515261
62
7-88014266
13
5-68026027
63
6-56986861
13
5 '374949 J 7
63
7-89341345
14
5-86384647
64
8-58498154
14
5-53904536
64
7-90623291
15
6-03258357
65
8-59958871
15
5-68936771
65
7-91861996
16
6-18815754
66
8-61371084
16
5-82754017
66
7-93059253
17
6-33200862
67
8*62736761
17
5-95494123
67
7-94216761
18
6-46537454
68
8-64057768
18
6-07274860
68
7-95336I32
19
6-58932490
69
8-65335879
19
6-18197451
69
7-96418894
20
6-70478881
70
8-66572777
20
6-28349382
70
7-97466501
21
6*81257721
71
8-67770067
21
6-37806650
71
7-98480334
22
6*91340107
72
8*68929273
22
6*46635594
72
7-99461705
23
7-00788635
73
8*7005 1 846
23
6-54894381
73
8-00411864
24
7-09658637
74
871139169
24
6*62634227
74
8-01332000
25
7-I7999202
75
8-72192561
25
6-69900406
75
8-02223246
26
7-25854031
76
873213279
26
6-76733087
76
8-03086684
27
7-33262161
77
874202524
27
6-83168034
77
8-03923342
28
7-40258571
78
8-75161441
28
6-89237197
78
8-04734206
29
7-46874693
79
876091124
29
6-94969202
79
8-05520213
3O
7-53I38853
80
8*76992620
3O
7-00389777
80
8-06282260
31
7-59076645
81
877866929
31
7-05522110
81
8*07021206
32
7-64711254
82
878715007
32
7-10387149
82
8-07737868
33
770063731
83
879537771
33
7-15003875
83
8-08433032
34
775153234
84
8-80336097
34
7-19389522
84
8*09107447
35
7-79997238
85
8-81110826
35
7*23559775
85
8*09761834
36
7-84611714
86
8-81862761
36
7-27528941
86
8-10396878
37
7-89011288
87
8-82592677
37
7-31310096
87
8-11013243
38
7-93209380
88
8-83301313
38
7-34915215
88
8-11611558
39
7-97218325
89
8-83989380
39
7-38355288
89
8-12192431
40
8-01049483
90
8-84657558
40
7-41640416
90
8-12756445
41
8-047I3332
91
8-85306504
4i
7-44779900
91
8-13304158
42
8-08219549
92
8-85936847
42
7-47782320
92
8-13836107
43
8-11577094
93
8*86549190
43
7-50655605
93
8-14352808
44
8-14794264
94
8*87144116
44
7-53407087
94
8-14854756
45
8-17878761
95
8-87722184
45
7-56943564
95
8-15342428
46
8-20837743
96
8-88283930
46
7-58571344
96
8-15816280
47
8-23677869
97
8-88829873
47
7-60996289
97
8*16276756
48
8-26405345
98
8-89360510
48
7-63323853
98
8-16724278
49
8-29025959
99
8-89876322
49
7-65559121
99
8-17159255
5O
8-3I545II7
100
8-90377770
50
7-67706830
100
8-17582079
TABLE VI.
Ixxiii
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
13 per cent.
Years
13 per cent.
Years
14 per cent.
Years
14 per cent.
,
0-89285714
51
7-14751858
I
0-87719298
51
6-67072712
'J
I '603008 1 1
52
7-16463438
2
I-5777I7I8
52
6-68513321
3
2-19713983
53
7-18109678
3
2-14990345
53
6-69996575
4
2-69674161
54
7-19693773
4
2-62592714
54
671375310
5
3-12259111
55
7-21218722
5
3-02803787
55
672702181
6
3-48979271
56
7-22687337
6
3-37211296
56
6-73979679
7
3-80959014
57
7-24102259
7
3-66978632
57
6-75210140
8
4-09052586
58
7-25465972
8
3-9297773I
58
676395761
9
4-33920635
59
7-26780812
9
4-15874963
59
677538607
10
4-56082113
60
7-28048982
10
4-36188343
60
6-78640620
ii
475950335
6l
7-29272555
n
4-54326643
61
6-79703634
12
4-93858555
62
7-30453489
12
470616744
62
6-80729375
13
5-10078459
63
731593635
13
4-85323170
63
6-81719472
H
5-24833756
64
7-32694738
'4
4-98662276
64
6-82675466
15
5-38310318
65
7-33758453
15
5-10812741
65
6-83598812
16
5-50663860
66
7-34786342
16
5-21923423
66
6-84490887
17
5-62025816
67
7^35779889
17
5-32II9335
67
6-85352994
18
572507894
68
7-36740498
18
5-41506235
68
6-86186369
19
5-82205647
69
7-37669501
19
5-50174194
69
6-86992183
20
5-91201286
70
7-38568164
20
5-58200406
70
6-87771547
2 1
5-99565936
71
739437689
21
4-65651405
71
6-88525517
22
6-07361442
72
7-40279217
22
572584846
72
6-89255095
23
6-14641833
73
7-41093834
23
5-79050940
73
6-89961233
24
6-21454523
74
7-41882575
24
5-85093616
74
6-90644838
25
6-27841292
75
7-42646424
25
5-90751475
75
6-91306773
26
633839098
76
7-433863I8
26
5-96058575
76
6-91947861
27
639480753
77
7-44103153
27
6-01045078
77
6-92568884
28
6-44795493
78
7-44797781
28
6-05737793
78
6-93170589
29
6-49809447
79
7-45471016
29
6*10160633
79
6-93753689
30
6-54546042
so
7-46123635
30
6-14334988
80
6-94318864
31
6-59026344
81
7-46756382
31
6-18280059
81
6-94866763
32
6-63269347
82
'7-47369966
32
6-22013123
82
6-95398008
33
6-67292223
83
7-47965065
33
6-25549773
83
6-95913190 .
34
671110534
84
7-48542330
34
6-28904116
84
6-96412878
35
674738418
85
7-49102382
35
6-32088948
85
6-96897616
36
678188747
86
7-49645816
36
6-35115901
86
6-97367921
37
6-81473268
87
7-50173202
37
6-37995575
87
6-9782429;
38
6-84692720
88
7-50685088
38
6*40737646
88
6-98267210
39 6-87586943
89
7-51181998
39
6-4335Q970
89
6-98697128
40 6-90434968
9O
7-51664434
40
6-45843663
90
6-99114485
4i
6-93155101
9 1
7-52132878
41
6-48223181
91
6-99519701
42
6-95754992
92
7-52587795
42
6*50496382
92
6-99913183
43 6-98241700
93
7-53029629
43
6-51669588
93
7-00295316
44 7-00621748
94
7-53458807
44
6-54748634
94
7-00666474
45 7-02901173
95
7-53875740
45
6-56738917
95
7-01027014
46 7-05085573
96
7-54280823
46
6-58645434
96
7-01377280
47 7-07180142
97
7-54674436
47
6-60472816
97
7-0171760.3
48 7-09189711
98
7-55056844
48
6-62225369
98
7-02048300
49 ! 7-11118774
99
7-55428699
49 6-63907094
99
7-02369678
5O 7-12971520 OO
7-55790040
so i 6-65521717
00
7-02682032
Ixxiv
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
15 per cent.
STears
15 per cent.
Years
16 per cent.
Years
16 per cent.
I
0-86956521
51
6-25356862
!
0-86206896
51
5-88551396
2
1-55321189
52
6-26666685
2
1-52945619
52
5-89711434
3
2-10465539
53
6-27925764
3
2-06127270
53
5-90826261
4
2-55873658
54
6-29136630
4
2-49489869
54
5-91898149
5
2-93904255
55
6-30301652
5
2-85512909
55
5-92929225
6
3-26211089
56
6-31423048
6
3-15905889
56
5-93921477
7
3-53988028
57
6-32502003
7
3-41885684
57
5-94876774
8
378118515
58
6-33543I70
8
3-64342067
58
5-95796866
9
3-99270310
59
6-34545687
9
3-83940698
59
5-96683399
10
4-17957523
60
6-35512182
10
4-01189506
60
5-97537919
ii
4-34582406
61
6-36444285
ii
4-16482797
61
5-98361885
12
4-49464206
62
637343529
12
4-30131342
62
5-99156666
13
4-62859525
63
6-38211361
T 3
4-42383388
63
5-99923558
H
474976967
64
6-39049148
H
4'53439629
64
6-00663781
15
4-85987862
65
6-39858183
15
4-63464070
65
6-01378488
16
4-96034235
66
6-40639684
16
472592051
66
6-02068770
i/
5-05234814
67
6-41394809
17
4-80936241
67
6-02735657
18
5-13689622
68
6-42124651
18
4-88591199
68
6-03380126
19
5-21483517
69
6-42830248
19
4-95636871
69
6-04003101
20
5-28688967
70
6-43512583
20
5-02141310
70
6-04605461
21
5-35368226
71
6-44172591
21
5-08162804
71
6-05188036
22
5-41575078
72
6-44811157
22
5-I375I573
72
6-05751617
23
5-47356226
73
6-45429125
23
5-18951114
73
6-06296954
24
5-52752424
74
6-46027296
24
5-23799291
74
6-06824760
25
5-57799394
75
6*46606433
25
5-28329222
75
6-073357I5
26
5-62528577
76
6-47167261
26
5-32569993
76
6-07830463
27
5-66967759
77
6-47710472
27
5-36547260
77
6-08309621
28
571141589
78
6-48236726
28
5-40283738
78
6-08773774
29
575072003
79
6-48746651
^9
5-43799610
79
6-09223482
30
578778594
80
6-49240847
30
5-47II2872
80
6-09659277
31
5-82278915
81
6-49719888
3 1
5-50239622
81
6-I008I668
32
5'85588735
82
6-50184319
32
5-53194300
82
6-10491143
33
5-88722265
83
6-50634665
33
5-55989902
83
6-10888164
34
5-91692341
84
6-51071426
34
5-58638150
84
6-11273176
35
5-94510591
85
6-51495079
35
5-61149650
85
6-11646604
36
5-97187569
86
6-51906082
36
5-63534018
86
6-12008853
37
599732882
87
6-52304875
37
5-65799996
87
6-12360313
38
6-02155290
88
6-52691877
38
5^7955546
88
6-12701357
39
6*04462797
89
6-53067490
39
5-70007938
89
6-13032341
40
6*06662735
90
6-53432100
40
571963821
90
6-I3353606
4i
6-08761828
91
6-53786078
41
573829291
91
6-13665483
42
6-10766258
9 2
6-54129778
42
5-75609944
92
6-13968284
43
6-12681716
93
6-54463541
43
577310930
93
6-14262312
44
6-14513450
94
6-54787696
44
5-78936993
94
6-14547860
45
6-16266310
95
6-55102555
45
5-80492513
95
6-14825199
46
6-17944783
96
6-55408422
46
5-81981537
96
6-15094604
47
6-19553023
97
6-55705587
47
5-83407816
97
6-15356329
48
6-21094890
98
6-55994329
48
5-84774824
98
6-15610622
49
6-22573967
99
6-56274918
49
5-86085791
99
6-15857720
50
6-23993588
100
6-56547611 so
5-873437I7
100
6-16097853
TABLE VI.
Ixxv
Present Value of 1 per Annum in n years ; Redemption of Capital being at
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
17 percent.
Years
17 per cent.
Years
18 per cent.
Years
18 per cent.
T
0-85470085
51
5-55837503
!
0-84745762
51
5-26568832
2
1-50641622
52
5-56872052
2
1-48406010
52
5-27497207
3
2-01964237
53
5-57866069
3
1-97966031
53
5-28389037
4
2-43416865
54
5-58821602
4
2-37632490
54
5-29246182
5
277587430
55
5-59740570
5
270090069
55
5-30070381
6
3-06231845
56
5-60624768
6
2-97132695
56
5-30863259
7
3-30583507
57
5-61475878
7
3-20004680
57
5-31626342
8
3-51534197
58
5-62295478
8
3-39596229
58
5-32371056
9
3-69744694
59
5-63085049
9
3-56561039
59
5-33068745
10
3-85715024
60
5-63845984
10
371389955
60
5-33750667
ii
3-99830543
61
5-64579694
ii
3-84458709
61
5-34408008
12
4-12393026
62
5-65287112
12
3-96059796
62
5-35041884
13
4-23642163
63
5-65969702
13
4-06424315
63
535653346
14
4-33770744
64
5-66628461
14
4-15737277
64
5-36243385
15
4-42935597
65
5-67264426
15
4-24148548
65
5-368I2938
16
4-51265598
66
5-67878574
16
4-31780815
66
5-37362887
17
4-58867633
67
5-6847I832
17
4-38735482
67
5-37894070
18
4-65831 101
68
5-69045077
18
4-45097094
68
5-38407276
19
472231345
69
5-69599137
19
4-50936700
69
5-38903254
20
478I323II
70
570134799
20
4-56314443
70
5-39382714
21
4-83588629
71
370652811
21
4-61281576
71
5-39846328
22
4-88647244
72
571153878
22
4-65882046
72
5-40294735
23
4-93348726
73
571638675
23
479 I 537Si
73
5-40728540
24
4-97728317
74
5-72107840
24
474129547
74
5-41148320
25
5-01816775
75
572561981
25
477838060
75
5-41554622
26
5-05641067
76
573001676
26
4-81304343
76
5-41947967
27
5-09224935
77
573427476
27
4-84550420
77
5-42328849
28
5*12589368
78
5-73839906
28
4-87595729
78
5-42697744
29
5-15752983
79
5-74239465
29
4-90457491
79
5-43055098
30
5-18732357.
80
574626631
30
4-93151018
80
5-43401343
31
5-2I542298
81
575001859
31
4-95689970
81
5-43736887
32
5-24196072
82
575365583
32
4-98086570
82
5-44062121
33
5-26705602
83
5757I82I9
33
5-00351793
83
5-44377419
34
5-29081631
84
576060163
34
5-02495517
84
5-44683138
35
5-3I333868
85
5-76391795
35
5-04526658
85
5-44979617
36
5-3347I006
86
576713478
36
5-06453287
86
5-45267184
37
5"355 OI 33i
87
577025558
37
5-08282723
87
5-45546161
38
5-37431809
88
577328369
38
5-10021624
88
5-45816816
39
5-39269167
89
577622230
39
5-11676055
89
5-46079466
40
5-41019465
90
577907445
40
5-I325I557
90
5-46334375
41
5-42688250
9 1
578184307
4i
5-14753199
91
5-46581805
42
5-44280611
92
578453098
42
5-16185628
92
5-46822010
43
5-45801229
93
578714087
43
5-17553116
93
5-47055230
44
5-47254411
94
578967532
44
5-18859591
94
5-47281699
45
5-48644132
95
579213683
45
5-20108674
95
5-47501639
46
5-49974062
96
5-79452776
46
5-21303710
96
5-47715263
47
5-51247600
97
5-79685043
47
5-22447791
97
5-47922779
48
5-52467893
98
5.79910703
48
5-23453780
9
5-48124383
49
5-53637863
99
5-80129968
49
5-24594334
99
5-48320266
50
5-54760224
100
5-80343043
50
5-25601920
100
5-48510611
lxx\ 7 i
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 2
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
19 per cent.
Years
19 percent.
Years
20 per cent.
Years
20 per cent.
I
0-84033613
51
5-00228366
I
0-83333333
51
4-76397606
2
1-46235783
52
5-OI066IIO
2
1-44128114
52
477I5737I
3
1-94123054
53
5-01870737
3
I -90426438
53
477886988
4
2-32116644
54
5-02643943
4
2-26851054
54
478588007
5
2-62987050
55
5-03387310
5
2-56248058
55
4-79261876
6'
2-88558674
56
5-04102319
6
2*80465596
56
4-79909947
7
3-10081914
57
5-04790356
7
3-00756014
57
4-80533489
8
3-28442447
58
5-05452722
8
3-17998041
58
4-8II33689
9
3-44285171
59
5-06090635
9
3-32826450
59
4-81711659
10
3-58090822
60
5-06705241
10
3-457II220
60
4-82268446
ii
370225083
61
5-07297617
ii
3-57007761
61
4-82805033
12
3-80971064
62
5-07868777
12
3-66989814
62
4-83322344
13
3-90551358
63
5-08419676
13
375871640
63
4-83821251
H
3-99 1 43399
64
5-08951213
H
3-83823343
64
4-84302575
15
4-06890353
65
5-09464238
15
3-90981685
65
4-84767089
16
4-13909017
66
5-09959553
16
3-97457878
66
4-85215524
17
4-20295622
67
5-10437917
17
4-03343280
67
4-85648572
18
4-26130164
68
5-10900046
18
4-08713643
68
4-86066886
19
4-31479697
69
5-11346618
19
4-13632303
69
4-86471084
20
4-36400842
70
5-11778278
20
4-18152627
70
4-86861751
21
4-40941746
71
5-12195635
21
4-22319899
71
4-87239443
22
4-45143605
72
5-12599267
22
4-26172795
72
4-87604686
23
4-49041879
73
5-12989722
23
4-29744549
73
4-87957979
24
4-52667255
74
5-13367523
24
4-33063872
74
4-88299797
25
4-56046426
75
5'13733l65
25
4-36155701
75
4-88630591
26
4-59202716
76
5-14087120
26
4-39041798
76
4-88950789
27
4-62156602
77
5-14429835
27
4-41741239
77
4-89260800
28
4-64926129
78
5-14761740
28
4-44270818
78
4-89561012
29
4-67527266
79
5-15083240
29
4-46645377
79
4-89851795
30
4-69974193
80
5-15394724
30
4-48878082
80
4-90133502
31
472279546
81
5-15696563
31
4-50980653
Si
4-90406470
32
4-74454623
82
5-15989109
32
4-52963557
82
4-90671018
33
4-76509552
83
5-16272699
33
4-54836174
83
4-90927455
34
4-78453445
84
5-16547658
34
4-56606930
84
4-91176073
35
4-80294519
85
5-16814292
35
4-58283418
85
4-91417151
36
4-82040202
86
5-17072896
36
4-59872499
86
4-91650957
37
4-83697229
87
5^7323753
37
4-61380387
87
4-91877748
38
4-85271717
88
5-17567132
38
4-62812725
88
4-92097769
39
4-86769239
89
5-17803291
39
4-64174645
89
4-92311253
40
4-88194879
90
5-18032480
40
4-65470831
90
4-92518425
41
4-89553287
91
5-18254934
4i
4-66705562
91
4-92719502
42
4-90848723
92
5-18470881
42
4-67882757
92
4-92914689
43
4-92085099
93
5-18680540
43
4-69006012
93
4-93104186
44
4-9326601 1
94
5-18884121
44
4-70078630
94
4-93288180
45
4-94394773
95
5-19081824
45
471103655
95
4-93466856
46
4-95474444
96
5-19273842
46
472083893
96
4-93640388
47
4-96507848
97
5-19460363
47
473021938
97
4-93808945
48
4-97497602
98
5-19641562
48
473920187
98
4-93972688
49
4-98446133
99
5-19817613
49
4-74780864
99
4'94I3I773
50
4-99355689 |ioo
5-19988681
50
475606031
100
4-94286350
TABLE VI.
Ixxvii
'resent Value of 1 per Annum in n years; Redemption of Capital being at
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years 21 per cent.
Years
21 per cent.
Years
22 per cent.
Years
22 per cent.
I
0-82644628
51
4-54734I79
I
0-81967213
51
4-34955276
2
1-42080377
52
4-55426366
2
I -40089934
52
4-355885I7
3
1-86867977
53
4-56090993
3
I -83440070
53
4-36196465
4
2-21819065
54
4-56729482
4
2-17005470
54
4-36780432
5
2-49845807
55
4-57343162
5
2-43755674
55
4-37341641
6
2-72814099
56
4.57933274
6
2-65569002
56
4-37881235
7
2-91974699
57
4-58500982
7
2-83691621
57
4-38400286
8
3-08197424
58
4-59047373
8
2-98982849
58
4-38899793
9
3-22105913
59
4'59573469
9
3-12054455
59
4-39380698
10
3-34158970
60
4-60080228
10
3-23353812
60
4-3984388I
ii
3-44701644
61
4-60568552
ii
3-33215646
61
4-40290171
12
3-53998432
62
4-61039286
12
3-41895389
62
4-40720346
13
3-62255484
63
4-61493228
13
3-4959 1 346
63
4-41135140
14
3-69635856
64
4-61931131
14
3-56459823
64
4-4I535243
15
3-76270210
65
4-62353703
15
3-62625685
65
4-41921308
16
3-82264475
66
4-62761612
16
3-68189884
66
4-42293946
17
3-87705442
67
4-63155492
17
373234921
67
4-42653741
18
3-92664893
68
4-63535939
18
. 377828880
68
4-43001240
19
3-97202716
69
4-63903519
19
3-82028442
69
4-43336962
20
4-01369265
70
4-64258768
20
3-85881181
70
4-43661398
21
4-05207193
71
4-64602192
21
3-89427318
71
4-439750I5
22
4-08752860
72
4-64934273
22
3-92701091
72
4-44278254
23
4-12037463
73
4-65255467
23
3-95731829
73
4-4457I534
24
4-15087914
74
4-65566209
24
3-98544801
74
4-44855251
25
4-17927553
75
4-65866909
25
4-01161892
75
4-45129785
26
4-20576722
76
4-66157959
26
4-03602155
76
4-45395494
27
4-23053233
77
4-66439732
27
4-05882253
77
4-45652719
28
4-25372748
78
4-66712584
28
4-08016825
78
4-45901786
29
4-27549094
79
4-66976850
29
4-10018779
79
4-46143005
30
4-29594525
80
4-67232855
30
4-11899546
80
4-46376670
31
4-3I5I9938
81
4-67480904
31
4-13669284
81
4-46603063
32
4-33335058
82
4-67721290
32
4-15337048
82
4-46822453
33
4-35048590
83
4-67954294
33
4-16910939
83
4-47035095
34
4-36668350
84
4-68180182
34
4-18398224
84
4-47241234
35
4-38201375
85
4-68399210
35
4-19805443
85
4-47441 104
36
4-39654020
86
4-68611622
36
4-21138496
86
4-47634929
37
4-41032034
87
4-68817651
37
4-22402721
87
4-47822922
38
4-42340637
88
4-69017521
38
4-23602957
QO
oo
4-48005288
39
4-43584574
89
4-69211445
39
4-24743603
89
4-48182222
40
4-44768170
90
4-69399629
40
4-25828667
90
4-483539I3
4i
4-45895377
9 1
4-69582268
4i
4-26861806
91
4-48520539
42
4-469698 1 1
92
4-6975955I
42
4-27846369
92
4-48682273
43
4-47994787
93
4-69931659
43
4-28785423
93
4-48839280
44
4-48973352
94
4-70098764
44
4-29681785
94
4-48991719
45
4-49908310
95
470261033
45
4-30538045
95
4-49139741
46
4-50892245
96
4-70418625
46
43I356593
96
4-49283493
47
4-51657545
97
470571694
47
4-32139632
97
4-49423114
48
4-52476416
98
4-70720387
48
4-32889201
98
4-49558740
49
4-53260904
99
4-70864845
49
4-33607185
99
4-49690500
50
4-54012904
100
471005205
so
4-34295335
100
4-49818519
Ixxviii
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
23 per cent.
Years
23 per cent.
Yeais
24 per cent.
Years
24 per cent.
I
0-81300813
5'
4-16825242
I
0-80645161
51
4-00146141
2
1-38154528
52
4-17406758
2
1-36271871
52
4-00682019
3
1-80135660
53
4-17964980
3
176948192
53
4-01196377
4
2-12396353
54
4-18501122
4
2-07978956
54
4-01690336
5
2-37955377
55
4-19016313
5
2-32424706
55
4-02164945
6
2-58698765
56
4-19511609
6
2-52175028
56
4-02621183
7
275865547
57
4-19988000
7
2-68459670
57
4-03059965
8
2-90303279
58
4-20446409
8
2-82113434
58
4-03482147
9
3-02611333
59
4-20887705
9
2-93722944
59
4-03888533
10
3-13225545
60
4-21312700
10
3-03712494
60
4-04279875
ii
3-22470427
61
4-21722159
n
3-12396562
61
4-04656881
12
3-30592581
62
4-22II6800
12
3-20013182
62
4-05020216
13
3-37782753
63
4-22497300
13
3-26745842
63
4-05370505
H
3-44190804
64
4-22864295
H
3-32738259
64
4-05708338
15
3-49936103
65
4-23218385
15
3-38104602
65
4-06034269
16
3-55114912
66
4-23560138
16
3-42936718
66
4-06348822
17
3-59805715
67
4-23890088
17
3-47309327
67
4-06652492
18
3-64073145
68
4-24208740
18
3-51283843
68
4-06945746
19
3-67970907
69
4-24516573
19
3-54911207
69
4-07229026
20
371543997
70
4-24814039
20
3-58234027
70
4-07502750
21
374830398
71
4-25101568
21
3-61288217
71
4-07767315
22
3-77862394
72
4-25379565
22
3-64104263
72
4-08023097
23
3-80667601
73
4-25648417.
23
3-66708207
73
4-08270450
24
3-83269783
74
4-25908489
24
3-69122435
74
4-08509713
25
3-85689499
75
4-26160128
25
3-71366291
75
4-08741208
26
3-87944626
76
4-26403667
26
373456579
76
4-08965239
27
3-90050784
77
4-26639417
27
3-75407967
77
4-09182096
28
3-92021680
78
4-26867680
28
377233317
78
4-09392056
2 9
3-93869394
79
4-27088739
29
3-7894395I
79
4-09595382
30
3-95604610
80
4-27302867
30
3-80549881
80
4-09792323
31
3-97236817
81
4-27510321
31
3-82059988
81
4*09983120
32
3-98774467
82
4-27711349
32
3-83482177
82
4-10167999
33
4-00225116
83
4-27906187
33
3-84823512
83
4-10347177
34
4-01595538
84
4-28095058
34
3-86090323
84
4-10520863
35
4-0289^825
85
4-28278178
35
3-87288296
85
4-10689254
36
4-04119470
86
4-28455753
36
3-88422558
86
4-10852540
37
4-05283438
87
4-28627979
37
3-89497740
87
4-11010902
38
4-06388231
oo
oo
4-28795043
38
3-90518038
88
4-11164513
39
4-07437937
89
4-28957127
39
3-91487261
89
4-II3I3539
40
4-08436279
90
4-29114401
40
3-92408877
90
4-11458139
4i
4-09386654
91
4-29267031
4i
3-93286048
91
4-11598466
42
4-10292168
92
4-29415174
42
3-94121665
9 2
4-11734664
43
4-11155668
93
4-29558985
43
3-94918375
93
4-11866874
44
4-11979765
94
4-29698607
44
3-95678607
94
4-11995229
45
4-12766862
95
4-29834180
45
3-96404594
95
4-121 19860
46
4-13519171
96
4-29965837
46
3-97098391
96
4-12240887
47
4-14238735
97
4-30093709
47
3-97761896
97
4-12358432
48
4-14927440
98
4-30217918
48
3-98396861
98
4-12472607
49
4-I5587033
99
4-30338583
49
3-99004906
99
4-12583522
50
4-16219132
100
4-30455819
50
3-99587535
100
4-12691283
TABLE VI.
Ixxix
Present Value of 1 per Annum in n years; Redemption of Capital being at
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
25 per cent.
Years
25 per cent. Years
25 percent.
Years
25 per cent.
I
O'SOOOOOOO
26
3-60011705
51
3-84750498
76
3-92897113
2
1-34459834
27
3-61824777
52
3-85245908
77
3-93097260
3
1-73871566
2S
3-63520126
53
3-85721375
78
3-93291034
4
2-03741560
29
3-65108390
54
3-86177941
79
3-93478677
5
2-27145288
30
3-66598962
55
3-86616582
so
3-93660422
6
2-45972223
56
3-87038205
7
2-61441032
31
3-68000173
57
3-87443662
81
3-93836489
8
274373 00 3
32
3-69319435
58
3-87833748
82
3-94007089
9
2-85341801
33
370563363
59
3-88209208
83
3-94172423
2-94760256
34
371737883
60
3-88570742
84
3-94332683
35
372848317
85
3-94488053
ii
3-02933038
36
373899460
61
3-88919006
86
3.94638708
12
3-10089897
37
3-74895640
62
3-89254617
87
3-94784815
13
3-16407363
33
375840778
63
3-89578156
88
3-94926535
H
3-22023311
39
376738431
64
3-89890168
89
3-95064021
15
3-27046993
40
377591838
65
3-90196170
90
3-95197420
16
3-31566099
66
3-90481646
17
3-35651826
4i
3-78403949
67
3-90762055
91
3-95326872
18
3-39362584-
42
379177460
68
3-91032831
92
3-95452513
19
3-42746741
43
379914840
69
3-91294383
93
3-95574472
20
3-45844693
44
3-80618353
70
3-91547098
94
3-95692872
45
3-81290080
95
3-95807833
21
3-48690442
46
3-81931936
71
3-91791345
96
3-95919468
22
3-51312813
47
3-82545687
72
3-92027470
97
3-96027888
23
3-53736403
48
3-83132964
73
3-92255804
98
3-96133198
24
3-55982329
49
3-83695277
74
3-92476660
99
3-96235499
25
3-58068822
50
3-84234022
75
3.92690336
100
3-96334887
TABLE VII.
FOE
VALUING MINERAL AND OTHER PROPERTIES,
OB
The present value (or years' purchase) of 1 per annum in
n years, allowing interest to a present purchaser upon his
purchase money or capital invested, at the rates of 3^,4,
4i 5. Si 6, 7, 8, 9, 10, n, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 25, 24, and 25 per cent, per annum, and redeeming
the capital so invested by an Annual Redemption Fund,
at the rate of 3 per cent, per annum.
Calculated to 8 places of decimals, and to 100 years for
each percentage.
TABLE VII.
Ixxxiii
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
3 per cent.
Years
3 per cent.
Years
4 per cent.
Years
4 per cent.
I
0-96618357
51
22-97064504
I
0-96153846
51
20*60418764
2
I-89533635
52
23-13894415
2
1-87754347
52
20-73949417
3
2-78916405
5J
23-30203549
3
275080186
53
20-87041924
4
3-64927483
54
23-46008908
4
3-58388198
54
20-997 1 1 78 1
5
4-47718618
55
23-61326887
5
4379 1 5472
55
21-11973855
6
5-27433115
56
23-76173297
6
5-13881215
56
21-23842415
7
6-04206411
57
23-90563402
7
5-86488408
57
2I-3533II74
8
6-77766575
58
24-04511909
8
6-55925283
58
21-46453285
9
7-49434980
59
24-18033027
9
7-22366639
59
21-57221398
10
8-18126365
60
24-31140457
10
7-85974980
6O
21-67647661
ii
8-84349638
61
24-43847430
ii
8-46901774
61
2177743756
12
9-48208065
62
24-56166184
12
9-05287996
62
21*87520491
13
10-09799661
63
24-68110677
13
9-61265388
63
21*96989959
14
10-69217517
64
24-79691199
14
10-14957026
64
22*06161265
15
11-26550098
65
24-90919800
15
10-66478051
65
22-15044847
16
11-82781528
66
25-01813220
16
11-15936304
66
22-23650325
17
12-35291852
67
25-12365309
17
11-63432894
67
22-31986976
18
12-86857266
68
25-22603339
18
12-09062710
68
22*40063727
19
13-36650354
69
25-32531718
19
12-52914897
69
22*47889185
20
13-84740292
70
25-42160131
2O
12-95073284
70
22-55471628
21
14-31193037
71
25-5I497955
21
13-35616766
71
22-62819046
22
14-76071520
72
25-60554253
22
1374619672
72
22*69939137
23
15-19435802
73
25-69337787
23
14-12152080
73
22*76839322
24
15-61343242
74
25-77857024
24
14-48280123
74
22-83526751
25
16-01848636 ^
75
25-86120175
25
14-83066253
75
22*90008337
26
16-41004359
76
25-94135060
26
15-16569501
76
22-96290717
27
16-78860502
77
26-01909611
27
15-48845708
77
23-02380335
28
17-15464972
78
26*09451002
28
1579947723
78
23-08283383
2 9
17-50863624
79
26-16766486
29
16-09925614
79
23-14005839
30
17-85100361
80
26-23863016
30
16-38826842
80
23-I9553485
31
18-18217230
81
26-30747306
31
16-66696423
8l
23-24931890
32
18*50254524
82
26-37425864
32
16-93577090
82
23-30146439
33
18-81250859
83
26-43904992
33
17-19509430
83
23-35202337
34
19-11243262
84
26-50190777
34
17-44532010
84
23-40104596
35
19-40267262
85
26-56289133
35
17-68681516
85
23-44858081
36
19-68356922
86
26-62205768
36
17-91992846
86
23-49467475
37
I9-95544970
87
26-67946207
37
18-14499229
87
23-53937302
38
20-21862803
88
2673515815
38
18-36232312
88
23-58271948
39
20-47340591
89
2678919781
39
18-57222265
89
23-62475645
40
20-72007314
90
26-84163123
40
18-77497850
90
23*66552478
41
20-95890824
91
26-89250714
4i
18-97086513
91
23*7050641 1
42
21-19017899
92
26-941872-58
42
19-16014453
9 2
2374341259
43
21-41414275
93
26-98977326
43
19-34306678
93
23-78060727
44
21-63104719
94
27-03625348
44
19-51987094
94
23-81668396
45
21-84113056
95
27-08135596
45
19-69078547
95
23-85167716
46 ! 22-04462203
96
27-12512225
46
19-85602878
96
23-88562038
47 22-24174232
97
27-16759267
47
20*01580989
97
23-91854608
48 22-43270390
98
27-20880612
48
20-17032883
98
23-95048553
49
22-61771135
99
27-24880037
49
20-31977709
99
23*98146906
50
22-79696180
100
27-28761200 || so
20-46433812
100
24*01152597
Ixxxiv
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Tears
4i per cent.
fears
4$ per cent.
Tears
5 per cent.
Years
5 per cent.
I
' 0-95693780
51
18-67977925
I
0-95238095
51
17-08413948
2
1-86008155
52
1879092298
2
1-84294144
52
17-17705901
3
2-71348062
53
18-89833805
3
2-67715853
53
17-26677162
4
3-52079148
54
19-00216439
4
3-45988383
54
I7'35340328
5
4-28532423
55
19-10253575
5
4-19543034
55
17-43707409
6
5-01008279
56
19-19958003
6
4-88764524
56
17-51789855
7
5-69779941
57
19-29341971
7
5-53997119
57
17-59598600
8
6-35096491
58
19-38417188
8
6-15549815
58
17-67144066
9
6-97185463
59
19-47194875
9
6-73700745
59
1774436219
10
7-56255138
60
I9'55685776
10
7-28700946
60
17-81484574
ii
8-12496536
61
19-63900188
ii
7-80777582
61
17-88298227
12
8-66085170
62
1971847636
12
8-30136716
62
17-94885590
13
9-17182594
63
1979538634
13
8-76965710
63
18-01255856
14
9-65937760
64
19-86981216
14
9-21435302
64
18-07416122
IS
10-12488227
65
19-94184448
15
9-63701411
65
18-13374306
16
10-56961234
66
20-01160293
16
10-03906710
66
18-19137709
17
10-99474645
67
20-07905977
17
IO'42l820IO
67
18-24713336
18
11-40137805
68
20-14440026
18
10-78647467
68
18-30107896
19
1179052288
69
20-20766255
19
11-13413643
69
18-35327828
2O
12-16312587
70
20-26891783
20
11-46582453
70
I8-40379299
21
12-52006709
71
20-32823464
21
1178247989
71
18-45268235
22
12-86216731
72
20-38567886
22
12-08497261
72
18-5000032^
23
13-19019289
73
20-44131386
23
12-37410850
73
18-54581022
24
13-50486020
74
20-49520057
24
12-65063492
74
18-59015572
25
13-80683963
75
20'54739776
25
12-91524598
75
18-63309018
26
14-09675925
76
20-59796175
26
13-16858723
76
18-67466190
27
14-37520811
77
20-64694710
27
13-41125985
77
1871491754
28
14-64273912
78
20*69440614
28
13-64382432
78
1875390183
29
14*89987187
79
20-74038930
29
13-86680387
79
1879165781
30
15-1470951!
80
2078494524
30
14-08068755
80
18-82822692
31
15-38486893
81
20-82812079
31
14-28593290
81
18-86364899
32
15-61362686
82
20-86996112
32
14-48296853
82
18-89796241
33
I5-83377779
83
20-91050980
33
14-67219631
83
18-93120415
34
16-04570757
84
20-94980877
34
14.85399340
84
18-9634097:
35
16-24978084
85
20-98789863
35
15-02871425
85
18-99461351
36
16-44634209
86
2 1 -0248 1 840
36
15-19669211
86
19-0248484^
37
16-63571747
87
21-06060575
37
15-35824070
87
19-0541464:
38
16-81821558
88
2I-095297II
38
I5-5I365556
88
19-0825380^
39
16-99412892
89
21*12892760
39
15-66321541
89
19-11005297
40
I7-I6373475
90
2I'l6l53I09
40
15-80718325
99
19-13671965
41
17-32729614
9 1
21-19314036
4i
15-94580750
91
19-1625656/1
42
17-48506287
92
21-22378694
42
16-07932301
92
19-18761742
43
17-63727212
93
2I-25350I42
43
16-20795183
93
19-2119006:
44
I7784H944
94
2I-2823I33I
44
16-33190430
94
19-23544000
45
17-92590930
95
2I-3I025I02
45
16-45137961
95
19-2582593:
46
18-06275579
96
2I337342II
46
16-56656656
96
19-2803816:
47
18-19488327
97
21-36361324
47
16-6776443!
97
19-3018291^
48
18-32247691
98
21-38909007
48
1678478292
98
19-32262341
49
18-44571319
99
21-41379745
49
16-88814389
99
19-3427850,
50
18-56476045
100
21-43775939
50
16-93788076
100
i9'3 62 334oc
TABLE VII.
1
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
5J per cent.
Years
5i per cent.
Years
6 per cent.
Years
6 per cent.
I
0-94786729
51
1573964779
I
0-94339622
51
I4-59I33539
2
1-82611433
52
15-81848386
2
1-80959173
52
14-65906309
3
2-64179600
53
I5-89453508
3
2-60735549
53
14-72435148
4
3-40104768
54
15-96791494
4
3-34417912
54
14-78730296
5
4-10923039
55
16-03873135
5
4-02650128
55
14-84801476
6
477104927
56
16*10708698
6
4-65988652
56
14-90657914
7
5-39065094
57
16-17307959
7
5-24916876
57
14-96308386
8
5-97170408
58
16-23680223
8
5-79856743
58
15-01761223
9
6-51746635
59
16-29834363
9
6-31178221
59
15-07024359
10
7-03084046
60
16-35778836
10
6-79207063
60
15-12105340
ii
7-5I442I24
61
16-41521709
ii
7-24231231
61
15-17011355
12
7-97053545
62
16-47070440
12
7-66506220
62
15-21749047
13
8-40127557
63
16-52433115
13
8-06259515
63
15-26325569
14
8-80852857
64
16-57616025
14
8-43694329
64
15-30746527
1
17
9-19400054
9-55923794
9-90564581
65
66
67
16-62626130
16-67472348
16-72153314
15
16
17
8-78992755
9-12318449
9-43818902
65
66
67
15-35018073
I5-39I45878
15-43135368
18
10-23450360
68
16-76682410
18
9-73627395
68
15-46991720
*9
10-54697892
69
16-81062764
19
10-01864665
69
15-50719891
20
10-84413953
70
16-85299759
20
10-28640355
70
15-54324614
21
11-12696376
71
16-89398560
21
10-54054258
71
15-57810426
22
11-39634974
72
16-93364115
22
1078197401
72
15-61181665
23
11-65312343
73
16-97201168
23
11-01152985
73
15-64442488
24
11-89804576
74
17-00914266
24
11-22997214
74
15-67596872
25
I2-I3l8l886
75
17-04507782
25
11-43800013
75
1570648640
26
12-35509172
76
17-07985894
26
11-63625663
76
1573601441
27
12-56846510
77
17-11352637
27
11-82533363
77
15-76458791
28
1277249587
78
17-14611870
28
12-00577717
78
15-79224054
2 9
12-96770103
79
17-17767304
29
12-17809177
79
15-81900459
30
I3-I5456I22
80
17-20822508
30
12-34274429
80
15-84491110
31
13*33352377
81
17-23780909
31
12-50016738
81
15-86998982
32
13-50500567
82
17-26645804
32
12-65076257
82
15-89426936
33
13-66939600
83
17-29420365
33
12-79490302
83
15-91777724
34
13-82705824
84
17-32107639
34
12-93293595
84
I5-94053935
35
T3-97833245
85
17-34710567
35
13-06518494
85
15-96258263
36
14-12353690
86
17-37231973
36
13-19195181
86
1 5 -9839300 1
37
14-26297006
87
17-39674572
37
13-31351849
87
16-00460546
38
14-39691190
88
17-42040988
38
13-43014857
88
16-02463163
39
14-52562541
89
I7-44333746
39
13-54208886
89
16-04403029
40
14-64935783
90
17-46555272
40
13-64957061
90
16-06282237
41
14-76834182
91
17-48707913
41
13-75281077
91
16-08102803
42
14-88276854
92
17-50793922
42
13-85201308
9 2
16-09866682
43
14-99292852
93
17-52815479
43
13-94736899
93
16-11575734
44
15-09893268
94
17-54774684
44
14-03905867
94
16-13231771
45
15-20099307
95
I7-56673558
45
14-12725179
95
16-14836526
46
15-29928356
96
17-58514052
46
14-21210819
96
16-16391678
47
I5-39396864
97
17-60298056
47
14-29377873
97
16-17898846
48
15-48520398
98
17-62027383
48
14-37240580
98
16-19359586
49
15-57313700
99
I7-63703788
49
14-44812393
99
16-20775403
50
15-65790744
100
17-65328964
50
14-52106035
100
16-22147744
Ixxxvi
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
7 per cent.
Years
7 per cent.
Years
8 per cent.
Years
8 per cent.
I
C'93457943
51
I2-73336709
I
0-92592592
51
11-29511823
2
177742755
52
1278491442
2
1-74638679
52
II-33565999
3
2-54109998
53
12-83454758
3
2-47812827
53
II-37466I27
4
3-23596273
54
12-88235073
4
3-13453049
54
11-41219109
5
3-87064953
55
12-92840350
5
3-72641314
55
11-44831867
6
4-45240930
56
12-97278124
6
4-26262001
56
1 1-48310336
7
4-98737312
57
I3-OI555539
7
4-75045044
57
11-51660525
8
5-48076177
58
13-05679360
8
5-19598235
58
11-54887815
9
5-93704863
59
13-09656008
9
5-60431757
59
11-57998092
10
6-36008890
60
I3'I349I577
10
5-97977020
60
11-60995762
ii
6-75322282
61
13-17191855
ii
6-32601306
61
11-63885769
12
7-11935891
62
13-20762187
12
6-64619261
62
11-66672495
13
7-46104157
63
13-24208274
13
6-94301997
63
11-69360579
H
7-78050638
64
13-27534625
H
7-21884378
64
II7I9537I2
15
8-07972553
65
13-30746136
15
7-47570879
65
1174455874
16
8-36044561
66
I3338473I8
16
771540350
66
11-76870731
17
8-62421894
67
13-36842477
17
7-939499I5
67
1179201775
18
8-87242987
68
I3-397357I4
18
8-14938169
68
11-81452327
J 9
9-10631693
69
13-42530947
19
8-34627837
69
11-83625553
20
9-32699156
70
13-45231908
20
8-53127981
70
11-85724469
21
9-53545399
71
13-47842168
21
8-70535854
71
11-87751951
22
9-73260687
72
I3'50365I36
22
8-86938454
72
11-89710745
2 3
9-91926682
73
13-52804071
23
9-02413845
73
11-91603469
24
10-09617455
74
13-55162087
24
9-17032276
74
11-93432623
25
10-26400341
75
13-57442171
25
9-30857133
75
II-9520060I
26
10-42336690
76
13-59647167
26
9-43945760
76
1 1 -9690968 1
27
10-57482526
77
13-61779815
27
9-56350167
77"
11-98562054
28
1071889100
78
13-63842730
28
9-68117627
78
12-00159807
29
10-85603399
79
13-65838417
29
9-7929I2I2
79
12-01704940
30
10-98668576
80
13-67769284
30
9-89910248
80
12-03199369
31
11-11124336
81
13-69637630
31
IO-OOOI07I2
81
12-04644927
3 2
11-23007273
82
13-71445668
32
10-09625586
82
12-06043372
33
11-34351170
83
I373I95520
33
10-18785156
83
12-07396389
34
11-45187260
84
13-74889221
34
10-27517289
84
12-08705592
35
11-55544472
85
13-76528728
35
10-35847667
85
12-09972533
36
11-65449628
86
13-78115918
36
10-43799996
86
12-11198697
37
11-74927640
87
13-79652592
37
10-51396195
87
12-12385511
38
11-84001673
88
13-81140487
38
10-58656559
88
12-13534346
39
11-92693299
89
13-82581271
39
10-65599912
89
12-14646518
40
12-01022629
90
I3-83976543
40
1072243731
90
12-15723291
4i
12-09008435
91
13-85327848
4i
10-78604269
9 1
12-16765882
42
12-16668261
92
13-86636665
42
10-84696661
92
12-17775456
43
12-24018519
93
13-87904425
43
10-90535014
93
12-18753138
44
12-31074584
94
13-89132502
44
10-96132498
94
I2-I97000IO
45
12-37850870
95
13-90322216
45
11-01501421
95
I2-206I7I08
46
12-44360902
96
13-91474842
46
11-06653293
96
12-21505434
47
12-50617391
97
13-92591610
47
11-11598899
97
12-22365953
48
12-56632288
98
I3'936737oo
48
11-16348350
98
12-23199590
49
12-62416843
99
13-94722251
49
11-20911134
99
12-24007238
90 j 12-67981654
100
I3-9573836I
50
11-25296164
100
12-24789756
TABLE VII.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at tht3 following rates per cent.
Years
9 per cent.
Years
9 per cent.
Years
10 per cent.
Years
10 per cent.
I
0-91743119
51
10-14879934
I
0-90909090
51
9-21371763
2
171641160
52
10-18151776
2
1-68744805
52
9-24067663
3
2-4I8202I2
53
10-21297047
3
2-36110581
53
9-26657763
4
3-03926384
54
10-24321656
4
2-94961719
54
9-29147106
5
3-59254024
55
10-27231169
5
3-46795265
55
9-31540432
6
4-08834922
56
10-30030831
6
3-92776833
56
9-33842205
7
4-53501671
57
10-32725595
7
4-33827521
57
9-36056631
8
4-93933536
58
10-35320134
8
4-70684834
58
9-38187675
9
5-30690193
59
10-37818866
9
5-03946260
59
9-40239080
10
5-64236947
60
10-40225968
10
5-34100996
60
9-42214381
ii
5-94963818
61
10-42545395
ii
5-61553421
61
9-44116920
12
6-23200176
62
10-44780794
12
5-86640717
62
9-45949778
13
6-49226099
63
10-46936009
13
6-09646272
63
9-47716189
14
6-73281256
64
10-49014113
14
6-30810001
64
9-49418747
15
6'9557I945
65
10-51018401
15
6-5033637I
65
9-51060221
16
7-16276711
66
10-52951904
16
6-68400724
66
9-52643161
17
7-3555086I
67
10-54817507
17
6-85154279
67
9-54169987
18
7-53530123
68
10-56617953
18
7-00728147
68
9-55642998
19
7-70333646
69
10-58355848
19
7-15236567
69
9-57064382
20
7-86066453
70
10-60033681
20
7-28779538
7O
9-58436215
21
8-00821473
71
10-61653813
21
7-41444968
71
9-59760476
22
8-14681242
72
10-63218498
22
7-53310452
72
9-61039048
23
8-27719308
73
10-64729886
23
7-64444741
73
9-62273727
24
8-40001433
74
10-66190027
24
7-74908969
74
9-63466219
25
8-51586588
75
10-67600879
25
7-84757677
75
9-64618160
26
8-62527813
76
10-68964308
26
7-94039682
76
9-65731100
27
8-72872949
77
10-70282102
27
8-02798812
77
9-66806530
28
8-82665248
78
10-71555967
28
8-11074519
78
9-67845866
29
8-91943927
79
1072787532
29
8-18902423
79
9-68850463
30
9-00744615
80
10-73978361
30
8-26314758
80
9-69821618
31
9-09099762
81
10-75129944
31
8-33340772
81
9-70760568
32
9-17038984
82
10-76243712
32
8-40007061
82
971668501
33
9-24589364
83
10-77321036
33
8-46337865
83
972546550
34
9-31775723
84
10-78363226
34
8-52355323
84
973395802
35
9-38620846
85
1079371541
35
8-58079697
85
9-74217298
36
9-45145689
86
10-80347187
36
8-63529565
86
9-75012036
37
9-51369561
87
10-81291318
37
8-6872I995
87
975780969
38
9-57310279
88
10-82205046
38
873672694
00
OO
976525016
39
9-62984312
89
10-83089437
39
8-78396322
89
977245057
40
9-68406907
90
10-83945511
40
8-82905708
90
977941934
4i
9-73592199
91
10-84774252
41
8-87213759
91
978616458
42
978553310
9 2
10-85576602
42
8-9I33I747
92
979269406
43
9*83302440
93
10-86353468
43
8-95270294
93
9-79901526
44
9-87850946
94
10-87105723
44
8-99039267
94
9*80513536
45
9-92209413
95
10-87834204
45
9-02647844
95
9-81106124
46
9-96387718
96
10-88539716
46
9-06104571
96
9-81679954
47
10-00395091
97
10-89223037
47
9-09417419
97
9-82235666
48
10-04240165
98
10-89884912
48
9-12593827
98
9-82773872
49
10-07931023
99
10-90526059
49
9-15640751
99
9-83295159
50
10-11475243
100
10-91147169
50
9-18564698
100
9-83800099
Ixxxviii
THE ENGINEEK'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
11 per cent.
Years
11 per cent.
Years
12 per cent.
Years
12 per cent.
I
0-90090090
51
8-43641058
I
0-89285714
51
778005334
2
1-65944576
52
8-45900713
2
1-63235767
52
7-7992666I
3
2-30664351
53
8-48070639
3
2-25463707
53
7-81770941
4
2-86510/49
54
8-50155183
4
2-78530549
54
7-83541958
5
3-35171670
55
8-52158429
5
3-24301986
55
7-85243263
6
3-77932519
56
8-54084216
6
3-64169375
56
7-86878192
7
4-15789431
57
8'55936l59
7
3-99191472
57
7-88449883
8
4-49526312
58
8-57717661
8
4-30188219
58
7-89961286
9
4-79768505
59
8-5943I93I
9
4-57804488
59
7-91415183
10
5-07020956
60
8-61081997
10
4-82554435
60
7-92814194
ii
5-31695858
61
8-62670718
ii
5-04853032
61
7-94160792
12
5-54133018
62
8-64200729
12
5-25038880
62
7-95457255
J 3
5-74615078
63
8-65674788
13
5-4339IOII
63
7-96705961
14
5-93379056
64
8*67095 1 1 1
14
5-60141437
64
7-97908827
15
6-10625194
65
8-68464059
15
5-75484651
65
7-99067885
16
6-26523826
66
8-69783802
16
5-89584926
66
8-00185006
17
6-41220764
67
8-71056399
17
6-02581957
67
8-01261963
18
6-54841556
68
8-72283807
18
6-14595301
68
8-02300439
19
6*67494892
69
8-73467882
19
6-25727876
69
8-03302030
20
679275341
70
8-74610388
20
6-36068759
70
8-04268251
21
6-90265574
71
875713003
21
6-45695441
71
8-05200544
22
7-00538179
72
8-76777324
22
6-54675650
72
8-06100279
23
7-10157151
73
8-77804870
23
6-63468843
73
8-06968759
24
7-19179133
74
878797089
24
6-70927432
74
8-07807225
25
7-27654436
75
879755360
25
6-78297796
75
8-08616859
26
7-35627907
76
8-80680998
26
6-85221129
76
8-09398785
27
7-43139649
77
8-81575258
27
6-91734142
77
8-10154079
28
7-50225630
78
8-82439339
28
6-97869659
78
8-10883766
29
7-56918207
79
8-83274383
29
7-03657119
79
8-II588222
30
7-63246568
80
8-84081484
30
7-09122998
80
8-I2270l8l
31
7-69237108
8l
8-84861685
31
7-14291180
81
8-12928736
32
774913758
82
8-85615985
32
7-19183258
82
8-I3565338
33
7-80298268
83
8-86345340
33
7-23818812
83
8-14180804
34
7-85410446
84
8-87050663
34
7-28215629
84
8-14775912
35
7-90268372
85
8-87732830
35
7-32389914
85
8-15351409
36
7-94888585
86
8-88392680
36
7-36356452
86
8-15908010
37
7-99286241
87
8-89031015
37
7-40128767
87
8-16446398
38
8-03475255
88
8-89648605
38
7-43719253
$8
8-16967229
39
8-07468427
89
8-90246188
39
7-47I39288
89
8-17471132
40
8-11277550
90
8-90824473
40
7-50399337
90
8-17958709
41
8-14913511
91
8-91384139
41
7-53509041
91
8-I8430539
42
8-18386372
9 2
8-91925838
42
7-56477300
92
8-18887175
43
8-21705446
93
8-92450195
43
7-593I2338
93
8-19329149
44
8-24879372
94
8-92957813
44
7-62021768
94
8-19756974
45
8-27916170
95
8-93449269
45
7-64612652
95
8-20171139
46
8-30823293
96
8-93925118
46
7-67091541
96
8-20572115
47
8-33607684
97
8-94385894
47
7-69464530
97
8-20960357
48
8-36275813
98
8-94832109
48
7-71737290
98
8-21336300
49
8-38833718
99
8-95264258
49
7-73915109
99
8*21700362
50
8-41287040
100
8-95682815
50
7-76002920
100
8-22052945
TABLE VII.
Ixxxix
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
13 per cent.
Years
13 per cent.
Years
14 per cent.
Years
14 per cent.
I
0-88495575
51
7-21845378
I
0*87719298
51
6-73247331
2
1-60613973
52
7-23499042
2
1-58075066
52
6-74685603
3
2-20492404
53
7-25085837
3
2-I5735598
53
676065300
4
2-70982849
54
7-26609087
4
2-63833416
54
6-77389360
5
3-14115169
55
7-28071907
5
3-04548828
55'
678660539
6
3-5I373430
56
7-29477220
6
3-39446193
56
679881419
7
3-83867796
57
7-30827775
7
3-69677084
57
6-81054426
8
4-12445308
58
7-32126154
8
3-96108019
58
6-82181838
9
4^7763479
59
7-33374789
9
4-19403525
59
6-83265798
10
4-60340500
60
7-34575968
10
4-40081/54
60
6-84308324
1 1
4-80590285
61
7'3573l853
ii
4-58552689
61
6*85311316
12
4-98847449
62
7-36244430
12
4-75144964
62
6-86276527
13
5-15385430
63
7-37915772
13
4-90125097
63
6-872057/4
14
5-30429862
64
738947550
14
5-03711500
64
6*88100530
15
5-44168585
65
7-3994I534
15
5-16084867
65
6-88962348
16
5-56759240
66
7-40899351
16
5-27395982
66
6-89792658
17
5-68335109
67
7-41822544
17
5-37771658
67
6-90592813
18
5-79009641
68
7-42712576
18
5-47319324
68
6-91364095
19
5-888800I2
69
7-43570834
19
5'56l30593
69
6-92107722
20
5-98029942
70
7-44398632
20
5-64284066
70
6-92824846
21
6-06531949
71
7-45197223
21
571847567
71
6-93516562
22
6-14449160
72
7-45967795
22
5-78879931
72
6*94183910
23
6-21836784
73
7-46711476
23
5-85432441
73
6-94827881
24
6-28743318
74
7-47429343
24
5-91550007
74
6-95449413
25
6-35211538
75
7-48122419
25
5-97272123
75
6-96049402
26
6-41279315
76
7-48791677
26
6-02633665
76
6-96628700
27
6-46980306
77
7-49438050
27
6-07665542
77
6-97188119
28
6-52344515
78
7-50062422
28
6-12395247
78
6-97728434
2 9
6-57398785
79
7-50665638
29
6-16847318
79
6-98250381
3O
6-62167199
80
7-51248505
30
6-2I04372I
80
6-98754666
31
6-66671428
81
7-51811795
31
6-25004184
81
6-99241960
32
6*70931022
82
7-52356242
3 2
6-28746471
82
6-99712905
33
6-74963672
83
7-52882552
33
6-32286622
83
7'OOl6SlI<3
34
678785415
84
7-5339I396
34
6-35639I56
84
7-00608178
35
6-82410833
85
7-53883418
35
6-38817251
85
7-01033654
36
6-85853208
86
7-54359236
36
6-41832893
86
7-01445078
37
6-89124668
87
7-54819437
37
6-44697007
87
7-01842965
38
6-92236306
88
7-55264587
38
6-47419573
88
7 02227808
39
6-95198292
89
7-55695229
39
6-50009727
89
7-02600076
40
6-98019965
90
7-56111880
4O
6-52475848
90
7-02960222
4i
7-00709916
91
7-56515038
41
6-54825634
91
7-03308679
42
7-03276063
92
7-56905180
42
6-57066172
92
7-03645861
43
7-05725714
93
7-57282765
43
7-59203993
93
7-03972166
44
7-08065626
94
7-57648233
44
7-61245131
94
7-04287978
45
7-10302058
95
7-58002002
45
7-63195168
95
7-04593662
46
7-12440809
96
7-58344482
46
7-65059272
96
7-04889570
47
7-14487269
97
7-58676060
47
7-66842240
97
7-05176042
48
7-16446446
98
7-58997112
48
6-68548525
98
7-05453402
49
7-18323006
99
7-59307996
49
6-70182272
99
7-05721963
50
7-20121297 100
7-59609059
j 50
671747341 ioo
7-05982025
m
xc
THE ENGINEER'S VALUING ASSISTANT.
Present Value o 1 per Annum in n years ; Redemption of Capital being at 3
pr cent, with interest allowed to a Purchaser at the following rates per cent.
Years
15 per cent.
Years
15 per cent.
Years
16 per cent.
Years
16 per cent.
I
0-86956522
51
6-30780221
!
0-86206897
51
5-93352706
2
1-55615178
52
6-32042599
2
1-53230676
52
5-94469589
3
2-11179700
53
6-33253245
3
2-o68l2245
53
5-95540453
4
2-5705I537
54
6-34414778
4
2-50609579
54
5-96567645
5
2-95547950
55
6-35529650
5
2-87063837
55
5-97553362
6
3-28302103
56
6-36600158
6
3-17866480
56
5-98499660
7
3-56498164
57
6-37628458
7
3-44226550
57
5-99408468
8
3-81015682
58
6-38616575
8
3-67031217
58
6-00281597
9
4-02521626
59
6-39596412
9
3-86946204
59
6-01120748
10
4-21530947
60
6-40479761
10
4-04480828
60
6-01927520
n
4-38447558
61
6-41358306
u
4-20031384
61
6-02703421
12
4-53592734
62
6-42203601
12
4-33910853
62
6-03449835
13
4-67225216
63
6-43017257
13
4-46369698
63
6-04168199
H
479555727
64
6-43800578
H
4-57610741
64
6-04859677
15
4-90757610
65
6-44554940
i-5
4-6/799970
65
6-05525495
16
5-00974773
66
6-45281606
16
4-77074542
66
6-06166779
17
5-10327681
67
6-45981776
17
4-85548783
67
6-06784596
18
5-18917943
68
6-46656581
18
4-93318748
68
6-07379956
19
5-26831861
69
6-47307098
19
5-00465732
69
6-07953816
20
5-34143215
70
6-47934344
20
5-07059003
70
6-08507081
21
5-40915449
71
6-48539288
21
5'I3I57943
71
6-09040612
22
5-47203423
72
6-49122847
22
5-18813757
72
6-09555225
23
5-53054818
73
6-49685894
23
5-24070828
73
6-10051696
24
5-58511272
74
6-50229257
24
5-28967823
74
6-10530761
25
5-63609310
75
6'5 753728
25
5-33538579
75
6-10993123
26
5-68381106
76
6-51260055
26
5-37812840
76
6-11439447
27
572855111
77
6-51748956
27
5-41816855
77
6-11870369
28
5-77056577
78
6-5222III2
28
5-45573877
78
6-12286494
29
5-81007995
79
6-52677172
29
5-49104580
79
6-12688399
30
5-84729465
80
6-53117758
30
5-52427407
80
6-13876634
31
5-88239001
81
6*53543459
31
5-55558862
81
6-13451723
32
5-91552798
82
6-5395484I
32
5-58513760
82
6*13814166
33
5-94685456
83
6-54352444
33
5-61305438
83
6-14164444
34
5-97650171
84
6-54736784
34
5^3945932
84
6-14503011
35
6*00458901
85
6-55I08353
35
5-66446138
85
6-14830306
36
6-03122507
86
6-55467624
36
5-68815937
86
6-15146747
37
6-05650876
87
6-55815048
37
571064316
87
6-15442731
38
6-08053030
88
6-56151056
38
573199463
88
6-15758644
39
6-10337215
89
6-56476063
39
5-75228857
89
6-16034850
40
6-12510986
90
6-56790465
40
577159342
90
6-16311700
41
6-14581277
91
6-57094642
41
5-78997193
91
6-16579532
42
6*16554464
9 2
6-57388959
42
5-80748176
92
6-16838666
43
6-18436417
93
6'57673764
43
5-82417592
93
6*17089412
44
6-20232556
94
6-57949393
44
5-84010334
94
6-17332067
45
6-21947885
95
6-58216168
45
5-85530914
95
6-17566915
46
6-23587038
96
6-58474397
46
5-86983508
96
6-17794228
47
6-25154310
97
6-58724377
47
5-88371982
97
6-18014271
48
6-26653685
98
6-58966394
48
5-89699922
98
6-18227293
49
6-28088869
99
6-59200721
49
5-90970660
99
6-18433537
50
6-29463310 100
6-59427620
50
5-92187293
1OO
6-18633236
TABLE VII.
xci
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
17 per cent.
Year
17 per cent.
Years
1-8 per cent.
Yeai
18 per cent.
I
0-85470085
51
5-60117955
I
0-84745762
51
5-30408806
2
1-50918147
52
5-6III3I20
2
1-48674381
52
5-3I30III7
3
2-02621779
53
5-62067084
3
1-98597756
53
5-32156329
4
2-44482611
54
5-62981963
4
2-38648080
54
5-32976355
5
279053228
55
5-63859734
5
271477559
55
5-33762988
6
3-08073845
56
5-64702249
6
2-98866548
56
5-34517903
7
3-32771666
57
5-65511245
7
3-22054601
57
5-35242670
8
3-54036956
58
5-66288350
8
3-41931323
58
5-35938762
9
372531249
59
5-67035092
9
3-59151725
59
5-36607561
10
3-88756378
60
5-67752911
10
3-74208773
60
5-37250365
ii
4-03099923
61
5-68443158
ii
3-87480583
61
5-37868397
12
4-15865977
62
5-69107078
12
3-99262027
62
5-38462780
13
4-27296478
63
5-69745960
J 3
4-09786448
63
5-39034677
1.4
4-37586321
64
5-70360849
H
4-19240912
64
5-3958503I
15
4-46894258
65
570952844
15
4-27777143
65
5-40114834
16
4-S53509IO
66
571522956
16
4355I9490
66
5-40624996
17
4*63064731
67
572072140
17
4-42570837
67
5-41116380
18
470126525
68
5-72601301
18
4-49017043
68
5-41589799
19
4-76612890
69
573111296
19
4-54930324
69
5 -42046026
20
4-82588898
70
573602936
20
4-60371863
70
5-42485792
21
4-88lIOl8l
71
5-74076991
21
4-65393835
71
5-42909789
22
4-93224587
72
574534193
22
470041008
72
5-43318677
23
4-97973490
73
5-74975234
23
474352017
73
5-43713078
24
5-02392857
74
5-75400774
24
478360374
74
5-44093587
25
5-06514098
75
575811440
2 5
4-82095292
75
5-44460766
26
5-10364768
76
576207827
26
4-85582,355
76
5-44815152
27
5-13969141
77
576590505
27
4-88844064
77
5-45157255
28
5-17348684
78
5-76960012
28
4-91900288
78
5-45486561
2 9
5-20522454
79
577316865
2 9
4-94768635
79
5-45806533
30
5-23507422
80
577661554
30
4-97464772
80
5-46114612
31
5-26318757
Si'
5-77994548
31
5-00002678
81
5-46412219
32
5-28970055
82
578316293
32
5-02394870
82
5-46699755
33
5'3i473539
83
578627217
33
5-04652589
83
5-46977604
34
5-33840230
84
578927728
34
5-06785957
84
5-47246132
35
5*36080089
85
5-79218215
35
5-08804113
85
5-47505688
36
5-38202142
86
5-79499051
36
5-I07I5333
86
5-47756608
37
5-40214588
87
579770592
37
5-12527125
87
5-47999209
38
5-42124893
88
5-80033179
38
5-14246320
88
5-48233800
39
5-43939866
89
5-80287140
39
5-15879143
89
5-48460672
40
5-45665734
90
5-80532785
40
5-17431282
90
5-48680106
41
5-47308202
91
5-80770417
4i
5-18907945
91
5-48892371
42
5-48872505
92
5-81000320
42
5-20313905
92
5-49097724
43
5-50363456
93
5-81222770
43
5-21653551
93
5-49296412
44
5-51785491
94
5-81438033
44
5-22930921
94
5-49488672
45
5-53142699
95
5-81646360
45
5-24149739
95
5-49674729
46
5-54438861
96
5-81847995
46
5-25313442
96
5-49854804
47
5-55677476
97
5-82043172
47
5-26425212
97
5-50029104
48
5-56861787
98
5-82232115
48
5-27487996
98
5-50197830
49
5-57994804
99
5-82415038
49
5-28504526
99
5-50361176
50
5-59079326
100
5-82592149
50
5-29477342
ICO
5-50519326
XC11
THE ENOINEEE'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
19 per cent.
Years
19 per cent.
Years
20 per cent.
Years
20 per cent.
I
0-84033613
51
5-03692511
~7
0-83333333
51
479538515
2
1-46496356
5 2
5-04497129
2
1-44381223
52
4-80267758
3
1-94730452
53
5-05268164
3
1-91010889
53
4-80966460
4
2-33 85539
54
5-06007360
4
2-27776400
54
4-81636213
5
2-64302344
55
5-06716345
5
2-57496647
55
4-82278505
6
2-90193631
56
5-07396644
6
2-82009884
56
4-82894728
7
3-12006295
57
5-08049683
7
3-02566044
57
4-83486183
8
3-30626179
58
5-08676801
8
3-20044664
58
4-84054092
9
3-46699937
59
5-09279251
9
3-35082624
59
4-84599599
10
3-60710664
60
5-09858214
10
3-48152434
60
4-85123779
ii
373026530
61
5-10414798
ii
3-59612046
61
4-85627644
12
3'83933039
62
5-10950023
12
3-69737591
62
4-86112123
13
3-93654999
63
5-11464943
13
3-78745494
63
4-86578175
14
4-02371839
64
5-11960414
14
3-86807783
64
4-87026581
15
4-10228505
65
5-12437334
15
3-94062921
65
4-87458158
16
4'I7343373
66
5-12896528
16
4-00623612
66
4-87873658
17
4-23814062
67
5-I3338778
17
4-06582523
67
4-88273799
18
4-29721801
68
5-13764820
18
4-12016552
68
4-88649228
19
4-35134726
69
5-I4I75355
!9
4-16990041
69
4-89030607
20
4-40110418
70
5-14571044
20
4-21557244
70
4-89388527
21
4-44697870
71
5-14952513
21
4-25764225
71
4-8973356I
22
4-48939033
72
5-15320359
22
4-29650352
72
4-90066248
23
4-52870036
73
5-15675146
23
4-33249466
73
4-90387102
24
4-56522163
74
5-16017410
24
4-36590824
74
4-90696611
25
459922638
75
5-16347662
2 5
4-39699847
75
4-90995237
26
4-63095266
76
. 5-16666384
26
4-42598728
76
4-91283421
27
4-6606095 1
77
5-16974040
27
4-45306934
77
4-91561582
28
4-68838127
78
5-17271068
28
4-47841605
78
4-91830119
29
471443109
79
5-I7557885
2 9
4-50217896
79
4-92089410
30
473890394
80
5-17834892
30
4-52449259
so
4-92339818
31
4-76192905
81
5-18102467
31
4-54547668
81
4-92581688
32
4-78362199
82
5-18360974
32
4-56523825
82
4-92815349
33
4-80408643
83
5-18610758
33
4-58387320
83
4-93041115
34
4-82341564
84
5-!8852i49
34
4-60146772
84
4-93259285
35
4-84169376
85
5-19085464
35
4-61809953
85
4-93470146
36
4-85899691
86
5-19311004
36
4-63383882
86
4-93673972
37
4-87539408
87
5-19529058
37
4-64874924
87
4-93871023
38
4-89094800
88
5-19739902
38
4-66288854
88
4-94061552
39
4-90571578
89
5-19943800
39
4-67630934
89
4-94245796
40
4-91974959
90
5-20141004
40
4-68905960
90
4-94423985
41
4-933097I2
9 1
5-20331758
41
4-70118319
9 1
4-94596340
42
4-94580209
92
5-20516293
42
4-71272027
92
4-94763069
43
4-95790466
93
5-20694832
43
472370773
93
4-94924375
44
4-96944174
94
5-20867588
44
473417945
94
4-95080452
45
4-98044737
95
5-21034765
45
4-74416665
95
4-95231483
46
4-99095295
96
5-21196560
46
475369812
96
4-95377648
47
5-00098753
97
5-21353162
47
4-76280047
97
4-95519117
43
5-01057799
98
5-21504752
48
4-77149834
98
4-95656053
49
5-01974924
90
5-21651502
49
477981454
99
4-95788615
so
5-02852445
100
5-21793581
50
4-78777025
100
4-95916952
TABLE VII.
XClll
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
fears
21 per cent.
Years
21 per cent.
Years
22 percent.
Years
22 per cent.
I
0-82644628
51
4-57595069
I
0-81967213
51
4'3757I99I
2
1-42326299
5 2
4-58259053
2
2-40329047
52
4-38179099
3
1-87430757
53
4-58895142
3
1-83982362
53
4-38760630
4
2-22703735
54
4-59504798
4
2-17852087
54
4-39317928
5
2-51032641
55
4-60089383
5
2-44885222
55
4-39852248
6
274275056
56
4-60650174
6
2-66953196
56
4-40364763
7
2-93680276
57
4-61188363
7
2-8530I533
57
4-40856571
8
3-10119456
58
4-61705069
8
3-00791332
58
4-41328699
9
3-24218622
59
4-62201341
9
3-14036959
59
4-41782112
10
3-3643922I
60
4-62678162
10
3-25488511
60
4-42217714
ii
3-47128874
61
4-63136458
ii
3-35483280
61
4-42636354
12
3-56554433
62
4-63577079
12
3-44279013
62
4-43038815
13
3-64924156
63
4-64000904
13
3-52076050
63
4-43425902
H
3-72402947 '
64
4-64408645
H
3-59032472
64
4-43798270
15
3-79123086
65
4-64801051
15
3-65274680
65
4-44156606
16
3-85191914
66
4-65178809
16
3-70904955
66
4-44501539
17
3-90697448
67
4-65542567
17
376007851
67
4-44833666
18
3-95712540
68
4-65892940
18
3-80649752
68
4-45I53550
19
4-00298013
69
4-66230508
19
3-84890906
69
4-45461723
20
4-04505041
70
4-66555821
20
3-88778745
70
4-45758689
21
4-08376994
71
4-66869399
21
3-92355I53
71
4-46044927
22
4-11950868
72
4-67171738
22
3-95651952
72
4-46320887
23
4-15258417
73
4-67463305
23
3-98701980
73
4-46587001
24
4-18327049
74
4-67744545
24
4-01529964
74
4-46843675
25
4-21180545
75
4-68015881
25
4-04158188
75
4-47091298
26
4-23839640
76
4-68277714
26
4-06606063
76
4-47330236
27
4-26322498
77
4-68530427
27
4-08890573
77
4-47560839
28
4-28645094
78
4-68774383
28
4-11026639
78
4-47783442
29
4-30821540
79
4-69009928
29
4-13027428
79
4-47998360
30
4-32864343
80
4-69237393
30
4-14904603
80
4-48205896
31
4-34784634
81
4-69457092
31
4-16668526
81
4-48406338
32
4-53592344
82
4-69669324
32
4-18328445
82
4-48599960
33
4-38296370
83
4-69874376
33
4-19892628
83
4-48787024
34
4-39904700
84
4-70072521
34
4-21368501
84
4-48967780
35
4-41424529
85
4-70264020
35
4-22762744
85
4-49142466
36
4-42862355
86
4-70449123
36
4-24081387
86
4-493II3I2
37
4-44224061
87
4-70628067
37
4-25329884
87
4-49474534
38
4-45514987
88
4-70801080
38
4-26513185
88
4-49632341
39
4-46739990
89
4-70968382
39
4-27635789
89
4-49784933
40
4-47903498
90
471130179
40
4-28701795
90
4-59932501
41
4-49009557
9 1
471286673
4i
4-29714945
9 1
4-50075228
42
4-50061870
92
4-71438055
42
4-30678666
92
4-50213288
43
4-51063836
93
4-71584508
43
4-31596097
93
4-50346849
44
4-52018574
94
471726209
44
4-32470122
94
4-50476072
45
4-52928960
95
471863326
45
4-33303394
95
4-50601112
46
4-53797642
96
471996020
46
4-34098361
96
4-50722115
47
4-54627067
97
472124448
47
4-34857278
97
7-50839226
48
4-55419500
98
472248757
48
4-35582236
98
4-50952578
49
4-56177037
99
4-72369093
49
4-36275166
99
4-51062304
53 4-56901625
100
472485591
50
4-36937863
100
4-51168528
XC1V
THE ENGINEER'S VALUING ASSISTANT.
Present Value of ^1 per Annum in n years; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
23 per cent.
Years
23 percent.
Years
24 per cent.
Years
24 per cent.
I
0-81300813
51
4-19227758
I
0-80645161
51
4-02359722
2
1-38387075
52
4-19784998
2
1-36498117
52
4-02872994
3
1-80658563
53
4-20318700
3
177452728
53
4-03364535
4
2-13207321
54
4-20830107
4
2-08756480
54
4-03835494
5
2-39031689
55
4-21320377
5
2-33451460
55
4-04286944
6
2-60012090
56
4-21790592
6
2-53422791
56
4-04719888
7
277387621
57
4-22241765
7
2-69900904
57
4-05135263
8
2-92007985
58
4-22674845
8
2-83723045
58
4-05533946
9
3-04475309
59
4-23090721
9
2-95478712
59
4-05916759
10
3-15228195
60
4-23490226
10
3-05594980
60
4-06284475
ii
3-24593704
61
4-23874144
ii
3-14388840
61
4-06637818
12
3-32820695
62
4-24243195
12
3-22100523
62
4-06977453
13
3-40101878
63
4-24598121
13
3-28915403
63
4-07304067
H
3-46588808
64
4-24939527
14
3-34978817
^4
4-07618218
15
3-52402315
65
4-25268045
15
3-40406318
6 5
4-07920490
16
3-57639914
66
4-25584254
16
3-45290932
66
4-08211418
17
3-62381168
67
4-25888703
17
3-49708395
67
4-08491511
18
3-66691644
68
4-26181911
18
3-53720991
68
4-08761246
19
370625854
69
4-26464368
19
3-57380412
69
4-09021076
20
3-74229498
70
4-26736537
20
3-69729920
70
4-09271430
21
37754II68
71
4-26998859
21
3-63805994
71
4-09512713
22
3-80593688
72
4-27251749
22
3-66639616
72
4'09745309
23
3-83415144
73
4-27495603
23
3-69257261
73
4-09969584
24
3-86029714
74
4-27730795
24
371781697
74
4-10185882
25
3-88458327
75
4-27957682
25
3-73932603
75
4-10394533
26
3-90719184
76
4-28176602
26
3-76027085
76
4-10595848
27
3-92828198
77
4-28387876
27
3-77980075
77
4-10790125
28
3-94799335
78
4-28591810
23
3-79804671
78
4-10977645
29
3-96644906
79
4-28788697
29
3-81512411
79
4-11158678
30
3-98375807
80
4-28978813
30
3-83113492
80
4-11333478
31
4-00001714
81
4-29162423
31
3-84616969
81
4-11502291
32
4-01531250
82
4-29339779
32
3-86030903
82
4-11665348
33
4-02972126
83
4-29511122
33
3-87362497
83
4-11822872
34
4-04331256
84
4-29676681
34
3-88618207
84
4-11975073
35
4-05614859
85
4-29836676
35
3-89803836
85
4-I2I22I54
36
4-06828545
86
4-29991315
36
3-90924616
86
4-12264308
37
4-07977387
87
4-30140800
37
3-91985274
87
4-12401720
38
4-09065982
88
4-30285322
38
3-92990094
88
4-12534565
39
4-10098509
89
4-30425063
39
3-93742967
89
4-12663012
40
4-11078774
90
4-30560199
40
3-94847434
90
4-12787224
41
4-I20I0249
9 1
4-30690897
41
3-95706726
91
4-12907354
42
4-12896111
92
4-30817319
42
3-96523798
92
4-13023550
43
4-13739271
93
4-30939619
43
3-97301354
93
4'I3I35954
44
4-14542401
94
4'31 057943
44
3-98041878
94
4-13244702
45
4-15307960
95
4-31172434
45
2-98747652
95
4-I3349925
46
4-16038210
96
4-31283227
46
3-99420779
96
4-13451746
47
4-16735243
97
4-31390452
47
4-00063200
97
4-13550287
48
4-17400990
98
4-31494234
48
4-00676705
98
4-13645662
49
4-18037240
99
4-31594694
49
4-01262954
99
4-13737982
59
4-18645649
100
4-31691946
50
4-01823484
130
4-13827353
TABLE VII.
xcv
Present Value of \ per Annum in n years; Redemption of Capital being at 3
per cent, with interest allowed to a Purchaser at the following rates per cent.
Years
25 per cent.
Years
25 per cent.
Years
25 per cent.
Years
25 per cent.
I
o '80000000
26
3-62399868
51
3-86796585
76
3-94401871
2
1-34660033
27
3-64213529
52
3-87270896
77
3-94581122
3
174358685
28
3-65907340
53
3-87725080
78
3'94754I33
4
2*04487668
29
3-67492130
54
3-88160207
79
3-94921152
5
2'28l25829
30
3-68977468
55
3-88577272
80
3-95082416
6
2-47159213
56
3-88977207
7
2-62807701
31
370171840
57
3-89360880
81
3-95238I5I
8
275895261
32
371682798
58
3-89729107
82
3-9538857I
9
2-86998516
33
372917088
59
3-90082651
83
3-95533882
10
2-96533078
34
3-74080748
60
3-90422226
84
3-95674279
35
375179207
85
3-95808949
ii
3-04806078
39
376217353
61
3-90748506
86
3-95941071
12
3-12049395
37
3-77199605
62
3-91062107
87
3-96067815
13
3-18441376
38
378129961
63
3-91363666
88
3-96190344
14
3-24121436
39
379012054
64
3-91653700
89
3-96308813
15
3-29200137
40
379849186
65
' 3-91932750
90
3-96422373
16
3-33766285
66
3-92201313
17
3-37892027
41
3-80644372
67
3-92459859
91
3-96534166
18
3-41636588
42
3*81400366
68
3-92708831
92
3-96651329
19
3-45049036
43
3-82119687
69
3-92948649
93
3-96744992
20
3-48170373
44
3-82804650
7O
3-93177908
94
3-96845281
45
3'83457379
95
3-96942317
21
3-51035126
46
3-84079833
71
3-93402385
96
3-97036215
22
3-53672578
47
3-84673816
72
3-93617036
97
3-97127085
23
3-56107725
48
3-85240996
73
3-92823998
98
3-97215035
24
3-58362036
49
3-85782915
74
3-94023591
99
3-97300165
25
3-60454051
50
3-86301003
75
3-94216119
100
3-97382575
TABLE VIII.
JOB
VALUING MINERAL AND OTHER PROPERTIES,
Olt
The present value (or years' purchase) of 1 per annum
in n years, allowing interest to a present purchaser upon
his purchase-money or capital invested, at the rates of 4,
5, 6, 8, 10, 12, 15, 1 8, 20, and 25 per cent, per annum,
and redeeming the capital so invested by an Annual
Redemption Fund, at the rate of 3| per cent, per annum.
Calculated to 8 places of decimals, and to 100 years
for each percentage.
TABLE VIII.
XC1X
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3^ per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
4 per cent.
Years
4 per cent.
Years
6 per cent.
Years
5 per cent.
I
0-96153846
M
21-13201494
r
0*95238095
51
I7-44544I6I
2
1-88181986
52
21-26560757
2
1*84706149
52
17-53638810
3
276293330
-53
21-39449319
3
2-68864776
53
17-62394045
4
3-60683820
54
21-51884394
4
3*48127427
54
17-70823622
5
4-41537415
55
21-63882521
5
4-22866286
55
1 77894066 1
6
5-19026988
56
21-75459601
6
4-93417298
56
17-86757685
7
5-93315140
57
21-86630921
7
5-60084480
57
17-94286655
8
6-64554948
58
21-97411174
8
6-22520486
58
18-01538984
9
7-32890640
59
22-07814490
9
6-82845530
59
18-08525590
10
7-98458223
60
22-17854463
10
7-39418726
60
18-15256901
ii
8-61386051
61
22-27544161
n
7-93071941
61
18*21742888
12
9-21795350
62
22-36896161
12
8-43996175
62
18*27993089
13
9-79800697
63
22-45922569
13
8-92366560
63
18-34016634
H
10-35510463
64
22-54635030
14
9-38343964
64
18*39822259
15
10*89027219
65
22*63044743
15
9-82076424
65
18-45418320
16
11-40448117
66
22-71162503
16
10*23700398
66
18-50812832
17
11-89865227
67
2278998699
17
10-63341875
67
18-56013470
18
12-37365863
68
22-86563319
18
11-01117360
68
18-61027579
19
12-83032881
69
22-93866003
19
II-37I34753
69
18*65862213
20
13-26944946
70
23*00916019
20
1171494125
70
18*70524126
21
13-69176795
71
23-07722297
21
12-04288419
71
1875019797
22
14-09799461
72
23-14293439
22
12-35604066
72
1879355442
23
14-48880504
73
23-20637735
23
12-65521553
73
18-83537025
24
14-86484209
74
23-26763169
24
12-9411592!
74
18-87570270
25
15-22671774
75
23-32677432
25
13-21457214
75
18*91460670
26
15-57501483
76
23'38387935
26
13-47610887
76
18-95213497
27
15-91028880
77
23-43901828
27
13*72638181
77
18-9883382!
28
16-23306916
78
23-49225988
28
13-96596448
78
19-02326502
29
16-54386089
79
23-53868290
29
14-19539456
79
19-05369423
30
16-84314589
80
23'5933H28
30
14-41517665
80
19-08947455
31
17-13138406
81
23-64125274
31
14-62578471
8l
19*12084536
32
17-40901467
82
23-68754530
32
14-82766440
82
19*1511160!
33
17-67645726
83
23-73224934
33
15*02123506
83
19-18032644
34
17-93411277
84
23-77542012
34
15-20689166
8 4
19-20851498
35
18-18236454
85
23-81711097
35
15-38500656
85
19-23571854
36
18-42157912
86
23-85737323
36
I5'55593098
86
19-26197255
37
18-65210718
87
23-89625646
37
1571999657 -
87
19*28731113
38
18-87428430
88
23-93380854
38
15-87751667
88
19-31176716
39
19-08843171
89
23-97007548
39
16-02878754
89
I9-335372I8
40
1 9-29485698
90
24-00510189
40
16-17408954
90
19-35815666
41
19-49385477
91
24-03893052
41
16-31368810
91
19-38014978
42
19-68570725
92
24-07160286
42
16-44783466
92
19-40137977
43
19-87068499
93
24-10315887
43
16-57676770
93
19-42187378
44
20-04904734
94
24-13363694
44
1670071340
94
19-44165782
45
20-22104293
95
24-16307440
45
16-81988646
95
19-46075717
46
20-38691024
96
24-19150695
46
16-93449080
96
I9'479I959I
47
20-34687800
97
24-21896930
47
17-04472015
97
19-49699746
48
20-701 16589
98
24-24549486
48
17-15075884
98
19-51418431
49
20-8499844.3
99
24-27111581
49
17-25278206
99
19-53077805
50
20-99353605
100
24-29586324
50
17-35095670
100
19-54679955
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum for n years ; Redemption of Capital being at 3J per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
6 per cent.
Years
6 per cent.
Years
8 per cent.
Years
8 per cent.
I
0^94339623
51
14-85408150
I
0-92592593
51
11-45192496
2
1-81356385
5 2
14-91996511
2
175008600
52 '
11-49104523
3
2-61825218
53
14-98329369
3
2-48796954
53
11-52857360
4
3-36415868
54
15-04417770
4
3-15207694
54
11-56458443
5
4-05710171
55
15-10272198
5
3-75260750
55
11-59914787
6
4-70216026
56
15-15902619
6
4-29796578
56
1 1 '63233022
7
5-30378787
57
15-21318504
7
479513979
57
11-66419416
8
5-86590610
58
15-26528859
8
5-24998743
58
1 1 -69479896
9
6-39198169
59
15-31542254
9
5-66745617
59
11-72420076
10
6-88509076
60
15-36366848
10
6-05I75334
6O
1175245273
it
734797233
61
15-41010412
ii
6-40647963
61
II77960525
12
778307334
62
15-45480349
12
6-73473466
62
11-80570612
13
8-19258657
63
I5-4978372I
13
7-03920125
63
1 1 -83080073
14
8-57848288
64
15-53927262
14
7-32221326
64
11-85493216
15
8-94253860
65
I5'579I7390
15
7-58581053
65
11-87814132
16
9-28635904
66
15-61604066
16
7-83178390
66
11-90046713
17
9-61139850
67
15-65461674
17
8-06171197
67
11-92194663
18
9-91897774
68
15-69027276
18
8-27699180
68
11-94261501
19
10-21029895
69
1572462396
19
8-47886419
69
11-96250584
20
10*48645876
70
I575772I45
20
8 "66843 504
70
11-98165105
21
1074845964
71
1578961407
21
8-84669316
71
I2-00008I09
22
10-99721972
72
15-82034860
22
9-01452540
72
12*01782498
23
11-23358157
73
15-84996976
23
9-17272948
73
12-03491043
24
11-45831980
74
15-87852040
24
9-32202495
74
12-05136386
25
11-67214775
75
15-90604151
25
9-46306248
75
12-06721049
26
11-87572345
76
15-93257234
26
9-59643200
76
12-08247440
27
12-06965490
77
15-95815060
27
972266957
77
12-09717863
28
12-25450471
78
15-98281228
28
9-84226344
78
I2-III345I6
29
12-43079427
79
16-00428643
29
9-95565924
79
12-12367203
30
12-59900747
80
16-02952286
30
10-06326456
80
12-13814833
31
1275959397
81
16-05163672
31
10-16545293
Si
12-15082435
32
12-91297221
82
16*07296403
32
10-26256729
82
12-16304146
33
13-05953205
83
16-09353407
33
10-35492306
83
12-17481732
34
13-19963714
84
16-11337494
34
10-44281086
84
I2-l86l688o
35
I3-333627I5
85
16-13251362
35
10-52649891
85
I2-I97II208
36
13-46181961 ,
86
16-15097598
36
10-60623513
86
12-20766265
37
13-58451178
87
16-16878689
37
10-68224903
87
12-21783536
38
1370198216
88
16-18597027
38
io-75475338
88
12-22764447
39
13-81449197
89
16-20254902
39
10-82394574
89
12-23710360
40
13-92228646
90
16-21854526
40
10-89000975
90
12-24622588
4i
1 4^2559610
91
16-23398012
41
10-95311637
91
12-25502385
42
14-12463762
92
16-24887402
42
11-01342490
92
12-26350957
43
14-21961513
93
16-26324656
43
11-07108404
93
12-27169464
44
14-31072092
94
16-27711652
44
1 1-12623269
94
12-27959013
45
14-39813629
95
16-29050211
45
11-17900076
95
12-28720675
46
14-48203236
96
16-30342066
46
11-22950986
96
12-29455471
47
14-56257072
97
16-31588900
47
11-27787397
97
12-30164388
48
14-63990418
98
16-32792327
48
1 1 -32420009
98
12-30848371
49
14-71417714
99
I6-33953896
49
11-36858861
99 12-31508329
50
14-78552641
100
16-35075102
50 11-41113396
100 12-32145135
TABLE VIII.
Cl
Present Value of 1 per Annum for n years ; Redemption of Capital being at 3^ per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
10 per cent.
ears
10 per cent.
ears
12 per cent.
ears
12 per cent.
I
0-90909091
51
9-31779189
I
0-89285714
51
7-85412909
2
1-69090154
S 2
9-34367369
2
I-635589I3
52
7-87251034
3
2-37003790
S3
9-36847137
3
2-26278040
53
7-89010661
4
2-96514936
54
9-39223788
4
279915132
54
7-90695738
5
3-49062834
55
9-41502300
5
3-26284103
55
7-92349968
6
3-95775949
56
9-43687362
6
3-66746092
56
7-93856830
7
4-3755I56I
57
9'45783394
7
4-02342448
57
7-95339597
8
475112093
58
9-47794560
8
4-33883439
58
7-96761346
9
5-09045730
59
9-49724794
9
4-62008989
59
7-98124978
10
5-39836221
60
9-51577809
10
4-87231210
60
7-99433226
ii
5-67885080
61
9-53357116
n
5-09964799
61
8-00688668
12
5-93528347
62
9-55066034
12
5-30549155
62
8-01893739
13
6-17049424
63
9-56707709
13
5-49264727
63
8-03050742
14
6-38688986
64
9-58285116
14
5-66345287
64
8*04161850
15
6-58652753
65
9-59801076
15
5-81987252
65
8-05229121
16
677117613
66
9-61258266
16
5-96356866
66
8-06254504
17
6-94236503
67
9-62659226
17
6-09595775
67
8-07239848
18
7-10142334
68
9-64006364
18
6-21825423
68
8-08186901
19
7-24951169
69
9-65301974
19
6-33150526
69
8*09097325
20
7-38764809
70
9-66548233
20
6-43661862
70
8*09972697
21
7-51672922
71
9-67747209
21
6'534385 J 4
71
8-10814513
22
7-63754799
72
9-68900876
22
6-62549697
72
8-11624197
23
775080815
73
9-70011108
23
671056250
73
8-12403101
24
7-85713650
74
9-71079692
24
679011871
74
8-13152514
25
7-95709310
75
9-72108332
25
6-86464130
75
8-13873659
26
8-05117998
76
973098650
26
6-93455325
76
8-14567703
27
8-13984844
77
9-74052195
27
7-00023190
77
8-15235759
28
8-22350532
78
9-74970445
28
7-06201497
78
8-15878885
29
8-30251836
79
9-75769110
29
7-12020561
79
8-16438095
30
8-37722078
80
9-76706634
30
7-17507674
80
8-17094341
31
8-44791524
81
9-77527208
31
7-22687473
8l
8-17668556
y-
8-51487727
82
9-78317758
32
7-27582255
82
8-l822l6lI
33
8-57835827
83
9-79079461
33
7-32212247
83
8-I8754348
34
8-63858804
84
979813441
34
7-36595843
84
8-19267566
35
8-69577714
85
9-80520773
35
7-40749809
85
8-19762033
36
875011979
86
9-81202487
36
7-44689455
86
8-20238480
37
8-80179064
87
9-81859566
37
7-48428793
87
8-20697607
38
8-85095633
88
9-82492956
38
7-51980672
88
8-2II40086
39
8-89776684
89
9-83103558
39
7'55356893
89
8-21566557
40
8-94236164
90
9-83692241
40
7-58568320
90
8-21977636
41
8-98486987
91
9-84259831
4i
7-61624963
91
8-22373910
42
9-02541115
92
9-84807125
42
7-64536068
92
8-22755942
43
9-06409655
93
9-85334887
43
7-67310184
93
8-23124275
44
9-10102930
94
9-85843846
44
7-69955228
94
8-23479422
45
9-13630545
95
9-86334706
45
772478546
95
8-23821883
46
9-17001450
96
9-86808139
46
774886957
96
8-24152132
47
9-20223993
97
9.87264791
47
777186804
97
8-24470627
48
9-23305977
98
9-87705284
48
7-79383996
98
8-24777805
49
9-26254691
99
9-88130212
49
7-81484039
99
8-25074086
50
9-29076963
10
9-88540149
50
7-83492075
100
8-25359874
Cll
THE ENGINEEE'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3J per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
15 per cent.
Years
15 per cent.
Years
18 per cent.
Years
18 per cent.
I
0-86956522
51
6-35640769
I
0-84745763
51
5-33841368
2
1-55908830
52
6-36844166
2
1-48942399
52
5-34689919
3
2-11893955
53
6-37995165
3
1-99229309
53
535501042
4
2-58230357
54
6-39096480
4
2-39663815
54
5-36276712
5
2-97193271
55
6-40150647
5
2-72865164
55
5-37018772
6
3'30394790
56
6*41160046
6
3-00599809
56
5-37728950
7
3-59009071
57
6*42126910
7
3-24102365
57
5-38408864
8
3-83911577
58
6-43053334
8
3-44261755
58
5-39060029
9
4-05768395
59
6-43941290
9
3-61734292
59
5-39683871
10
4-25095301
60
6-44792630
10
3-77015097
60
5-40281727
ii
4-42297893
61
6-45609101
ii
3-90484722
61
5-40854856
12
4-57699526
62
6-46392347
12
4-0244048 1
62
5-41404441
13
4-71561154
63
6-47143920
13
4-13118030
63
5-41931598
H
4-84095693
64
6-47865286
14
4-22706565
64
5-42437381
15
4-95478586
65
6-48557826
15
4-3I359733
65
5-4292278!
16
5-05855708
66
6-49222850
16
4-39203612
66
5-43388735
17
5-15349341
67
6-49861595
17
4-46342627
67
5-43836131
18
5-24062759
68
6-50475232
18
4-52864010
68
5-44265805
19
5-32083787
69
6-51064871
19
4-58841198
69
5-44678550
20
5-39487587
70
6-51631564
20
4-64336460
70
5-45075119
21
5-46338859
71
6-52176308
21
4-69402939
71
5-4545622I
22
5-52693603
72
6-52700050
22
4-74086269
72
5-45822532
23
5-58600536
73
6-53203690
23
4-78425854
73
5-46174693
24
5-64102236
74
6-53688082
24
4-82455091
74
5-46513310
25
5-69236084
75
6-54I54037
25
4-86206243
75
5-46838963
26
574035031
76
6*54602329
26
4-89703024
76
5-47152198
27
578528236
77
6-55033692
27
4-92969247
77
5-47453539
28
5-82741600
78
6-55448827
28
4-96025238
78
5-47743481
29
5-86698205
79
6-55809691
29
4-98889018
79
5-47995469
3O
5-90418692
8O
6-56233048
30
5-01576627
80
5-48291038
31
5-93921570
81
6-56603376
31
5-04102386
Si
5-48549533
32
5-97223491
82
6-56959960
32
5-06479122
82
5-48798390
33
6-00339473
83
6-57303354
33
5-08718359
83
5-49037999
34
6-03283097
84
6-57634084
34
5-10830479
84
5-49268732
35
6*06066677
85
6-57952652
35
5-12824859
85
5-49490945
36
6-08701401
86
6-58259539
36
5-14709993
86
5-49704976
37
6-11197460
87
6-58555203
37
5-16493589
87
5-499III49
38
6-13564156
88
6-58840085
38
5-18182663
88
5-50109773
39
6-15809996
89
6-59114603
39
5-19783612
89
5-50301146
40
6-17942776
90
6-59379I59
40
5-21302282
90
5-50485550
41
6-19969654
91
6-59634138
4i
5-22744024
91
5-50663254
42
6-21897213
92
6-59879908
42
5-25363428
92
5-50834518
43
6-23731520
93
6-6oil682I
43
5-25415969
93
5-50999591
44
6-25478172
94
6-60345214
44
5-26654840
94
5-51158709
45
6-27142344
95
6-60565411
45
5-27834192
95
5-51312100
46
6-28728827
96
6-60777722
46
5-28957566
96
5-5I4599SI
47
6-30242060
97
6-60982444
47
5-30028234
97
5-51602561
48
6-31686169
98
6-61179862
48
5-31049233
98
5-51740041
49
6-33064985
99
6-61370250
49
5-32023374
99
5-51872612
so 6-34382076
100
6-61553869
SO
5-32953275
100
5-52000457
TABLE VIII.
SIT? J
\^T ciii
Present Value of 1 per Annum in n years ; Redemption of Capital being at 3-J- per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
20 per cent.
Yean
20 per cent.
Years
25 per cent.
Years
25 per cent.
I
0-83333333
51
4-82342493
~T
0-80000000
51
3-886l88lO
2
1-44633973
52
4-83035117
2
1-34879867
52
3-89068293
3
1-91595040
53
4-83696994
3
1-74845294
53
3-89497588
4
2*28701519
54
4-84329758
4
2-05232973
54
3-89907786
5
2-58744682
55
4-84934939
5
2-29104851
55
3-90299908
6
2-83552635
56
4-85513967
6
2-48343420
56
3-90674906
7
3-04372777
57
4-86086180
7
2-64169739
57
3-91033669
8
3-22085416
58
4-86598833
8
2-77410481
58
3-91377030
9
337329558
59
4*87107102
9
2-88645268
59
3-91705771
10
3-50580285
60
4-87594092
10
2-98292543
60
3-92020622
ii
3-62198153
6l
4-88060840
ii
3-06661956
61
3-92322272
12
372461744
62
4-88508325
12
3-13987566
62
3-92611365
13
3-81589712
63
4-88937466
13
3-20449580
63
3-92888510
H
3-89756074
64
4-89349129
14
3-26189002
64
3-93154277
15
3-97101052
65
4-89744132
15
3-3I3I7740
65
3-93409206
16
4-03738896
66
4-90123245
16
335925750
66
3-93653805
17
4-09763632
67
4-90487199
17
3-40086162
67
3-93888552
18
4-I525335I
68
4-90836680
18
3-43859041
68
3-94113901
19
4-20273444
69
4-91172342
19
3-47294183
69
3-94330279
20
4-24879089
70
4-91494801
20
3-50433216
70
3-94538091
21
4-29117167
71
4-91804641
21
3-533II2I4
71
3-94737720
22
433027765
72
4-92102415
22
3-5595793I
72
3-94929528
23
4-36645368
73
4-92388649
23
3-58398783
73
3-95113859
24
4-39999801
74
4-92663841
24
3-60655604
74
3-95291040
25
4-43II6993
75
4-92928465
25
3-62747256
75
3-9546I379
26
4-46019595
76
4-93182969
26
3-64690124
76
3-95625171
27
4-48727478
77
4-93427782
27
3-66498503
77
3-95782693
28
4-51258151
78
4-93663309
28
3-68184927
78
3-959342I2
29
4-53627102
79
4-93867985
29
3-69760427
79
3-96065861
30
4*55848079
80
4-94108037
30
371234754
80
3-96220235
31
4-57933329
81
4-943 1 7956
31
372616558
81
3-96355208
32
4-59893800
82
4-94520030
32
3739I354I
82
3-96485115
33
4-61739307
83
4-94714578
33
375 J 32578
83
3-96610163
34
4-63478672
84
4-94901904
34
3-76279834
84
3-96730551
35
4-65119854
85
4-95082297
35
3-77360844
85
3-96846467
36
4-66670045
86
4-95256034
36
3-78380600
86
3-96958090
37
4-68135765
87
4-95423381
37
379343609
87
3-97065592
38
4-69522934
88
4-95584589
38
3-80253957
88
3-97169137
39
4-70836947
89
4-95739899
39
3-81115352
89
3-97268882
40
4-72082722
90
4-95889544
40
3-81931169
90
3-97364976
41
4-73264759
91
4-96033743
41
3-82704486
9 1
3-97457562
42
4-74387180
92
4-96172708
42
3-83438117
92
3-97546777
43
4-75453769
93
4*96306640
43
3-84134638
93
3-97632752
44
476468004
94
4-96435733
44
3-84796414
94
3-97715613
45
4-77433090
95
4-96560173
45
3-85425618
95
3-97795478
46
478351985
96
4-96680137
46
3-86024252
96
3-97872462
47
479227422
97
4-96795795
47
3-86594160
97
3-97946677
48
4-80061929
98
4-96907309
48
3-87137049
98
3-98018226
49
4-80857851
99
4-97014836
49
3-87654497
99
3-98087211
50
4-81617365
100 4-97118527
50
3-88147965
LOO
3-98153729
TABLE IX.
FOR
VALUING MINERAL AND OTHER PROPERTIES,
OB
The present value (or years 9 purchase) of 1 per annum
in n years, allowing interest to a present purchaser upon
his purchase-money or capital invested, at the rates of 5,
6, 8, 10, 12, 15, 1 6, iS,' 20, and 25 per cent, per annum,
and redeeming the capital so invested by an Annual
Redemption Fund, at the rate of 4 per cent, per annum.
Calculated to 8 places of decimals, and 'to 100 years
for each percentage.
TABLE IX.
cvi:
Present Value of 1 per Annum in n years ; Redemption of Capital being at 4 pei
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
6 per cent.
Years
5 per cent.
Years
6 per cent.
Years
6 per cent.
I
0-95238095
51
1777498127
I
0-94339623
51
15-09232358
2
1-85117967
52
17-86284506
2
I-I7753386
52
15-15562012
3
2-70015916
53
17-94715260
3
2-62916745
53
15-21626610
4
3-50274910
54
18-02805444
4
3-38420876
54
15-27438076
5
4-2620820!
55
18*10569440
5
4-08785431
55
15-33007743
6
4-98102472
56
18-18020966
6
4-74469052
56
I5'38346370
7
5-66220597
57
18-25173113
7
5-35878077
57
15-43464181
8
6-30804060
58
18-32038400
8
5-93373800
58
15-48370905
9
6-92075084
59
18-38628770
9
6-47278548
59
15-53075788
10
7-50238514
60
18-44955639
10
6-97880808
60
I5-57587633
ii
8-05483478
61
18-51029920
ii
7*45439554
61
15-61914821
12
8-57984864
62
18-56862064
12
7-90187935
62
15-66065333
13
9-07904626
63
18-62462018
13
8-32336418
63
15-70046770
14
9-55392960
64
18-67839328
H
872075482
64
15-73866376
15
10-00589343
65
18-73003124
15
9-09577943
65
1577531063
16
10-43623469
66
1877962133
16
9-45000952
66
15-81047415
17
10-84616084
67
18-82724705
17
9-78487731
67
15-84421714
18
11-23679741
68
18-87298835
18
10-10169087
68
15-87659957
19
11-60919479
69
18-92050099
19
10-40164729
69
15-91020962
20
11-96433427
70
18-95912065
20
10-68584416
7O
15-93750907
21
I2-303I3365
71
18-99965508
21
10-95528971
71
15-96614298
22
12-62645216
72
19-03859225
22
II-2I09II75
72
15-99363021
23
12-93509507
73
19-07599657
23
11-45356549
73
16-02001840
24
13-22981771
74
19-11192967
24
1 1 '68404046
74
16-04535307
25
13-51132927
75
19-14645065
25
11-90306673
75
16-06967773
26
13-78029623
76
19-17961612
26
I2-III32040
76
16-09303398
27
I4'03735I30
77
19-21148035
27
12-30943295
77
16-11546160
28
14-28306677
78
19-24209535
28
12-49797295
78
16-13699867
29
14-51801619
79
19-27151098
29
I2-67749536
79
16-15768159
30
1474271766
80
19-29977501
30
12-84849963
80
16-17754519
31
I4-95766552
81
I9'32693332
31
13-01145553
81
16-19662282
32
15-16332653
82
19-35302987
32
13-16680143
82
16-21494644
33
15-36014159
83
19-37810679
33
13-31494690
83
16-23254657
34
15-54852760
84
19-40220446
34
13-45627497
84
16-24945246
35
15-72887882
85
19-42536178
35
13-59114421
85
16-26569222
36
15-90156852
86
19-44761583
36
13-71989070
86
16-28129259
37
16-06695021
87
19-46900238
37
13-84282966
87
16-29627936
38
16-22535878
88
I9-4895557I
38
13-96025699
88
16-31067719
39
16-37711185
89
19-50930858
39
14-07245083
89
16-32450962
40
16-52251070
90
19-52829260
40
14-17967275
90
16-33779934
41
16-66184125
9 1
19-54653802
4i
14-28216894
91
16-35056802
42
l6795375 2
92
19-56407393
42
14-38017133
92
16-36283650
43
16-92336996
93
19-58092819
43
14-47389855
93
16-37462468
44
17-04607118
94
19-59712748
44
14-56355690
94
16-38595163
45
17-16371179
95
19-61269758
45
14-64934110
95
16-39683577
46
17-27651354
96
19-62766315
46
H73I435I5
96
16-40729462
47
17-38468743
97
19-64204787
47
14-81001296
97
16-41734509
48
17-48843432
98
19-65587450
48
14-88523906
98
16-42700334
49
I7-58794553
99
19-66916480
49
14-95726917
99
16-43628485
50
17-68340320
100
19-68193985
SO
15-02625076
100
I6-14520457
CV111
THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n year* ; Kedemption of Capital being at 4 per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
8 per cent.
Years
8 per cent.
Years
10 per cent.
Tears
10 per cent.
I
0-92592593
51
II'5930I339
I
0-90909090
51
9-41098085
2
175378267
52
1 1 -6303245 1
2
1-69435216
52
9*43555353
3
2-49782353
53
11-66600528
3
2-37897817
53
9-45902465
4
3-16967212
54
1170013456
4
2-98071437
54
9-48144979
5
377890227
55
1173278682
5
3-51336873
55
9-50288123
6
4-33347094
56
1174603239
6
3-98784660
56
9-52336817
7
4-84004587
57
H79393772
7
4-41287548
57
9-54295693
8
5-30425662
58
11-82256569
8
479552293
58
9-56169124
9
573088916
59
11-84997578
9
5-14157341
59
9-57961231
10
6-12403832
60
11-87562431
10
5-45580691
60
9-59675905
ii
6-48722823
61
11-90136464
n
5-74220796
61
9-61316823
12
6-82350853
62
11-92544738
12
6-00412462
62
9-62887463
13
7-I3553I6I
63
11-94852050
13
6-24439067
63
9-64391111
14
7-42561540
64
11-97062950
14
6-46542083
64
9-65830879
15
7-69579446
65
11-99181766
15
6-66928545
65
9-67209715
16
7-94786208
66
I2-OI2I2600
16
6-85776989
66
9-68530413
17
8-18340503
67
12-03159353
17
7-03242189
67
9-69795619
18
8-40383251
68
I2-05025735
18
7-19458993
68
971007847
19
8-61040035
69
12-06960933
19
7-34545430
69
9-72264000
20
8*80423129
70
12-08531327
20
7-48605253
70
9-73282781
21
8-98633225
71
12-10177089
21
7-61730040
71
974349904
22
9-15760886
72
12-1175560!
22
7-74000930
72
975372889
23
9-3I887792
73
12-13269762
23
7-85490070
73
9-76353682
24
9-47087802
74
12-14722333
24
7-96261829
74
977294132
25
9-61427862
75
12-16115946
25
8-06373819
75
078195997
26
9-74968840
76
12-17453112
26
8-15877761
76
9-79060952
27
9-87766408
77
12-18736224
27
8-24820426
77
9-79890592
28
9-99870265
78
12-19967567
28
8-33243238
78
9-80686438
29
10-11327533
79
12-21149321
29
8-41184853
79
9-81449937
30
10-22180299
80
12-22283566
3O
8-48679588
80
9-82182468
31
10*32467463
81
12-23372291
31
8-55758833
81
9-82885351
32
10-42224803
82
12-24417394
32
8-62451197
82
9-83559840
33
10-51485277
83
12-25420689
33
8-68782810
83
9-84207133
34
10-6027930!
84
12-26383906
34
8-74777587
84
9-84828373
35
10-68634979
85
12-27308708
35
8-80457453
85
9-85424656
36
1076578330
86
12-28196671
36
8-85842551
86
9-85997020
37
10-84133467
87
12-29049316
37
8-90951418
87
9-86546465
38
10-91322772
88
12-29868090
38
8-95801137
88
9-87073942
39
10-98167047
89
12-30654377
39
9-00407482
89
9-87580359
40
11-04685654
90
12-31409506
40
9-04785043
90
9-88066588
41
11-10896627
91
12-32134743
41
9-08947324
91
9'8853346o
42
11-16816795
92
12-32831307
42
9-12906854
92
9-88981770
43
11-22461870
93
12-33500359
43
9-16675264
93
9-89412279
44
11-27846544
94
12-34143010
44
9-20263372
94
9-89825713
45
11-32984563
95
12-34760330
45
9-23681245
95
9-90222771
46
II-378888IO
96
I2-35353338
46
9-26938273
96
9-90604118
47
11-42571362
97
12-35923016
47
9-30043214
97
9-90970393
48 11-47043555
98
12-36470299
48
9-33004253
98
9-91322206
49
11-51316039
99
12-36996084
49
9-35829042
99
9-91660142
50
II-55398826
100
12-^7501237
50
9-38524748
100
9-91984763
TABLE IX.
cix
Present Value of 1 per Annum in n years ; Eedemption of Capital being at 4 per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
12 per cent.
ears
12 per cent.
ears
15 per cent.
Tears
15 per cent.
I
0-89285714
51
7-92023690
I
0-86956522
51
6-39963754
2
1-63881748
52
7-937634IO
2
1-56202144
52
6-41099106
3
2-27092839
53
7-95423799
3
2-12608293
53
6-42181794
4
2-81301829
54
7-97008969
4
2-59410071
54
6-43214622
5
3-28270189
55
7-98522780
2-98840091
55
6-44200216
6
3-69328178
56
7-99968858
6
3-32488920
56
6-45141036
7
4-05499198
57
8-01350607
7
3-61520336
57
6-46039390
8
437583462
58
8-02671234
8
3-86805549
58
6-46897443
9
4-66215697
59
8-03933757
9
4-09009677
59
6-47717232
10
4-91905827
6O
8-05141018
10
4-28649300
60
6-48500671
n
5-15068220
61
8-06295699
ii
4-46131736
61
6*49249561
12
5-36043073
62
8-07400332
12
4-61782475
62
6-49965600
13
5-55112305
63
8-08457304
13
4-75864786
63
6-50650386
H
572511524
64
8-09468872
H
4-88593842
64
6-5I30543I
15
5-88439170
65
8-10437174
15
5-00147292
65
6-51932157
16
6*03063566
66
8-11364227
16
5-10673069
66
6-52531912
17
6-16528429
67
8-12251944
17
5-20295364
67
6-53105967
18
6-28957209
68
8-13102136
18
5-29119207
68
6-53655525
19
6-40456544
69
8-13982771
19
5-37234029
69
6-54224524
20
6-51119028
7O
8-14696723
20
5-44716454
70
6-54685647
21
6-61025452
71
8-15444290
21
5-51632512
71
6-55168313
22
6-70246628
72
8-16160687
22
5-58039417
72
6-55630689
23
6-78844887
73
8-16847307
23
5-63986983
73
6-56073697
24
6-86875311
74
8-17505472
24
5-69518792
74
6-56498208
25
6'9438l937
75
8-18136439
25
574673134
75
6-56905051
26
7-01422721
76
8-18741404
26
5-79483792
76
6-57295012
27
7-08022193
77
8-19321505
27
5-83980786
77
6-57668838
28
7-I42I9520
78
8-19877825
28
5-88190401
78
6-58027242
29
7-20046424
79
8-20411394
29
5-92136659
79
6-58370898
30
7-25530930
80
8-20923195
30
5-95846777
80
6*58700451
31
730698495
81
8-21414161
31
5-99324994
81
6-59016513
32
7-35572I76
82
8-21885187
32
6-02596263
82
6-59319667
33
7*40172910
83
8-22337104
33
6-05680435
83
6-59610469
34
7-44519749
84
8-23777104
34
6-0858801 1
84
6-59889448
35
7-48630068
85
8*23186919
35
6-11331684
85
6-60157110
36
7-52519748
86
8-23586294
36
6-13922995
86
6-60413934
37
7-56203332
87
8-23969605
37
6-16372459
87
6-60660382
38
7-59694158
88
8-24337524
38
6-18689678
88
6-60896892
39
7-63004492
89
8-24690693
39
6-20883436
89
6-61123880
40
7-66145623
90
8-25029727
40
6*22961789
90
6-61341747
41
7-69127963
91
8-25355211
41
6-24926130
91
6-61550873
42
771961132
92
8-25667708
42
6-26801267
92
6-61751624
43
774654027
93
8-25967752
43
6-28575471
93
6-61944347
44
777214892
94
8-26255855
44
6-30260531
94
6-62129373
45
779651375
95
8-26532509
45
6-31861799
95
6-62307023
46
7-81970581
96
8-26798181
46
6-3338423I
96
6-62477599
47
7-84179120
97
8-27053322
47
6-34832421
97
6-62641392
48
7-86283148
98
8-27298359
48
6-36210637
98
6-62798681
49
7-88288405
99
8-27533704
49
6-37522845
99
6-6294973
SO
7-90200250
100 8-27759751
! so
6-38772737
100
6-6309479.6
CX THE ENGINEER'S VALUING ASSISTANT.
Present Value of 1 per Annum in n years ; Redemption of Capital being at 4 pc
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
16 per cent.
Years
16 per cent.
Years
18 per cent.
Years
18 per cent.
I
0*86206897
51
6*01471742
I
0-84512714
51
5-36887241
2
1*53799759
5 2
6-02474519
2
1-49210064
5 2
5-37686085
3
2-08182167
53
6-03430581
3
1-99860681
53
5-38447449
4
2-52850865
54
6-04342433
4
2-40679653
54
5-39173364
5
2-90168425
55
6-05212419
5
274252781
55
5-39865730
6
3-21789766
56
6-06042733
6
3-02332280
56
5-40526323
7
3-48906651
57
6-06835430
7
3-26147635
57
5-41156806
8
3-72400876
58
6-07592443
8
3-46587015
58
5-41758740
9
3-92938127
59
6-08315584
9
3-64308025
59
5-42333589
10
4-1 1030506
60
6-09006555
10
3-79807974
60
5-42882727
ii
4-27078413
61
6*09666960
ii
3-93469911
61
5-43407447
12
4-41399430
62
6*10298309
12
4-05593668
62
5-43908964
*3
4-54248690
63
6-10902023
13
4-16417289
63
5-44388424
H
4-65833504
64
6-11479442
H
4-26132175
64
5-44846906
15
4-76324073
65
6-12031834
15
4-34893979
65
5-45285426
16
4-85861434
66
6*12560392
16
4-42830575
66
5-45704945
17
4-94563457
67
6-13066244
17
4-50047998
67
5-46106368
18
5-02529411
68
6-13550460
18
4-56634916
68
5-46490554
19
5-09843502
69
6-14051752
19
4-62666046
69
5-46888219
20
5-16577621
70
6-14457966
2O
4-68204797
70
5-47210407
21
5-22793522
71
6-14883119
21
4-73305330
71
5-47547568
22
5-28544547
72
6-15290365
22
4-78014189
72
5-47870479
23
5-33877014
73
6-15680518
23
4-82371593
73
5-48179794
24
5-3883I335
74
6-16054351
24
4-86412478
74
5-48476129
25
5-43442929
75
6-16412596
25
4-90167334
75
5-48760072
26
5-47742974
76
6-16755951
26
4-93662898
76
5-49032178
27
5-51759114
77
6-17085076
27
4-96922779
77
5-49292976
28
5-555I55I2
78
6-17400600
28
4-99967564
78
5-49542969
2 9
5-59034195
79
6-17703122
29
5-02815935
79
5-49782633
30
5-62334501
so
6-17993210
3O
5-05484254
80
5-50012422
31
5^5433834
81
6-18271406
31
5-07987204
81
5-50202192
32
5-68347835
82
6-18538225
32
5-10337942
82
5-50444084
33
571090595
83
6-18794158
33
5-12548293
83
5-50646759
34
5-73674848
84
6-19039673
34
5-14628915
84
5-50841166
35
576112125
85
6-19275216
35
5-16589437
85
5-51027661
36
578412897
86
6-I950I2II
36
5-18438584
86
5-51206582
37
5-80586695
87
6-19718065
37
5-20184280
87
5-51378252
38
5-82642206
88
6-19926164
38
5-21833735
88
5-51542980
39
5-84587375
89
6*20125877
39
5-23393525
89
5-51701057
40
5-86429473
90
6-20317557
40
5-24869665
90
5-51852765
41
5-88175174
91
6-20501540
41
5-26267660
91
5-51998372
42
5-89830610
92
6-20678147
42
5-27592562
92
5-52138132
43
5-91401428
93
6-20847685
43
5-28849016
93
5-52272291
44
5-92892836
94
6-21010448
44
5-30041298
94
5-52401079
45
5-94309643
95
6-21166715
45
5'3 ri 73354
95
5-52524722
46
5-95656300
96
6-21316756
46
5-32248827
96
5-52643431
47
5-96936930
97
6-21460826
47
5-33271089
97
5-52757410
48
5-98I55357
98
6-21599170
48
5-34243263
98
5-52866854
49
5-99315136
99
6*21732023
49
5-35168250
99
5-52971949
50
6-00419572
100
6-21859609
50
5-36048741
100
5-53072873
TABLE IX.
cxi
Present Value of 1 per Annum in n years ; Redemption of Capital being at 4 per
cent, with interest allowed to a Purchaser at the following rates per cent.
Years
20 per cent.
Years
20 per cent.
Years
25 per cent.
Years
25 per cent.
I
0-83333333
51
4-84827682
I
o* 80000000
51
3-90230426
2
1-44886364
52
4-85479022
2
1 -35O99338
52
3-90652279
3
1-92178881
53
4-86099628
3
I7533I386
53
3-91054021
4
2-29626374
54
4-86691180
4
2-05977447
54
3-91436769
5
2-59992072
55
4-87255248
5
2-30082286
55
3-91801564
6
2-85093675
56
4-87793299 !
6
2-49524716
56
3-92149379
7
3-06175925
57
4-88306706
7
2-65526946
57
3-92481124
8
3-24119867
58
4-88796757
8
278918374
58
3-9 2 797649
9
3-39566653
59
4-89264657
9
2-90281666
59
3-93099750
10
3-52993987
60
4-89711540
10
3-00038155
60
3-93388I75
n
3-64765094
61
4-90138468
ii
3-08500066
6l
3-93663625
12
375161076
62
4-90546443
12
3-15903692
62
3-93926758
13
3-84402887
63
4-90936405
13
3-22431154
63
3-94178193
14
3-92666601
64
4-91309242
14
3-28225086
64
3-94418512
15
4-00094262
65
4-91665788
15
333398790
65
3-94648263
16
4-06801726
66
4-92006832
16
3-38043406
66
3-94867964
17
4-12884435
67
4-92333118
17
3-42233079
67
3-95078101
18
4-18421722
68
4-92645348
18
3-46028750
68
3-95279135
19
4-23480076
69
4-92968485
19
3-49480963
69
3-95487139
20
4-28115638
70
4-93230261
20
3-52632001
70
3-95655603
21
4-32376143
71
4-93504167
21
3-555I7500
71
3-95831836
22
4-36302438
72
4-93766465
22
3-58167714
72
3-96000566
23
4-39929677
73
4-94017691
23
3-60608489
73
3-96162138
24
4-43288287
74
4-94258348
24
3-62862041
74
3-96316884
25
4-46404731
75
4-94488917
25
3-64947570
75
3-96465113
26
4-49302138
76
4-94709852
26
3-66881759
76
3-96607126
27
4-52000873
77
4-94921586
27
3-68679211
77
3-96743199
28
4-54518648
78
4-95124528
28
370352573
78
3-96873601
29
4-56871482
79
4-95319068
29
37I9I32I2
79
3-96998584
30
4-59073381
80
4-95505000
30
3-7337I930
80
3-97118389
31
4-61136877
81
4-95684408
31
3-74734848
8l
3-97233245
32
4-63073179
82
4-95855890
32
370012522
82
3-97343369
33
4-64892338
83
4-96020358
33
3772II070
83
3-97448968
34
4-66603395
84
4-96178101
34
378336782
84
3-97550240
35
4-68214504
85
4-96329414
35
3-793953IO
85
3-97647371
36
4-69733038
86
4-96474572
36
3-8039I752
86
3-97740540
37
471165684
87
4-96613838
37
3-81330711
87
3-97829917
38
4-72518514
88
4-96747464
38
3.82216361
88
3-979I5665
39
473797062
89
4-96875688
39
3-83052490
89
3*97997939
40
4-75006377
90
4-96998739
40
3-83842548
90
3-98076884
41
4-76151077
91
4-97116835
41
3-84589681
91
3-98152644
42
477235393
92
4-97230183
42
3-85296766
9 2
3*98225351
43
4-78263210
93
43
3^5966437
93
44
479238101
94
4-97443423
44
3-8660IIIO
94
3-98362115
45
4-80163357
4-97543685
3-87203009
3-98426412
46
4-81042017
96
4-97639942
46
3-87774180
96
3-98488136
47
4-81876886
97
4-97732360
47
3-88316511
97
3-98547393
48
4-82670564
98
4-97821098
48
3-88831738
98
3-98604286
49
4-83425458
99
4-97906305
49
3-89321497
99
3-98658912
50
4-84143805 100
4-97988128
50
3-89787261
100
3-98711365
TABLE X.
FOR
VALUING MINERAL AND OTHER PROPERTIES,
OB
The present value (or. years' purchase) of 1 per annum
in n years, deferred i, 2, 3, 4, 5, 6, 7, 8, 9, and 10 years,
allowing interest to a present purchaser upon his purchase-
money or capital invested, at the rate of 4, 5, 6, 8, 10, 12,
15, 1 8, and 20 per cent, per annum, and redeeming the
capital so invested, by an Annual Redemption Fund at the
rate of 3 per cent, per annum.
Calculated to 6 places of decimals, and to 100 years for
each percentage.
P
TABLE X.
cxv
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deferrence. Eedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 4 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
I
924555
51
19-811710
I
888996
51
19-049726
2
1-805329
52
19-941812
2
1735894
52
19-174824
3
2*645001
53
20-067701
3
2-543270
53
19-295871
4
3-446039
54
20-189527
4
3-3I3500
54
I9-4I30II
5
4-210724
55
20-307432
5
4-048774
55
19-526381
6
4-941163
56
20-421552
6
475III9
56
19-636112
7
5-639309
57
20-532021
7
5-422414
57
19-742333
8
6-306971
58
20-638964
8
6*064397
58
19*845163
9
6-945829
59
20-742504
9
6-678684
59
I9*944720
10
7-557448
60
20-842756
10
7-266779
60
20-04III7
ii
8-143283
61
20-939834
1 1
7-830081
61
20-134461
12
8-704688
62
21-033841
12
8-369895
62
20-224852
13
9-242932
63
21-124894
13
8-887437
65
20-312403
H
9759197
64
21-213079
14
9-383846
64
20-397197
15
10-254592
65
21-298497
15
9-860187
65
20*479330
16
10-730152
66
21-381243
16
10-317456
66
20-558892
17
11-186849
67
21-461403
17
10-756589
67
20*635970
18
11-625597
68
21-539064
18
11-178462
68
20-710643
19
12-047253
69
21-614309
19
11-583900
69
20-782994
20
12-452622
70
21-687217
20
11-973678
70
20-853098
21
12-842463
71
21757865
21
12-348525
71
20*921029
22
13-217491
72
21-826327
22
12-709129
72
20-986858
23
I3-578379
73
21-892675
23
13-056137
73
21-050654
24
13-925764
74
21-956978
24
13-390161
74
2 1 ' 1 1 2484
25
14-260246
75
22-019300
25
I37II778
75
21*172409
26
14-582392
76
22-079708
26
14-021534
76
2I-230493
27
14-892740
77
22-138261
27
14-319946
77
2I-286795
28
15-191798
78
22-I95022
28
14-607501
78
2I-34I373
29
15-480046
79
22-250045
29
14-884664
79
21-394279
30
15757942
80
22-303388
30
I5-I5I872
80
2I-44557I
31
16-025919
81
22-355104
31
15-409542
81
21-495297
32
16-284387
82
22-405243
32
15-658069
82
21-543508
33
16-533736
83
22-453857
33
15-897827
83
21-590253
34
I6-774338
84
22-500995
34
16-129175
84
2I-635577
35
17-006545
85
22-546702
35
16-352451
85
21-679535
36
17-230692
86
22-591023
36
16-567977
86
2I-722I43
37
17-447099
87
22-634002
37
16-776061
87
21763469
38
17-656071
88
22-675680
38
16-976996
88
21-803544
39
17-857898
89
227l6lOI
39
17-171060
89
21-842410
40
18-052856
90
22755302
40
17-358519
90
2I-880I03
41
18-241208
91
22-793320
41
17-539627
9 1
21-916659
42
18-423208
92
22-830194
42
17-714627
92
2I'952II5
43
18-599094
93
22-865957
43
17-883749
93
21-986503
44
18-769098
94
22-900647
44
18-047214
94
22*019858
45
I8-933438
95
22-934294
45
18-205233
95
22-0522II
46
19-042326
96
22-966931
46
18-358011
96
22-083593
47
19-245962
97
22-998591
47
I8-505737
97
22-II4035
48
19394538
98
23-029302
48
18-648599
98
22-143566
49
19-538238
99
23-059094
49
18-786772
99
22-172211
S.)
19-677239
100
23-087995
50
18-920426
1OO; 22'2OOOOO
CXV1
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of \ per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 4 per cent.
n
Tears
Deferred 3 Years .
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
I
854803
51
18-317041
I
821927
51
17-612542
2
1-669128
52
18-437327
2
I '60493 1
52
17-728202
3
2-445452
53
18-553719
3
2-35I397
53
17-840118
4
3-186057
54
18-666354
4
3-063517
54
17-948420
5
3-893051
55
18775363
5
3743319
55
18-053237
6
4-568383
56
18-880874
6
4-392677
56
18-154690
7
5-2I3858
57
18-983009
7
5-013326
57
18-252897
8
5-831150
58
19-081884
8
5-606876
5*
18-347969
9
6-421810
59
19-177612
9
6-174819
59
18-440015
10
6-987286
60
19-270301
10
6-718546
60
18-529139
ii
7-528923
61
19-360055
ii
7-239350
61
18-615441
12
8-047974
62
19-446970
12
7-738438
62
18-699013
13
8-545611
63
I9'53II53
13
8-216935
63
18779958
H
9-022927
64
19-612686
H
8-675893
64
18-858355
15
9-480948
65
19-691660
15
9-116297
65
18-934292
16
9-920629
66
19-768162
16
"9-539068
66
19007852
17
10*342872
67
19-842275
17
9-945071
67
19-079114
18
10748519
68
19-914077
18
10-335116
68
19-148154
!9
11-138363
69
19-983645
19
10-709967
69
19-215047
20
11-513150
70
20-051052
20
1 1 -070338
70
19-279861
21
11-873580
71
20-116370
21
11-416906
71
19-342667
22
12*220314
72
20-179668
22
11-750304
72
19-403530
23
12-553976
73
2O-24IOIO
23
12-071133
73
19-462513
24
12-875152
74
20-300462
24
12-379956
74
19-519678
25
13-184400
75
20-358082
25
12-677310
75
19-575083
26
13-482242
76
20-413932
26
12-963697
76
19-628785
27
13769176
77
20-468069
27
I3-239595
77
19-680839
28
14-045672
78
20-520547
28
13-505456
78
19731299
29
14-312174
79
20-571419
29
13761708
79
19780214
30
14-569105
80
20-620738
30
14-008757
80
19-827636
31
14-816864
81
20-668552
31
14-246987
81
19-873611
32
15-055833
82
20-714908
32
14-476765
82
19-918185
33
15-286370
83
20-759855
33
14-698435
83
19-961403
34
. 15-508820
84
20-803436
34
14-912329
84
20-003308
35
15-723508
85
20-845695
35
-15-118760
85
20-043941
36
15-930744
86
20-886672
36
15-318026
86
20-083342
37
16-130825
87
20-926408
37
15-510412
87
20-I2I550
38
16-324032
88
20-964943
38
15-696187
88
20*158603
39
16-510632
89
21-002314
39
15-875611
89
20-194536
40
16-690881
90
21-038557
40
16-048927
9O
20-229385
41
16-865023
91
21-073707
41
16-216371
91
20-263184
42
17-033292
9 2
21-107799
42
16-378169
92
20-295964
43
17-195909
93
21-140865
43
16-534531
93
20-327758
44
I7353I77
94
21-172937
44
16685664
94
20-358597
45
17-505029
95
21-204045
45
16*831762
95
20-388509
46
17-651930
96
2I-23422I
46
16-973013
96
20-417524
47
17793975
97
21-263492
47
17-109594
97
20-445669
48
17-931342
98
21-291886
48
17-241678
98
20-472971
49
18-064200
99
21-319430
49
17-369427
99
20-499456
50
18-192715
100
21-346151
50
17-492998 100
20-525148
TABLE X.
cxvil
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deferrerice. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 4 per cent.
n
Years
Deferred 5 Years
n
Years
Deferred 5 Years
n
Years
Deferred 6 Years
n
Years
Def erred 6 Years
I
790314
51
16-935138
I
759918
51
16-283799
2
I'543203
$3
17-046350
2
1-483850
52
16-390733
3
2-260958
53
17-153961
3
2-174000
53
16-494205
4
2-945689
54
17-258098
4
2-832396
54
I6-594337
5
3-599346
55
17-358884
5
3-460912
55
16-691247
6
4-223728
56
17-456434
6
4-061280
56
16-785045
7
4-820507
57
17-550864
7
4-635106
57
I6-875843
8
5-391227
58
17-642279
8
5-183876
58
16-963742
9
5-937326
59
17730785
9
5-708972
59
17-048844
10
6-460141
60
17-816482
10
6-211678
60
I7-I3I245
ii
6-960915
61
17-899464
ii
6-693192
6l
17-211036
12
7-440806
62
17-979822
12
7-154627
62
17-288303
13
7-900900
63
18-057654
13
7-597025
63
17-363142
14
8-342206
64
I8-I33035
H
8-021357
64
17-873867
15
8-765671
65
18-206051
15
8-428536
65
17-50583!
16
9-172182
66
18-276782
1.6
8-819412
66
17-573842
17
9-562569
67
18-345304
17
9-194785
67
17-639728
18
9-937613
68
18411688
18
9-555404
68
I7-703559
19
10*298046
69
18-476008
19
9-901974
69
17-765406
20
10-644557
70
I8-538330
2O
10-235159
70
17-825330
21
10-977795
71
18-598720
21
10-555580
71
17-883398
22
11-298370
72
18-657242
22
10-863826
72
17-939669
23
11-606859
73
18713957
23
11-160450
73
17-994203
24
1 1 -903805
74
18-768923
24
H'445975
74
18-047055
25
12-189722
75
18*822197
25
11720895
75
18-098279
26
12-465094
76
18-873833
26
11-985676
76
18-147930
27
12-730380
77
18-923885
27
12-240760
77
18-196057
28
12-986017
78
18-972405
28
12-486564
78
18-242710
29
13-232413
79
19-019438
29
12-723484
79
18-287935
30
13-469960
so
19-065036
30
12-951894
80
I8-33I779
31
13-699028
81
19-109243
31
13-172152
81
18-374286
32
13-919967
82
19-152102
32
13-384594
'82
18-415497
33
14-133112
83
19-193658
33
13-589541
83
18-455454
34
14-338780
84
19-233952
34
13787298
84
18-494198
35
14-537271
85
19-273022
35
13-978155
85
18-531765
36
H728873
86
19-310908
36
14-162388
86
18-568194
37
14-913859
87
19-347646
37
14-340259
87
18-603520
38
15-092489
88
I9-383273
38
14-512019
88
18-637777
39
15-265012
89
19-417825
39
14-677906
89
18-670999
40
15-431662
90
19-451334
4O
14-838148
90
18-703219
4i
15-592666
91
19-483832
41
14-992959
91
18-734468
42
15-748240
92
19-515352
42
15-142550
92
18-764775
43
15-898589
93
19-545923
43
15-287116
93
18-794170
44
16-043909
94
19-575576
44
15-426847
94
18822683
45
16-184388
95
19-604337
45
15-561923
95
18-850338
46
16-320206
96
19-632236
46
15-692518
96
18-877164
47
i6-45!535
97
19-659299
47
15-818795
97
18-903186
48
16-578538
98
19-685551
48
15-940914
98
18-928428
49
16-701373
99
19-711017
49
16-059025
99
18-952915
50 i 16-820192
100
19735722
so
16-173273
100
18-976669
cxvin THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Eedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 4 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
I
730690
51
I5'657493
I
702586
51
15-055274
2
1-426779
52
15760315
2
I-37I902
5 2
15-154141
3
2-090384
53
15-859807
3
2-009984
53
15-249806
4
2723456
54
15-956088
4
2-618707
54
15-342384
5
3-327799
55
16-049270
5
3-199805
55
15-431982
6
3-905076
56
16-139461
6
3754879
56
15-518704
7
4-456831
57
16-226766
7
4-285412
57
15-602652
8
4-984494
58
16-311285
8
4792781
58
15-683920
9
5-489394
59
16-393114
9
5^78252
59
15762601
10
5-972766
60
16-472345
10
5743041
60
15-838785
ii
6-435759
6l
16-549067
ii
6-188227
61
15-912556
12
6-879446
62
16-623362
12
6*614849
62
1 5 -983994
13
7-304829
63
16-695322
13
7-023870
63
16-053186
H
7712841
64
16765017
14
7-416189
64
16-120200
15
8-104359
65
16-832524
15
7792649
65
16-185111
16
8-480201
66
16-897919
16
8-154035
66
16-247990
17
8-841136
67
16-961271
17
8-501088
67
16-308906
18
9-187885
68
17-022647
18
8-834500
68
16-367921
19
9-521126
69
17-082115
19
9-154924
69
16-425102
20
9-841495
70
I7-I39735
20
9-462971
70
16-480505
21
10-149592
71
17-195569
21
9759218
71
16-534192
22
10-445983
72
17-249676
22
10-044209
72
16-586218
23
10-731198
73
I7-302II2
23
10-318454
73
16-636637
24
10-005741
74
17-352931
24
10-582438
74
16-685502
25
11-270088
75
17-402185
25
10*836617
75
16732862
26
11-524685
76
17-449926
26
11-081422
76
16778767
27
11-769957
77
17-496202
27
11-317261
77
16-823263
28
12-006307
78
17-541061
28
II-544520
78
16-866396
29
12-234114
79
I7-584547
29
11763565
79
16-908209
30
12-453740
80
17-626705
30
11-974744
80
16-948745
31
12-665526
81
17-667576
31
12*178384
81
16-988045
32
12-869797
82
17-707202
32
12-374799
82
17-026147
33
13-066861
83
17-745623
33
12-564283
83
17-063090
34
13-257013
84
17782876
34
I2747I2I
84
17-098910
35
13-440529
85
17-818999
35
12-923579
85
17-133644
36
13-617676
86
17-854026
36
13-093912
86
17-167324
37
13-788706
87
17-887993
37
13-258364
87
17-199984
38
13-953860
88
17-920933
38
13-417166
88
17-231657
39
14-113367
89
17-952877
39
I3-570538
89
17-262373
40
14-267444
90
17-983858
40
13718689
90
17-292162
4i
14-416302
91
18-013905
41
I3-86l82I
9 1
17-321053
42
14-560139
92
18-043047
42
I4-OOOI26
9 2
17-349074
43
14-699145
93
18-071311
43
14-133786
93
17-376252
44
14-833501
94
18-098727
44
14-262975
94
17-402613
45
14-963382
95
18-125319
45
14-387860
95
17-428182
46
15-088954
96
18-151113
46
14-508602
96
17-452984
47
15-210374
97
18-176134
47
14-625352
97
17-477042
48
15-327796
98
18-200405
48
14-738258
98
17-500381
49
15-441364
99 18-223950
49
14-847458
99
17-523020
50 ; 15-551219 100 18-246791
50
14-953087 .100; 17-544982
TABLE X.
cxix
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Kedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 4 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
675564
51
14-476235
I
649580
51
13-919448
2
1-319137
52
14-571299
2
I "268400
52
14-010856
3
1-932678
53
14-663285
3
I-858343
53
14-099304
4
2-517989
54
14-752302
4
2-421142
54
14-184897
5
3-076737
55
14-838454
5
2-958399
55
14-267735
6
3-610463
56
14-921841
6
3-471596
56
14-347195
7
4-120591
57
15-002559
7
3-862104 '
57
14-425529
8
4-608446 58
1 5 -080702
8
4-431195
58
14-500666
9
5-075254 59
15-156357
9
4-880049
59
I4-5734II
10
5-522158
60
15-229611
10
5-309764
60
14-643848
ii
5-950222
61
15-300545
ii
5721364
61
I47I2053
12
6-360436
62
15-369235
12
6-115800
62
14-778101
13
6-753726
63
15-435766
13
6-493963
63
14-842074
14
7-130956
64
15-500202
H
6-856684
64
14-904032
15
7-492936
65
15-562617
15
7-204742
65
14-964045
16
7-840423
66
15-623078
16
7-538864
66
I5-022l8l
17
8-174128
67
15-681651
17
7-859834
67
15-078501
18
8-494717
68
15738396
18
8-167972
68
15-133064
19
8-802817
69
15793377
19
8-464242
69
15-185930
20
9-099017
70
15-846650
20
8-749049
7O
15-237154
21
9-383870
71
15-898272
21
9-022946
71
15*286791
22
9-657899
72
15-948297
22
9-286436
72
I5'33489I
23
9-921597
73
15-996777
23
9-53999I
73
15-381507
24
10-175428
74
16-043762
24
9784059
74
15-426685
25
10-419831
75
16-089301
25
10-019062
75
15-470472
26
10-655220
76
16-133440
26
10-245398
76
15-512913
27
10-881989
77
16-176225
27
10-463444
77
15-554052
28
11*100507
78
16-217699
28
10-673558
78
1 5 "593932
2 9
11-311128
79
16-257904
29
10-876078
79
15-632590
30
11-514184
80
16-296881
30
11-071324
80
15-670068
31
11709992
81
16-334669
31
11-259601
81
15706403
32
11-898853
82
16-371306
32
11-441197
82
15741630
33
12-081050
83
16-406828
33
11-616386
83
15775786
34
12-256855
84
16-441271
34
11785430
84
15-808904
35
12-426526
85
16-474668
35
11-848575
85
15-841017
36
12-590308
86
16-507053
36
12-106058
86
15-872157
37
12-748435
87
16-538457
37
12-258103
87
15-902353
38
12-901129
88
16-568912
38
12-404924
88
15-931636
39
13-048602
89
16-598446
39
12-546725
89
15-960035
40
13-191056
9O
16-627090
40
12-683700
90
15-987577
41
13-328683
91
16-654870
41
12-816033
91
16-014288
42
13-461669
92
16-681813
42
12-943904
92
16-040195
43
13-590187
93
16-707945
43
13-067480
93
16-065322
44
13-714408
94
16733293
44
13-186922
94
16-089694
45
13-834490
95
16-757878
45
13-302385
95
16-113334
46
13-950588
96
16-781726
46
13-414018
96
16-136265
47
14-062848
97
16-804859
47
13-521961
97
16-158509
48
14-171411
98
16-827300
48'
13-626348
98
.16-180086
49
14-276411
99
16-849068
49
13-727310
99
16-201017
50
i4'377978
100
16-870186
50
13-824970
100
16-221323
cxx
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deterrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 5 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Year.-
I
907030
51
16-270609
j
863837
51
15-495810
2
I755I82
52
16-359105
2
1-671601
52
15-580091
3
2-549675
53
16-444546
3
2-428261
53
15-661463
4
3-295128
54
16-527051
4
3-138215
54
15-740040
5
3-995648
55
16-606738
5
3-805377
55
15-815932
6
4-654900
56
16-683714
6
4-433236
56
15-889242
7
5-276163
57
16-758083
7
5-024914
57
15-960070
8
5-862379
58
16-829945
8
5-583215
58
16-028509
9
6-416197
59
16-899393
9
6-i 10661
59
16*094651
10
6-940009
60
16-966521
10
6-609528
60
16-158582
ii
7-435978
61
17-031412
ii
7-081879
61
16-220383
12
7-906064
62
17-094149
12
7-529581
62
16*280133
13
8-352055
63
17-154819
13
7-954333
63
16-337913
H
8775575
64
17-213488
14
8-357685
64
16-393788
15
9-178109
65
17-270232
15
8741051
65
16-447831
16
9-561017
66
17-325122
16
9-105725
66
16-500106
17
9'925543
67
17-378223
17
9-452893
67
16-550679
18
10-272834
68
17-429600
18
9-783646
68
16-599609
19
10-603940
69
I7-4793I3
19
10-098984
69
16-646955
20
10-919834
70
17-527423
20
10-399836
70
16-692774
21
ir22I4IO
71
I7'573984
21
10-687051
71
16-737118
22
11-509499
72
17-619051
22
10-961421
72
16-780039
23
11-784865
73
17-662677
23
11-223675
73
16-821587
24
12-048224
74
I77049II
24
11-474493
74
16-861811
25
12-300235
75
I774580I
25
11714503
75
16-900753
26
12-541512
76
17785393
26
11-944290
76
16-938460
27
12-772629
77
17-823732
27
12-164402
77
16-974973
28
12-994119
78
17-860860
28
12-375344
78
17-010333
29
13-206481
79
17-896818
29
12-577593
79
17-044579
30
13-410180
BO
17-931646
30
12771592
80
17-077748
31
13-605651
81
17-965381
31
12-957756
81
17-109877
32
I3-793304
82
17-998060
32
13-136473
82
17-141000
33
13-973521
83
18-029719
33
13-308107
83
17-171151
34
14-146661
84
18-060391
34
13-473002
84
17-200363
35
14-313062
85
18-090109
35
i3- 6 3H79
85
17-228666
36
14-473041
86
18-118904
36
13783840
86
17-256089
37
14-626897
87
18-146807
37
13-930370
87
17-282663
38
14-77491 1
88
18-173847
38
14-071336
88
17-308415
39
14-917348
89
18-200051
39
14-206990
89
I7-333372
40
15-054461
90
18-225449
4O
I4-337573
90
17-357560
41
15-186484
91
18-250064
41
14-463309
91
17-381003
42
15-313642
92
18-273922
42
14-584412
92
17-403725
43
15-436146
93
18*297049
43
14-701082
93
17-425751
44
I5-554I95
94
18-319468
44
14-813511
94
17-447102
45
15-667982
95
18-341200
45
14-921879
95
17-467799
46
15-777684
96
18-362269
46
15-026357
96
17-487866
47
15-883471
97
18-382695
47
15-127107
97
17-507319
48
15-985508
98
18-4024(59
48
15-224285
98
17-526179
49
16-083947
99
18-421701
49
15-318036
99
17-544467
50
16:178935
100
18-440319
1 50
1 5 -408 so i
100
17^6219?
TABLE X.
CXXl
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 5 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
j
822703
51
14-757928
I
783526
51
14-055155
2
I-592002
52
14-838196
2
1-516191
52
14-131601
3
2-312632
53
14-915694
3
2-202504
53
14-205408
4
2-988779
54
14-990529
4
2-846453
54
14-276679
5
3-624172
55
15-062807
5
3-45I589
55
14-345516
6
4-222133
56
15-132627
6
4-021075
56
I4-4I20II
7
4785637
57
15-200081
7
4-557745
57
14-476253
8
5317353
58
15-265262
8
5-064141
58
14-538330
9
5-819683
59
15-328254
9
5-542549
59
14-598322
10
6-294795
6O
15-389141
10
5-995037
60
14-656309
n
6744654
61
15*447999
ii
6-423473
61
14712365
12
7-171036
62
15^504904
12
6-829551
62
14-766560
13
7-575563
63
I5-559933
13
7-214814
63
14-818968
H
7-959708
64
15-613147
14
7-580667
64
14-869648
15
8-324819
65
15-664616
15
7-928391
65
14-918667
16
8-672128
66
15714403
16
8-259160
66
14-966082
17
9-002764
67
15-762567
17
8-574052
67
15-011953
18
9-317767
68
15-809167
18
8-874055
68
15-056334
19
9-618090
69
15-854259
19
9*160076
69
15-099279
20
9-904615
70
15-897896
20
9 - 432957
70
15-140837
21
10-178154
71
15-940128
21
9-693470
71
15-181058
22
10-439459
72
15-981006
22
9-94233I
72
15-219989
23
10-689225
73
16*020575
23
10-180203
73
15-257675
24
10-928099
74
16-058883
24
10-407703
74
15-294159
25
11-156680
75
16-095971
25
10-625399
75
15-329480
26
11-375526
76
16-131883
26
10-833823
76
15-363682
27
11-585156
77
16-166657
27
11-033470
77
15-396800
28
11786054
78
16-200333
28
1 1-224801
78
15-428873
29
11-978672
79
16-232948
29
11*408247
79
I5-459935
3O
12-163433
80
16-264538
3O
11-584210
80
15-490020
31
12-340732
81
16-295137
31
II-753066
81
15-519162
32
12-510939
82
16-324778
32
11-915168
82
I 5"54739 I
33
12-674400
83
I6-353493
33
12*070845
83
I5-574739
34
12-831444
84
16-381314
34
I2-22O4IO
84
15-601235
35
12-982374
85
16-408269
35
12-364153
85
15-626907
36
13-127480
86
16-434387
36
12-502349
86
15-651780
37
13-267032
87
16-459695
37
12-635256
87
15-675884
38
13-401286
88
16-484221
38
12-763116
88
15-699242
39
13-530480
89
16-507990
39
12-886158
89
15721879
4O
13-654845
90
16-531026
40
13-004601
9O
15743818
41
13774594
91
I6-553353
4i
13-118647
9^
1 576508 1
42
13-889930
92
I6-574993
42
13-228491
92
15785691
43
14-001045
93
16-595970
43
I3-3343I5
93
15-805669
44
14-108119
94
16-616304
44
13-436290
94
15-825035
45
14-211327
95
16*636016
45
I3-534583
95
15-843808
46
14-310830 i 96
16-655127
46
13-629348
96
15-862009
47
14-406783 97
16-673653
47
13720731
97
15-879653
48
H'499333
98
16-691616
48
13-808875
98
15-896761
49
14-588621
99
16-709033
49
13-893910
99
15-913348
50
14-674777 100
16-725920 50
I3-975964
100
15-929431
CXX11
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 5 per cent.
n
Years
Deferred 5 Years
n
Y-.ars
Deferred 6 Years
n
Years
Deferred 6 Years
n
Years
Deferred 6 Years
I
746215
51
13-385867
I
710680
51
12748441
2
I-443992
52
13-458672
2
I-375230
52
12-817779
3
2-097624
53
13-528965
3
1-997736
53
12-884724
4
2710909
54
13-596842
4
2-581817
54
12-949370
3-28/228
55
13-662401
5
3-130693
55
13-011806
6
3-829597
56
13725729
6
3-647234
56
13-072119
7
4-340711
57
13786913
7
4-134009
57
I3-I30389
8
4-822993
58
13-846033
8
4-593325
58
13-186694
9
5-278620
59
13-903169
9
5-027256
59
13-241109
10
5709561
60
I3-958395
10
5-437675
60
13-293705
II
6-II7595
61
14-011781
ii
5-826280
61
I3-344549
12
6-504337
62
14-063395
12
6*194605
62
13-393706
13
7-001653
63
14-113308
13
6-544050
63
13-441242
14
7-219685
64
14-161575
H
6-875888
64
13-487210
15
7-550851
65
14-208259
15
7-191284
65
13-531671
16
7-865870
66
14-253417
16
7-491302
66
13-574678
17
8-165767
67
14-297103
17
7776918
67
13-616284
18
8-451484
68
I4-33937I
18
8-049029
68
13-656540
19
8723885
69
14-380270
19
8-308459
69
1 3-69549 1
20
8-983772
70
14-419850
20
8-555971
70
I3733I86
21
9-231879
71
14-458516
21
8792263
71
13769668
22
9-46889!
72
14-495233
22
9-017988
72
13-804980
23
9^95435
73
14-531124
23
9-233745
73
13-839162
24
9-91210!
74
14-565871
24
9-440094
74
13-872253
25
10-119431
75
I4-5995IO
25
9-637550
75
13-904291
26
10-317930
76
14-632083
26
9-826597
76
13-935313
27
10-508071
77
14-663625
27
10-007683
77
I3-965353
28
10-690291
78
14-694170
28
I0-l8l226
78
13-994443
29
10-86500!
79
H723753
29
10-347617
79
14-022617
30
11-032585
80
14-752405
30
10-507221
&o
14-049905
3 1
II-I93400
81
14780159
31
10-660377
81
14-076338
32
11-347783
82
14-807045
32
10-807409
82
14-101943
33
11-496047
83
14-833091
33
10*948613
83
14-126748
34
1 1 -638490
84
14-858325
34
1 1 -084272
84
14-150781
35
II-775388
85
14-882774
35
ii'2i4652
85
14-174066
36
1 1 -907003
86
14-906463
36
1 1 -340000
86
14-196627
37
12-033581
87
14-929419
37
11-460550
87
14-218490
38
12-155353
88
14-951665
38
11-576523
88
14-239676
39
12-272536
89
14-973223
39
11-688126
89
14-260208
40
I2-385339
90
14-994118
40
1 1795557
90
14-280108
41
12-493954
91
15-014369
4i
1 1 -899000
9*
14-299394
42
12-598568
92
I5-033997
42
11-998632
92
14-318088
43
12-699352
93
15-053024
43
12-094617
93
14-336209
44
12796471
94
15-071467
44
12-187112
94
14353774
45
12*890084
95
15-089347
45
12-276267
95
14-370802
46
12-980336
96
15-106681
46
12-362221
96
14-387310
47
13-067368
97
15-123485
47
12-445108
97
14-403314
48
I3'I5I3I4
98
I5-I39778
48
12-525057
98
14-418831
49
13-232300
99
I5-I55575
49
12-602186
99
14-433876
50
13-310446 ,1OO
15-170892
50
12-676612
zoo
14-448464
TABLE X.
cxxiii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deferrence. Redemption of Capital being 3 per cent., with Interest
allowed to a Purchaser at 5 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Yean?
Deferred 8 Years
I
676839
51
12-141373
I
644609
51
11-563212
2
I'309743
52
12-207409
2
1-247374
52
11-626103
3
I -902066
53
12-271167
3
1-812006
53
II-686825
4
2-458874
54
12-332734
4
2-341784
54
II-745460
5
2-981612
55
12-392197
5
2-839631
55
1 1 -802092
6
3'473556
56
12-449638
6
3-308149
56
11-856797
7
3-937152
57
12-505133
7
3-749668
57
1 1 -909650
8
4*374595
58
12-558757
8
4-166281
58
1 1 -960720
9
4787863
59
12-610581
9
4-559869
59
I2-OI0076
10
5-178739
60
12-660673
10
4-932132
60
12-057783
ii
5-548838
61
1 2*709906
ii
5-284607
61
I2-I03900
12
5-899624
62
12755911
12
5-618689
62
12-148486
13
6-232429
63
12-801183
13
5-935646
63
12*191602
14
6-548466
64
12-844963
14
6-236633
64
12-233297
15
6-848843
65
12-887307
15
6-522707
65
12-273624
16
7-I34574
66
12-928266
16
6-794832
66
12-312633
17
7-406589
67
12-967891
17
7'053894
67
12-350371
18
7-665743
68
13-006229
18
7-300707
68
12-386884
19
7-912819
69
13-043326
19
7-536017
69
12-422214
20
8-148544
70
13-079226
20
7760518
70
12-456405
21
8-373585
71
13-113970
21
7-974842
71
12-489495
22
8-588561
72
13-147601
22
8-179581
72
12-521524
23
8-794043
73
13-180155
23
8-375279
73
12-552527
24
8-990566
74
13-211671
24
8-562443
74
12-582543
25
9-178620
75
13-242183
25
8741542
75
I2-6ll6o2
26
9-358665
76
13-271727
26
8-913013
76
12-639740
27
9-53II28
77
I3-300337
27
9-077264
77
12-666986
28
9-696406
78
13-328042
28
9-234672
78
12-693372
29
9-854874
79
13-354874
29
9385594
79
12718927
30
10-006877
80
13-380863
30
9-530359
so
12743678
31
10-152741
81
13-406037
31
9-669277
81
12767653
32
10-292771
82
13-430423
32
9-802638
82
12790878
33
10-427251
83
13-454047
33
9-930714
83
I2-8I3377
34
10-556451
84
I3-476935
34
10-053762
84
12-835175
35
IO-68o62I
85
13-499111
35
10-172020
85
12-856296
36
IO-800000
86
13-520598
36
10-285714
86
12-876759
37
10-914810
87
13^41420
37
10-395056
87
12*896589
38
11-025261
88
13-561597
38
10-500247
88
12-915806
39
II-I31549
89
13-581152
39
10-601475
89
12-934429
40
11-233865
90
13-600103
40
10-698918
90
12-952478
41
11-332382
91
13-618472
4i
10-792744
91
12-969972
42
11-427269
92
13-636275
42
10-883113
92
12-986928
43
11-518684
93
I3-653533
43
10-970174
93
13-003364
44
11-606774
94
13-670262
44
1 1 -054070
94
13-019296
45
11-691683
95
13-686479
45
11-134936
95
13-034741
46
n-773544
96
13-702201
46
11-212899
96
13-049714
47
11-852485
97
13-717443
47
1 1 -288080
97
13-064231
48
11-928626
98
13-732221
48
11-360596
98
13-078305
49
12-002083
99
13-746550
49
II-430554
99
13-091951
50
12-072964
100
13-760443
50
1 1 -498060
100
13-105183
CXX1V
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years,, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Int
allowed to a Purchaser at 5 per cent.
Interest
n
Tears
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
'613913
51
1 1 '012590
I
584679
51
10-488175
2
1-187976
52
11-072487
2
1-131405
52
10-545220
3
I72572I
53
II-I303I7
3
1-643543
53
10-600296
4
2*230271
54
11-186160
4
2-124068
54
10-653480
5
2704412
55
11-240095
5
2-575629
55
10704846
6
3-150620
56
11-292195
6
3-000589
56
10-754466
7
3-57III5
57
11-342531
7
3-401060
57
10-802405
8
3-967889
58
11-391170
8
3-778940
58
10-848727
9
4-342735
59
11-438175
9
4'135936
59
10-893495
10
4-697272
60
11-483610
10
4-473590
6O
10-936766
n
5-032963
6l
11-527531
1 1
4793295
61
10-978595
12
5-35II36
62
11-569994
12
5-096317
62
1-019036
13
5-653000
63
11-611058
13
5383806
63
1-058144
14
5'939655
64
11-650767
H
5-656811
64
1-095962
15
6-212106
65
11-689174
15
5-916288
65
1-132541
16
6-471273
66
11726325
16
6-163114
66
1-167923
17
6717999
67
11762266
17
6-398091
67
I-202I52
18
6-953059
68
11797040
18
6-621957
68
1-235270
19
7-177164
69
11-830688
19
6-835391
69
11-267316
20
7-390974
70
11-863251
20
7-039019
70
1 1 '298328
21
7-595093
71
11-894765
21
7-233418
71
11-328341
22
7-790082
72
11-925268
22
7-419122
72
II-357392
23
7-976461
73
11-954796
23
7-596626
73
11-385514
24
8-154713
74
11-983382
24
7766389
74
11-412738
25
8-325284
75
12*01 1058
25
7-928837
75
1 1 -439096
26
8-488590
76
12-037855
26
8-084367
76
11-464618
27
8-645019
77
12-063805
27
8-233347
77
11-489331
28
8-794932
78
12-088934
28
8-376121
78
11-513264
29
8-938667
79
12-113272
29
8-51301!
79
11-536443
30
9-076538
80
12-136845
30
8-644317
80
11-558893
3 1
9-208841
8l
12-159678
3 1
8770320
81
11-580639
32
9-335852
82
12-181796
32
9-871305
82
11-601705
33
9-457830
83
12*203224
33
9-007452
83
II-622II2
34
9-575018
8 4
12-223985
34
9-119059
84
11-641884
35
9-687644
85
12-244099
35
9-226323
85
11-661040
36
9-795924
86
12-263588
36
9-329447
86
11-679602
37
9-900060
87
12-282474
37
9-428624
87
11-697588
38
10-000242
88
12-300776
38
9-524035
88
11-715018
39
10-096649
89
12-318512
39
9-615851
89
II73I9IO
40
10-189452
90
12-335702
4.0
9704235
90
11748281
41
10-278811
9 1
12-352363
41
9-789338
91
I 1-764148
42
10-364876
92
12-368511
42
9-871305
92
11779528
43
10-447792
93
12-384164
43
9-950272
93
1 1 -794436
44
10-527692
94
I2-399338
44
10-026368
94
1-808887
45
10-604708
95
12-414047
45
10-099716
95
1-822896
46
10-678958
96
12-428308
46
10-170431
96
1-836477
47
10750559
97
12-442133
47
10-238622
97
1-849644
48
10-819622
98
12-455537
48
10-304396
98
I '862409
49
10-886250
99
12-468533
49
10-367851
99
1-874787
50
10-950541
100
12-481135
50
10-429081
100
11-886789
TABLE X.
cxxv
Present Value (or Years' Purchase) of 1 per Annum in n year?, after
t years' Deferrence. Redemption of Capita) being at 3 per cent., ""^ T ~*
with Interest
allowed to a Purchaser at 6 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
I
889996
51
13765407
I
839619
51
12-986230
2
1707162
5 2
13-829301
2
1-610530
52
13-046507
3
2-459768
53
13-990894
3
2-320536
53
13-104613
4
3-154685
54
13-950283
4
2-976306
54
13-160641
5
3798585
55
14-007558
5
3-583570
55
13-214674
6
4-396119
56
14-062807
6
4-I4728I
56
13-266796
7
4-952045
57
14-116114
7
4-671739
57
13-317085
8
5-470345
58
14-167555
8
5-160701
58
13-365615
9
5-954510
59
14-217208
9
5-617461
59
13-412457
10
6-407613
60
14-265141
10
6-044916
60
I3-457677
n
6733368
61
14-311425
ii
6-445629
61
13-501341
1 2
7-231189
62
14-356119
12
6-821875
62
I 3'54355
1 3
7-606220
63
I4-399295
13
7-175677
63
13-584237
14
7-959378
64
14-441001
H
7-508846
64
13-623583
15
8-292383
65
14-481299
15
7-823001
65
13-661600
16
8-606775
66
14-520241
16
8-119597
66
13-698337
17
8-903950
67
14-557878
17
8-399950
67
13733843
18
9-185162
68
14-594258
18
8-665245
68
13768164
19
9-451552
69
14-629430
19
8-916556
69
13-801345
20
9704152
70
14-663436
20
9-154858
7O
13-833427
21
9-943906
71
14-696321
21
9-381041
71
13-864450
22
10-171671
72
14-728126
22
9-5959I4
72
i3'894455
23
10-388233
73
14-758888
23
9-800218
73
13-923476
24
10-594311
74
14-788646
24
9-994630
74
I 3'9S 1 SS
25
10790563
75
14-817436
25
10-179774
75
13-978710
26
10-977598
76
14-845293
26
10-356222
76
14-004990
27
11-155937
77
14-872249
27
10-524500
77
14-030420
28
11-326202
78
14-898337
28
10-685094
78
14-055031
2 9
11-488763
79
14-923586
2 9
10-838453
79
14-078851
30
11-644095
80
14-948026
30
10-984993
80
14-101907
31
11-792608
81
14-971685
31
11-125099
81
14-124228
32
1 1 -934679
82
14-994590
32
11-259128
82
14-145836
33
12-070660
83
15-016767
33
11-387412
83
14-166758
34
I2-200880
84
15-038242
34
11-510261
84
14-187017
35
12-325643
85
15-059037
35
11-627962
85
14-206635
36
12-445235
86
15-079176
36
11740785
86
14-225634
37
12-559920
87
15-098680
37
11-848978
87
14-244034
38
12-669949
88
I5-II7574
38
11-952779
88
14-261858
39
12-775553
89
I5'I35874
39
12*052405
89
14-279123
40
12-881951
90
15-153602
40
12-148064
90
14-295847
41
12-974347
91
15-170777
41
12-239947
9 1
14-3 1 205 1
42
13-067934
92
15-187418
42
12-328236
92
14-327749
43
13-157892
93
15-203541
43
12-413103
93
14-342959
44
13-244392
94
15-219164
44
12-494706
94
14-357698
45
13327593
95
15-234303
45
12-573198
95
14-371980
46
13-407646
96
15-248975
46
12-648719
96
14-385821
47
13-484694
97
15-263193
47
12721406
97
14-399235
48
13-558870
98
15-276974
48
12791384
98
14-412236
49
13-630302
99
15-290330
49
I2-858773
99
14-424836
50
13-699110
100
15-303277
SO
12-923685
100
14-437050
CXXV1
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 6 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
I
792093
51
I2-25II62
I
747258
51
II'557709
2
1-519368
5 2
12-308028
2
1-433367
5 2
11-611356
3
2-189185
53
12-362845
3
2*065270
53
1 1 -663070
4
2-807836
54
12-41570!
4
2-648904
54
II7I2934
5
3*380734
55
12-466676
5
3-189367
55
11-761024
6
3-912530
56
12-515847
6
3-691069
56
II-8074I2
7
4-407302
57
12-563290
7
4-I57835
57
11-852169
8
4-868587
58
12-609072
8
4-593010
58
11-895360
9
5-299492
59
12-653263
9
4-999525
59
II-937040
10
5702752
60
12-695923
10
5-379959
60
11-977295
ii
6-080783
61
12-737116
ii
5736592
61
I2-Ol6l56
12
6-435732
62
12776894
12
6-071450
62
12-053683
13
6-769508
63
12-815320
13
6-386333
63
12-089933
H
7-083818
64
12-852438
14
6-682852
64
I2-I2495I
IS
7-380191
65
12-888304
15
6-962449
65
12-158786
16
7-659999
66
12-922961
16
7-226419
66
12-191482
17
7-924483
67
12-956458
17
7-475933
67
12-223083
18
8-174761
68
12-988836
18
7-712044
68
12-253628
19
8-411846
69
13-020139
19
7-9357IO
69
12-283159
20
8-636660
70
13-050405
20
8-147799
7O
I2-3II7I2
21
8-850040
7i
13-079672
21
8-349101
71
I2-339323
22
9-052750
72
13-107978
22
8-540337
72
12-366027
23
9-245490
73
I3'I35356
23
8-722167
73
12-391855
24
9-428898
74
13-161841
24
8-895193
74
12-416841
25
9-603562
75
13-187464
25
9-059971
75
I2-44IOI3
26
9-770022
76
13-212256
26
9-217009
76
12-464402
27
9-928775
77
13-236248
27
9-366776
77
12-487036
28
10*080278
78
13-259466
28
9-509704
78
12-508939
29
10-224957
79
13-281937
29
9-646194
79
12-530139
30
10-363202
ao
13-303688
30
9776613
80
12-550659
31
10-495378
81
13-324745
31
9-901307
81
12-570524
32
IO-62I82I
82
I3-345I30
32
10-020593
82
12-589755
33
10-742844
83
13-364868
33
10-134766
83
12-608376
34
10-858739
84
I3'383980
34
IO-244IOI
84
12*626406
35
10-969778
85
13-402488
35
10-348855
85
12-643866
36
11-076214
86
13-420411
36
10-449266
86
I2-660775
37
11-178283
87
13-437770
37
10-545558
87
I2-677I52
38
11-276208
00
OO
13-454585
38
10-637940
88
12-693015
39
II-370I95
8 9
13-470872
39
10-726607
89
12708380
40
11-460439
90
13-486651
40
10-811743
90
12723265
41 -
II-547I2I
91
I3-50I937
41
10-893519
91
12737686
42
11-630413
92
13-516747
42
10-972096
92
12758658
43
11-710476
93
13-531096
43
11-047627
93
12765194
44
11-787461
94
I3-54500I
44
II-I20254
94
I27783I2
45
11-861509
95
I3-558474
45
II-I90II2
95
I279I023
46
11-932756
96
I3-57I532
46
11-257325
96
12-803342
47
12-001328
97
13-584186
47
II-3220I7
97
12-815279
48
12-067345
98
13-596451
48
11-384297
98
12-826850
49
12-130919
99
13-608338
49
11-444272
99
12-838065
50
12-192158
100
13-619860
50
1 1 -502044
100
12-848935
TABLE X.
cxxvn
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deterrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 6 per cent.
n
Years
Deferred 5 Years
n
ears
Deferred 5 Years
n
ears
Deferred 6 Years
n
Tears
Deferred 6 Years
I
704960
51
10-903492
I
665057
51
IO-286322
2
I-352232
52
10-954102
2
1-275692
52
10-334068
3
1-948367
53
11-002889
3
1-838084
53
10-380093
4
2-498965
54
11-049930
4
2-357516
54
10-424472
5
3-008835
55
11-095298
5
2-838526
55
10-467272
6
3-482138
56
II'I39o6o
6
3-285039
56
10-508557
7
3-922484
57
11-181284
7
3700459
57
10-548391
8
4-333026
58
II'22203I
8
4-087764
58
10-586831
9
4716530
59
11-261360
9
4-449560
59
10-623934
10
5-075429
60
11-299328
10
4788145
60
10-659753
ii
5-411876
61
II-335989
n
5-105548
61
10-694339
12
5727779
62
II-37I39I
12
5-403570
62
10727737
13
6-024839
63
11-405590
13
5-683815
63
10760000
H
6-304573
64
1 1 -438626
H
5-947716
64
10-791166
15
6-568344
65
11-470546
15
6-196556
65
IO-82I279
16
6-817372
66
11-501391
16
6-431489
66
10-850378
17
7-052762
67
II-53I203
17
6-653555
67
10-878503
18
7-275509
68
11-560019
18
6-863693
68
10-905688
19
7-486514
69
11-587879
19
7-062755
69
10-931971
20
7-686598
70
11-614815
20
7-251514
70
10-957382
21
7-876505
71
1 1 -640863
21
7-430672
71
10-981956
22
8-056916
72
11-666055
22
7-600871
72
II-005722
23
8-228454
73
11-690422
23
7762699
73
11-028709
24
8-391686
74
H7I3993
24
7-916692
74
11-050947
25
8-547I37
75
11736797
25
8-063344
75
11*072460
26
8-695286
76
II-758862
26
8-203107
76
1 1 -093276
27
8-836575
77
II702I4
27
8'336399
77
II-II3420
28
8-971413
78
11-800878
28
8-463605
78
11-132914
29
9-IOOI77
79
11-820878
29
8-585080
79
11-151782
3O
9-223214
80
11-840237
30
870II53
80
11-170044
31
9-340850
81
11-858977
31
8-8I2I30
81
11-187724
32
9-453384
82
i r -877 1 20
32
8-918295
82
1 1 -204840
33
9-561094
83
1 1 -894686
33
9-019908
83
II-22I4I2
34
9-664240
84
11-911696
34
9-II72I5
84
11-237460
35
9-763064
85
11-928168
35
9*210446
85
11-252998
36
9-857792
86
11-944120
36
9-299812
86
1 1 -268047
37
9-948633
87
11-959569
37
9-385511
87
II-282622
38
10-035786
88
11-974534
38
9-467731
oo
00
11-296741
39
10-119434
89
1 1 -989030
39
9-546645
89
11-310415
40
10-199751
90
12-003072
4O
9-622415
90
11-323663
41
10-276898
91
12016677
41
9-695195
91
11-336498
42
10-351028
92
12-029858
42
9765129
92
11-348932
43
10-422283
93
12-042628
43
9-832351
93
1 1 -360980
44
45
10-490799
10-556702
94
95
12-055004
12-066995
44
45
9-896989
9-959162
94
95
11-372655
11-383968
46
IO-620III
96
12-078616
46
10-018982
96
II-39493I
47
IO-68II4I
97
12-089878
47
10-076557
97
11-405556
48
10-739895
98
12-100794
48
10-131986
98
11-415854
49
10-796476
99
12-111374
49
10-185364
99
11-425834
50
10-850978 100
12-121628
50
10-236781
100
II-435509
CXXVlll
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 6 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
I
627412
51
9-704069
I
591898
51
9-154779
2
1-203482
52
9749II2
2
1-135360
52
9-197272
3
1734040
53
9792533
3
1-635886
53
9-238235
4
2-224070
54
9-834399
4
2-098178
54
9-277731
5
2-6/7853
55
. 9-874776
5
2-526275
55
9-315823
6
3-099090
56
9-913725
6
2-923669
56
9-352567
7
3-490997
57
9-951304
7
3-293392
57
9-388018
8
3-856378
58
9-987568
8
3-638091
58
9-422230
9
4-197695
59
IO-02257I
9
3-960088
59
9-455252
10
4-5I7II4
6O
10-056362
10
4-261427
60
9-487130
n
4-816550
61
10*088991
ii
4'5439I3
61
'9-517912
12
5-097703
62
10*120498
12
4-809152
62
9-547636
13
5-362085
63
10-150935
13
5-058569
63
9-576350
H
5-611048
64
10-180337
H
5-293439
64
9-604087
15
5-845803
65
10-208745
15
5-514906
65
9-630888
16
6-067437
66
10-236198
16
5723995
66
9-656786
17
6-276934
67
10-262730
17
5-921633
67
9-681817
18
6-475177
68
10-288377
18
6-108655
68
9706012
19
6-662971
69
10-313171
19
6-285819
69
9-729403
20
6-841045
70
IO-337H5
20
6-4538I3
70
9752019
21
7-OI0062
71
10-360327
21
6-613263
71
9773889
22
7-170627
72
10-382748
22
6-764740
72
9795041
23
7-323295
73
10-404434
23
6-908766
73
9-815100
24
7-468571
74
10-425413
24
7-045819
74
9-835291
25
7-606922
75
10-445708
25
7-176338
75
9-854438
26
7738774
76
10-465346
26
7-300727
76
9-872964
27
7-864521
77
10-484350
27
7-419356
77
9-890892
28
7-984526
78
10*502740
28
7-532569
78
9-908242
29
8*099125
79
10-520540
29
7-640681
79
9-925034
30
8-208628
80
10-537769
30
7743986
80
9-941287
31
8-3I3324
81
10-554448
31
7-842755
81
9-957022
32
8-413478
82
10-570595
32
7-937241
82
9W2255
33
8-509340
83
10*586229
33
8-027676
83
9-987004
34
8-601140
84
10-601368
34
8-114279
84
10-001286
35
8-689093
85
10*616028
35
8-197254
85
IO-OI5II6
36
8-773400
86
10*630225
36
8-276789
86
10-028509
37
8-854248
87
10-643975
37
8-353061
87
10-041481
38
8-931815
88
10-657294
38
8-426237
88
10-054046
39
9-006261
89
10-670194
39
8-496469
89
10-066217
40
9-077743
90
10-682692
40
8-563905
90
10-078007
41
9-146403
91
10*694800
4i
8-628679
91
10*089430
42
9-212378
92
10706531
42
8*690919
9 2
10-100497
43
9-275795
93
10717897
43
8750747
93
IO-III2I9
44
9^36774
94
10-72891 1
44
8-808274
94
10-121610
45
9-395428
95
10739583
45
8-863607
95
10-131678
46
9-451862
96
10*749926
46
8-916847
96
10-141435
47
9-506178
97
10759049
47
8-968088
97
10-150891
48
9-558469
98
10-769664
48
9-017420
98
10-160056
49
9-608826
99
10-779080
49
9-064926
99
10-168939
SO
9^57333
100
10788207
50
9-110687
100
10-177549
TABLE X.
cxxix
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 6 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
558394
5t
8-636582
I
526788
51
8-147729
2
1-071094
52
8-676670
2
1-010467
52
8-185547
3
1-543288
53
8715314
3
1-455934
53
8*222004
4
1-979413
54
8752575
4
1-867373
54
8-257156
5
2-383278
55
8788510
5
2-248378
55
8-291057
6
2758178
56
8-823174
6
2-602058
56
8323759
7
3-106973
57
8-856619
7
2-931110
57
8-445311
8
3-432160
58
8-888895
8
3-237891
58
8385759
9
3735931
59
8-920047
9
3-524468
59
8-415149
10
4-0202 1 3
60
8-950121
10
3792658
60
8-443520
ii
4-286710
61
8-979160
ii
4-044071
61
8-470916
12
4-536935
62
9*007202
12
4-280132
62
8-497370
13
4772234
63
9-03429J
13
4-502113
63
8-522836
H
4-993810
64
9-060458
14
4711147
64
8-547612
15
5-202741
65
9-085741
15
4-908252
65
8-571464
16
5^399994
66
9-110174
16
5-094340
66
8-594514
17
5*586445
67
9 '133788
17
5-070238
67
8-61679!
18
5-762881
68
9-156613
18
5-436687
68
8-638324
19
5-930017
69
9-178680
19
5-594362
69
8-659142
20
6-088502
70
9-2000I6
20
5743877
70
8-679271
21
6-238926
71
9-220649
21
5-885787
71
8-698735
22
6-381829
72
9-240603
22
6-020600
72
8717561
23
6-517703
73
9-259904
23
6-148783
73
8735769
24
6-646998
74
9-278575
24
6-270760
74
8753383
25
6770129
75
9-296638
25
6-386922
75
8770423
26
6-887477
76
9-314115
26
6-497628
76
8786912
27
6-999392
77
9-331028
27
6-603207
77
8-802867
28
7-106195
78
9-347396
28
6703966
78
8-818308
29
7-208188
79
9-363237
29
6-800186
79
8-833253
30
7-305645
80
9-378571
.30
6-892127
80
8-8477I9
31
7-398824
81
9-3934I5
31
6-980031
81
8-861723
32
7-487961
82
9-407786
32
7-064123
82
8-875280
33
7-573277
83
9-42 1 700
33
7-144610
83
8-888407
34
7-654979
84
9'43 5 i 74
34
7-221687
84
8-901118
35
7733257
85
9-448221
35
7-295534
85
8-913427
36
7-808290
86
9-460856
36
7-366320
86
8-925347
37
7-880245
87
9-473094
37
7-434202
87
8-936891
38
7-949278
88
9-484948
38
7-499328
88
8-948074
39 8-015535
89
9-496429
39
7-561835
89
8-958906
4O 8-079154
90
9-507552
40
7-621852
90
8-969399
41
8-140261
91
9-518328
41
7-679501
91
8-979566
42
8-198979
92
9-528769
42
7734895
92
8-989415
43
8-255420
93
9-538884
43
7788141
93
8-998958
44
8-309691
94
9-548687
44
7-839340
94
9-008206
45
8-361892
95
9-558185
45
7-888587
95
9-017166
46
8-412118
96
9-567390
46
7-935970
96
9-025850
47
8-460459
97
9-576311
47
7-981575
97
9-034266
48
8-506998
98
9-584957
48
8-025480
98
9-042423
49
8-551816
99
9-593337
! 49
8-067760
99
9-050329
50
8-594986
100
9-601460
50
8-108487
100
9-057992
cxxx
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Kedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 8 per cent.
n
rears
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
I
857339
51
10-458443
!
793832
51
9-683745
2
1-617025
52
10-495982
2
I ^97246
5 2
9718503
3
2-294563
53
10-532094
3
2-124596
53
9751940
4
2-902343
54
10-566844
4
2-687355
54
9784116
5
3-450383
55
10-600296
5
3-I94799
55
9-815090
6
3-946871
56
10-632504
6
3-654510
56
9-844912
7
4'3985 6 5
57
10-663524
7
4-072746
57
9^73635
8
4-811095
58
10-693406
8
4-4547I8
58
9-901304
9
5-189184
59
IO-722205
9
4-804800
59
9-927969
10
' 5'536825
60
10-749962
10
5-126690
6O
9'953670
n
5-857420
61
10776721
ii
5-423538
61
9-978447
12
6-153883
62
10-802524
12
5-698040
62
10-002338
13
6-428723
63
10-827414
13.
5-952522
63
10*025384
H
6-684115
64
10-851424
H
6-188996
64
10*047616
15
6-921953
65
10-874593
15
6-409217
65
10-069068
16
7-143892
66
10-896952
16
6*614716
66
10*089771
17
7-35I389
67
10-918536
17
6-806842
67
10-109757
18
7'545725
68
IQ'939374
18
6-986783
68
10-129051
19
7-728036
69
10-959497
!9
7-I55590
69
10-147684
20
7-899334
70
10-978931
20
7-314199
70
10-165679
21
8-060518
71
10-997705
21
7-463444
71
10-183061
22
8-212394
72
11-015841
22
7-604070
72
10-199854
23
8-355684
73
II-033367
23
7-736745
73
I0'2l6o82
24
8-491040
74
1 1 -050303
24
7-862076
74
10-231763
25
8-619048
75
I I -066673
25
7-980601
75
10-246921
26
8740240
76
I I -082498
26
8-092815
76
10-261574
27
8-855095
77
11-097798
27
8*199163
77
10-275740
28
8-964053
78
II-II2592
28
8-300050
78
10-289438
2 9
9-067512
79
11-126898
29
8395845
79
10-302685
30
9-165836
8t>
11-140736
3O
8-486886
80
10-315498
3'
9^59359
81
ii'i54i2o
31
8-573482
81
10-327891
32
9-348386
82
11-167069
32
8-655914
82
10-339880
33
9-433I97
83
11-179597
33
8734443
83
10-351480
34
9-514050
84
i -191719
34
8-809307
84
10-362705
35
9-591183
85
i -203450
35
8-880726
85
10-373566
36
9-664816
86
i -214804
36
8-948904
86
10-384079
37
9735I5 1
87
i -225793
37
9-014030
87
10-394254
38
9-802377
88
i -236430
38
9-076276
88
10-404103
39
9-866667
89
11-246728
39
9-135804
89
10-413638
40
9'9:8l83
90
11-256698
40
9-192763
90
10-422870
41
9-987078
91
11-266352
4i
9-247295
91
10-431809
42
10-043489
9 2
11-275700
42
9-299528
92
10-440464
43
10-097547
93
11-284752
43
9-349582
93
10-448846
44
10-149376
94
11-293519
44
9-39757I
94
10-456964
45
10-199088
95
11-302011
45
9-443601
95
10-464826
46
10-246791
96
11-310236
46
9-487770
96
10-472442
47
10-292583
97
11-318:05
47
9-530171
97
10-479820
48
10-336560
98
11-325923
48
9-570890
98
10-486967
49
10-378807
99
11-333401
49
9-610008
99
10-4938 I
50
10-419410
100
1 1 -340647
50
9-647603
100
10-500601
TABLE X.
cxxxi
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 8 per cent.
n
Years
Deferred 3 Years
Years
n
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
I
735030
51
8-966426
I
680583
51
8-302251
2
1-386338
52
8-998610
2
1-283647
5 2
8-332050
3
1-967217
53
9-029570
3
1-821498
53
8-360717
4
5
2-488290
2-958146
54
55
9-059362
9-088042
4
5
2-303974
2-739025
54
55
8-388303
8-414858
6
3-383804
56
9-115655
6
3-I33I54
56
8-440425
7
3771059
57
9-142250
7
3-49I723
57
8-465050
8
4-124737
58
9-167869
8
3-819203
58
8-488772
9 4-448887
59
9-192559
9
4MI9342
59
8-511633
10 4746933
9-216356
10
4-3953IO
60
8-533667
ii
5-021792
61
9-239298
ii
4-649809
61
8-554910
12 5' 2 7596l
62
9-261420
12
4-885151
62
8-575393
13
5-5II59I
63
9-282759
13
5-103328
63
8-595151
H
5730549
64
9-303343
14
5-306067
64
8-614211
15
5-934457
65
9-323207
15
5-494870
65
8-632603
16
6-124734
66
9-342376
16
5-671053
66
8-650353
17
6-302628
67
9-360881
17
5-835770
67
8-667487
18
6-469240
68
9-378746
18
5-990040
68
8-684029
19
6-625543
69
9-395999
19
6-134765
69
8-700003
20
6-772403
70
9-412661
20
6-270747
70
8-715431
21
6-910593
71
9-428755
21
6-398700
71
8-730334
22
7-040802
72
9-444304
22
6-519264
72
8-74473I
23
7-163650
73
9-459330
2 3
6-633012
73
8-758643
24
7-279696
74
9-473850
24
6740463
74
8772088
25
7-389442
75
9-487885
25
6-842079
75
8-785083
26
7-493344
76
9-501452
26
6-938285
76
8-797645
27
7-591814
77
9-514569
27
7-029461
77
8-809791
28
7-685227
78
9-527253
28
7-II5955
78
8-821535
29
7773927
79
9-5395I8
29
7-198084
79
8-832892
30
7-858224
80
9-551382
30
7-276137
8t>
8-843877
31
7-938405
81
9-562857
31
7^50379
81
8-85450!
32
8-014731
82
9-573958
32
7-421051
82
8-864781
33
8-087443
83
9-584699
33
7-488377
83
8-874726
34
8-156761
84
9-595092
34
7-552560
84
8-884349
35
8-222891
85
9-605149
35
7-6I379I
85
8-893661
36
8-286018
86
9-614883
36
7-672243
86
8-902674
37
8-346319
87
9-624304
37
7-728077
87
8-911397
38
8-403955
88
9-633424
38
7781444
88
8-919841
39
8-459073
89
9-642253
39
7-832479
89
8-928016
40
8-511814
90
9-650801
40
7-88I3I3
90
8-93593I
41
8-562306
91
9-659077
4i
7-928065
91
8*943594
42
8-610670
92
9-667092
42
7-972846
92
8-951015
43
8-657016
93
9-674852
43
8-015760
93
8-958201
44
8-701451
94
9-682369
44
8-056903
94
8-965161
45
8-744071
95
9-689649
45
8-096366
95
8-971902
46
8-784968
96
9-696701
46
8T34234
96
8-978431
47
8-824228
97
9-703532
47
8-170585
97
8-984757
48
8-861931
98
9-710150
48
8-205496
98
8-990884
49
8-898151
99
9-716561
49
8-239033
99
8-996820
50
8-932961
LOO
9-722773
50
8-271265
100
9-002572
CXXX11
THE ENGINEEK'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deterrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 8 per cent.
n
Years
Deferred 5 Years
n
Years
Deferred 5 Years
n
Years
Deferred 6 Years
n
Years
Deferrrd 6 Years
I
630169
51
7-687265
I
583491
51
7-II7845
2
1-188561
52
7714857
2
I-IOO52I
52
7-H3393
3
1-686572
53
774I40I
3
1-561642
53
7-167970
4
2-133308
54
7766943
4
1-975287
54
7-191620
5
2-536I33
55
779I53I
5
2-348274
55
7-214387
6
2-901067
56
7-815205
6
2-686175
56
7-236307
7
3-233076
57
7-838006
7
2-993591
57
7-257419
8
3-536297
58
7-859970
8
3-274352
58
7-277756
9
3-814204
59
7-881138
9
3-53I673
59
7-297357
10
4-069730
69
7-901540
10
3768272
60
7-316247
ii
4-099730
61
7-921209
ii
3-986464
61
7-334459
12
4-523286
62
7-940175
12
4-188231
62
7-352020
13
4725301
63
7-958469
13
4-375283
63
7-368960
14
4-913023
64
7-976118
14
4-549099
64
7-385301
15
5-087840
65
7-993I47
15
4*710968
65
7-401069
16
5-250972
66
8-009582
16
4-862016
66
7-416286
17
5-403488
67
8-025447
17
5-003234
67
7-430976
18
5-54633I
68
8-040764
18
5-135496
68
7-445158
19
5-680335
69
8-055555
19
5^59574
69
7-458853
2O
5-806244
70
8-069839
20
5-376157
70
7-472080
21
5-924719
71
8-083638
21
5-485856
71
7-484857
22
6-036353
72
8-096969
22
5-589220
72
7-497200
23
6-141675
73
8-109851
23
5-686741
73
7-509128
24
6*241166
74
8-I22299
24
5-778862
74
7-520654
2 5
6335255
75
8-I34332
25
5-865982
75
7-531796
26
6-424335
76
8-145964
26
5-948463
76
-7-542566
27
6-508757
77
8-157210
27
6-026632
77
7-552979
28
6-588844
78
8-168084
28
6-100787
78
7-563047
29
6-664889
79
8-178599
29
6-171199
79
7-572784
30
6-737161
33
8-188771
30
6-238117
80
7-582202
31
6-805903
81
8-198608
31
6-301767
81
7-591311
32
6-871340
82
8-208I26
32
6-362358
82
7-600124
33
6-933679
83
8-217335 -
33
6-420079
83
7-608650
34
6-993108
84
8-226245
34
6-475106
84
7-616900
35
7-04Q803
85
8-234867
35
6-527601
85
7-624884
36
7-103925
86
8-2432I2
36
6-577714
86
7-63261 1
37
7-155624
87
8-251290
37
6-625583
87
7-640090
38
7-205037
88
8-259108
38
6-671336
88
7-647329
39
7-252292
89
8-266678
39
6715091
89
7-654338
40
7-297508
90
8*274006
40
6-756958
90
7-661124
41
7-340797
9 1
8-28II02
41
6-797041
91
7-667694
42
7-382261
92
8-287973
42
6-835433
92
7-674056
43
7-421996
93
8-294626
43
6-872224
93
7-680216
44
7-460091
94
8-301071
44
6-907498
94
7-686183
45
7-496631
95
8-307312
45
6-94I33I
95
7-691963
46
7'53i6:)4
96
8-3I3358
46
6-973797
96
7-697561
47
7'565355
97
8-319215
47
7-004963
97
7-702984
48
7-597677
98
8-324889
48
7-034893
98
7708237
49
7-628730
99
8-330385
49
7-063645
99
7713326
50
7-658575
100
8-3357II
59
7-091279
100
7718258
TABLE X.
CXXXlll
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with -Interest
allowed to a Purchaser at 8 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
I
540269
51
6-590588
I
500249
51
6-I02402
2
1-018999
52
6-614244
2
943519
52
6-124306
3
1-445963
53
6-637001
3
I-338856
53
6-145377
4
1-828967
54
6-658899
4
1-693489
54
6*165653
5
2-I74325
55
6-679980
5
2-013265
55
6-185172
6
2-487196
56
6*700276
6
2-302961
56
6-203965
7
2-771840
57
6-719824
7
2*566521
57
6-222065
8
3-031804
58
6738655
8
2-807228
58
6-239501
9
3-270054
59
6756803
9
3-027839
59
6-256305
10
3-489136
60
6774294
10
3-230684
60
6-272500
ii
3-691165
61
6791157
ii
3-4I7749
61
6-288114
12
3-877987
62
6*807417
12
3-590732
62
6-303 1 70
13
4-051183
63
6-823102
13
3751098
63
6-317693
H
4-2I2I23
64
6-838233
14
3-900118
64
6-331703
15
4-362001
65
6-852833
15
4-038894
65
6-345221
16
4-501860
66
6-866923
1 6
4-168393
66
6-358268
17
4-632618
67
6-880525
17
4-289465
67
6-370862
18
4755083
68
6-893656
18
4-402858
68
6-383021
!9
4-869970
69
6-906337
19
4-509235
69
6-394762
20
4-9779I7
70
6-918584
20
4-609186
70
6-406102
21
5-079490
71
6-930414
21
4-703236
71
6-417056
22
5-I75I97
72
6-941843
22
4791854
72
6-427638
23
5-265494
73
6-952887
23
4-875462
73
6-437864
24
5-350792
74
6-963560
24
4-95444I
74
6-447746
2 5
5'43!45 8
75
6-973876
25
5-029132
75
6-457298
26
5-507829
76
6-983848
26
5-099847
76
6-466532
27
5-580208
77
6-993490
27
5-166864
77
6-475459
28
5-648869
78
7-0028I2
28
5-230439
78
6-484091
29
5-714066
79
7-011828
29
5-290807
79
6-492439
30
5-776027
80
7-020548
30
5-348178
80
6-500513
3 1
5-834962
81
7-028983
3i
5-402748
81
6-508323
32
5-891064
82
7*037143
32
5-454694
82
6-515879
33
5-944510
83
7-045037
33
5-504181
83
6-523188
34
5-995461
84
7-052676
34
5-55I357
84
6-530262
35
6-044068
85
7-060069
35
5-596364
85
6-537106
36
6-090469
86
7-067223
36
5-639328
86
6-54373I
37
6-134792
87
7-074148
37
5-680368
87
6-550143
38
6-177155
88
7-080851
38
5719593
88
6-556350
39
6-217669
89
7-087341
39
5-757106
89
6-562358
40
6-256435
90
7-093624
40
5793000
90
6-568176
41
6-293548
91
7-099707
41
5-827365
91
6-572809
42
6-329097
9 2
7-105598
42
5-860280
92
6-579254
43
6-363163
93
7-111302
43
5-891823
93
6-584545
44
6-395824
94
7-116828
44
5-922064
94
6-589661
45
6-427151
95
7-122179
45
5-951071
95
6-594616
46
6-457211
96
7-127362
46
5-978905
96
6-599415
47
6-486068
97
7-132383
47
6-005624
97
6-604065
48
6-513781
98
7-137247
48
6-031284
98
6-608568
49
6-540404
99
7-141960
49
6-055935
99
6-612931
50
6-565991
100
7-146526
50
6-079627
100
6-617160
CXXX1V
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 8 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
463194
51
5-650371
I
428882
51
5-231820
2
8/3628
52
5-670653
2
808914
52
5-250598
3
1-239681
53
5-690163
3
I-I47852
53
5-268663
4
1-568045
54
5-708937
4
1-451892
54
5-286047
5
1-864134
55
5-7270IO
5
1726048
55
5-302781
6
2-132371
56
57444II
6
1-974416
56
5-3I8893
7
2-376408
57
576II70
7
2-200375
57
5-3344II
8
2-599285
58
5777315
8
2-406742
58
5 g 349359
9
2-803554
59
5-792874
9
2-595881
59
5-363766
10
2-991374
60
5-807870
10
2-769788
60
5-37765I
ii
3-164582
61
5-822327
ii
2-930165
61
5-391038
12
3-32475I
62
5-836268
12
3-078470
62
5 ! 403945
13
3*473239
63
5-849715
13
3-215958
63
5-416396
H
3-611219
64
5-862687
H
33437I8
64
5-428408
15
3739716
65
5-875204
15
3-462696
65
5-439998
16
3-859623
66
5-887284
16
3-573721
66
5-451183
17
3-971726
67
5-898945
17
3-677520
67
5-461980
18
4-076720
68
5-910203
18
3774737
68
5-472404
19
4-I752I7
69
5-921075
19
3-865938
69
5-482471
20
4-267764
7O
5-93I575
20
3-951629
70
5-492193
21
4'354847
71
5-94I7I8
21
4-032261
71
5-50I584
22
4-436901
72
5-95I5I6
22
4-108237
72
5-510657
23
4-514316
73
5-960985
23
4-179918
73
5-519424
24
4-587445
74
5-970135
24
4-247629
74
5-527896
25
4-656603
75
5-978979
25
4-311665
75
5-536086
26
4722079
76
5-987529
26
4-372291
76
5-544002
27
4784132
77
5-995795
27
4-429747
77
5-551656
28
4-842999
78
6-003787
28
4-484253
78
5-559056
29
4-898894
79
6-011517
29
4-536008
79
5-566213
30
4-952016
80
6-018993
30
4-585195
80
5-573I35
31
5-002544
81
6-026224
31
4-631980
Bi
5-57983I
32
5-050642
82
6-033220
32
4-676515
82
5-586309
33
5-096463
83
6-039988
33
4-718942
83
5-592576
34
5-140145
84
6-046538
34
4759388
84
5-598640
35
5-l8l8l8
85
6-052875
35
4797974
85
5 -604508
36
5-22I599
86
6-059009
36
4-834809
86
5-610188
37
5^59599
87
6-064946
37
4-869994
87
5-615685
38
5-295919
88
6-070693
38
4-903623
88
5-621006
39
5330653
89
6-076257
39
4'935784
89
5-626158
40
5-363888
90
6-081644
4O
4-966558
90
5-631145
41
5-395707
91
6-086859
41
4-996020
91
5-635974
42
5-426184
92
6-091910
42
5-024239
92
5-640651
43
5-455390
93
6-096800
43
5-051282
93
5-645179
44
5-483392
94
6-101537
44
5-077209
94
5-649565
4 I
5-5I0250
95
6-106125
45
5-102077
95
5-653813
46
5-536022
96
6-110569
46
5-125941
96
5-657928
47
5-560762
97
6*114874
47
5-148848
97
5-661914
48
5-584522
98
6-119044
48
5-170848
98
5-665775
49
5-607347
99
6-123084
49
5-191982
99
5-669516
SO
5-629283
100
6-126999
50
5-212293
100
5-673141
TABLE X.
cxxxv
Present Value (or Years' Purchase) of 1 per Annum in n years, atter
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 10 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
826446
51
8-376107
I
75I3I5
51
7-614643
2
1-534044
52
8-400615
2
I-394585
52
7-636923
3
2-146460
53
8-424161
3
1-951327
53
7-658329
4
2-681470
54
8-446792
4
2-437700
54
7-678902
5
3-152684
55
8-468549
5
2-866077
55
7-698681
6
3-570698
56
8-489475
6
3-246090
56
7717693
7
3-943887
57
8-509606
7
3-58535I
57
7-736005
8
4-278953
58
8-528979
8
3-889957
58
7753617
9
4-581330
59
8-547628
9
4-164845
59
7770571
10
4-855464
60
8-565585
10
4-414058
60
7-786896
ii
5-105031
61
8-582881
n
4-640937
61
7-802619
12
5-333097
62
8-599543
12
4-848270
62
7-817767
U
5-542239
63
8-615602
13
5^38399
63
7-832365
H
5'734636
64
8-631079
14
5-213306
64
7-846436
15
5-912149
65
8-646002
15
5374681
65
7-860002
16
6-076370
66
8-660392
1 6
5-523973
66
7-873084
i?
6-228675
67
8-674273
17
5-662432
67
7-885702
18
6-370256
68
8-687664
18
5-791142
68
7-897876
19
6-502151
69
8700585
19
5-911046
69
7-909623
20
6-625268
70
8-713056
20
6-022971
70
7-920960
21
6-740409
71
8-725095
21
6-127644
71
7-931905
22
6-848277
72
8736719
22
6-225706
72
7-942471
23
6-949498
73
8747943
23
6-317725
73
7-952675
24
7-044627
74
8758784
24
6-404206
74
7-962531
25
7-134(61
75
8-769256
25
6-485601
75
7-972051
26
7-218542
76
8779374
26
6-562311
76
7-981249
27
7-298171
77
8-789150
27
6-634701
77
7-990137
28
7-373405
78
8-798599
28
6703095
78
7-998726
2 9
7-444567
79
8-807731
29
6-767789
79
8-007029
30
7-511952
80
8-816560
30
6-829048
80
8-015055
31
7-575825
81
8-825096
31
6-887114
81
8-022815
32
7-636428
82
8-833350
32
6-942207
82
8-030318
33
7-693981
83
8-841332
33
6-994528
83
8-037575
34
7-748685
84
8-849053
34
7-044259
84
8-044593
35
7-800724
85
8-856521
35
7-091568
85
8-051383
36
7-850269
86
8-863746
36
7-136608
86
8-057951
37
7-897473
87
8-870736
37
7-I7952I
87
8-064306
38
7-942479
88
8-877500
38
7-220435
88
8-070455
39
7-985421
89
8-884046
39
7-259474
89
8-076405
40
8-026415
90
8-890381
40
7-296471
90
8-082165
41
8-065580
91
8-896513
41
7-332345
91
8-087739
42
8-103016
92
8-902449
42
7-366378
92
8-093136
43
8-138821
93
8-908196
43
7-398928
93
8-098360
44
8-173084
94
8-913759
44
7-430077
94
8-103418
45
8-205889
95
8-919146
45
7-459900
95
8-108315
46
8-237314
96
8-924363
46
7-488468
96
8-113057
47
8-267431
97
8-929415
47
7-515846
97
8-117650
48
8-296307
98
8-934308
48
7-542098
98
8-122098
49
8-324007
99
8-939047
49
7-567279
99
8-126406
50
8-350588 100
8-943637
so 7'59!444
100
8-130579
CXXXV1
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 10 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
I
683013
51
6-922402
I
620921
51
6-293093
2
1-267805
52
6-942657
2
1-152550
52
6-311507
3
1773934
53
6*962117
3
1-612667
53
6-329197
4
2-216091
54
6-980820
4
2*014628
54
6*346200
5
2-605524
55
6-998801
5
2-368658
55
6-362547
6
2-950990
56
7-016095
6
2-682719
56
6-378268
7
3-259410
57
7-032732
7
2-963100
57
6-393393
8
3-536325
58
7-048743
8
3-214841
58
6-407948
9
3786223
59
7-064155
9
3-44202I
59
6-421959
10
4-012780
60
7-078996
10
3-647982
60
6-43545I
ii
4-219034
61
7-093290
ii
3-835485
61
6-448446
12
4-407519
62
7-107061
12
4-006835
62
6-460964
13
4-580363
63
7-120332
13
4-163966
63
6-473029
14
4739369
64
7-I33I24
14
4-308517
64
6-484658
1|
4-886073
65
7-H5456
15
4-44I885
65
6-495869
16
5-02I794
66
7-I57349
16
4-565267
66
6-506681
17
5-147666
67
7-I68820
17
4-679696
67
6-517109
18
5-264674
68
7-I79887
18
4-786068
68
6-527170
19
5'373678
69
7-190566
19
4-885162
69
6-536879
20
S'475429
70
7-200873
20
4-977662
70
6-546248
21
5-570586
71
7-210823
21
5-064169
71
6-555293
22
5^59733
72
7-220429
22
5-I452I2
72
6-564026
23
5743386
73
7-229705
23
5-221260
73
6-572459
24
5-822006
74
7-238664
24
5-292733
74
6-580604
25
5-896001
75
7-247319
25
5-360001
75
6-588472
26
5-965738
76
7-25568I
26
5-423398
76
6-596073
27
6-031546
77
7-263761
27
5-483224
77
6-603419
28
6-093723
78
7-271569
28
5-539748
78
6-610518
29
6-152535
79
7-279117
29
5-5932I4
79
6-617379
30
6-208225
80
7-286413
30
5-643841
80
6-624012
31
6-261013
81
7-293468
31
5-691830
81
6-630425
32
6-311097
82
7-300289
32
5737361
82
6-636627
33
6-358662
83
7-306886
33
5780602
83
6*642624
34
6-403872
84
7-313267
34
5-821702
84
6-648424
35
6-446880
85
7-3I9439
35
5-860800
85
6-654035
36
6-487825
86
7-325410
36
5-898023
86
6-659463
37
6-526837
87
7-331187
37
5-933488
87
6-664715
38
6-564032
88
7-336777
38
5-967302
88
6-669797
39
6-599522
89
7-342187
39
5-999565
89
6-674715
40
6-633401
90
7-347422
40
6-030365
90
6-679475
41
6-665768
91
7-352490
41
6-059789
91
6-684082
42
6-696707
92
7357596
42
6-087916
92
6-688542
43
6-726298
93
7-362145
43
6-114817
93
6-692859
44
6754615
94
7366743
44
6-140559
94
6-697039
45
6781727
95
7-371196
45
6-165206
95
6-701087
46
6-807698
96
7-375507
46
6-188816
96
6-705006
47
6-832588
97
7-379682
47
6-211443
97
6-708802
48
6-856452
98
7-383726
48
6-233139
98
6-712478
49
6-879344
99
7-387642
49
6-253950
99
6-716038
50
6-901313
100
7-39H36
53
6-273920
100
6719487
TABLE X.
CXXXVll
Present Value (or Years' Purchase) of 1 per Annum in n years after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 10 per cent.
n
Yean,
Deferred 5 Years
n
Years
Deferred 5 Years
n
Years
Deferred 6 Years
n
Years
Deferred 6 Years
,
564474
51
5720994
I
5I3I58
51
5-200903
2
1-047772
52
5737733
2
952520
52
5-216121
3
1-466061
53
5-753816
3
I-332783
53
5-230741
4
1-831480
54
5769272
4
I '664982
54
5-244793
5
2-153326
55
5784133
5
1-957569
55
5-258303
6
2-438835
56
5798425
6
2-2I7I23
56
5-271296
7
2-693728
57
5-812175
7
2-448843
57
5-283796
8
2-922582
58
5-825407
8
2-656893
58
5-295825
9
3-129110
59
5-838145
9
2-844645
59
5-307404
10
3-3I6347
60
5-850410
10
3*014861
60
5-318555
ii
3-486805
61
5-862223
ii
3-169823
61
5-329294
12
3-642577
62
5-873604
12
3-3II434
62
5-339640
13
3785424
63
5-884572
!3
3-441294
63
5-349611
H
3-916834
64
5-895I43
H
3-560758
64
5-359221
15
4-038077
65
5-905336
15
3-670979
65
5-368487
16
4-150243
66
5-915164
16
3772948
66
5-377422
17
4-254269
67
5-924645
17
3-867517
67
5-386041
18
4-350970
68
5-93379I
18
3-955428
68
5-394356
19
4-441056
69
5-942617
1 9
4-037324
69
5-402379
20
4-525148
70
5-95II35
20
4-II377I
70
5-410123
21
4-603790
71
5*959357
21
4-185264
71
5-417598
22
4-677465
72
5-967296
22
4-252241
72
5-424815
23
4746600
73
5-974963
23
4-315091
73
5-431784
24
4-811575
74
5-982367
24
4-374I59
74
5-438516
25
4*872728
75
5-989520
2 5
4-429753
75
5-445018 ,
26
4-930362
76
5-996430
26
4-482147
76
5-451300
27
4-984749
77
6-003108
27
4-53 1 59
77
5-457371
28
5-036135
78
6-009561
28
4-578304
78
5-463238
29
5-084740
79
6-015799
29
4-622491
79
5-468908
30
5-130765
80
6-021829
30
4-664331
80
5-474390
31
5-I7439I
81
6-027659
31
4-703991
81
5-479690
32
5-215783
82
6-033297
32
4741621
82
5-484815
33
5-255092
83
6-038749
33
4777357
83
5-489772
34
5-292456
84
6*044022
34
4-811324
84
5-494566
35
5-328000
85
6-049123
35
4-843636
85
5-499203
36
5-361839
86
6-054058
36
4-874399
86
5-503689
37
5-394080
87
6-058832
37
4-903709
87
5-508029
38
5-424820
88
6-063452
38
4-931655
88
5-512229
39
5'454I50
89
6-067923
39
4-958318
89
5-516294
40
5-482150
90
6-072250
40
4-983773
90
5-520227
41
5-508899
91
6-076438
4i
5-008090
91
5-524035
42
5-534469
92
6-080493
42
5-03I335
92
5-527721
43
5-558924
93
6-084417
43
5-053567
93
5-531289
44
5-582326
94
6-088218
44
5-074842
94
5-534743
45
5-604733
95
6-091897
45
5-095212
95
5-538088
46
5-626196
96
6-095460
46
5-114724
96
5-541327
47
5-646767
97
6-098911
47
5-I33424
97
5-544464
48
5 -666490
98
6-102252
48
5'i5!354
98
5-547502
49
5-685409
99
6-105489
49
5-168553
99
5-550445
50
5-703564 100
6-108625
50
5-185058
100
5-553295
d THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 12 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
j
797194
51
6-946476
I
7II780
51
6-2022 1 1
2,
I-457462
52
6-963631
2
1-301306
52
6-2I7528
3
2 '013069
53
6-980098
3
1797383
53
6-232230
4
2-486880
54
6-995910
4
2-220428
54
6-246349
5
2^95553
55
7'OHIOI
5
2-585316
55
6-259911
6
3-251512
56
7-025698
6
2-903136
56
6-272945
7
3-564210
57
7-039731
7
3-182330
57
6-285474
8
3-840966
58
7-053226
8
3-429434
58
6-297523
9
4-087540
59
7-066207
9
3-649589
59
6-309113
10
4-308522
60
7-078698
10
3-846894
60
6-320266
n
4-507616
61
7-090721
ii
4-024657
6l
6-33IOOI
12
4-687847
62
7'102297
12
4-185578
62
6-34I337
13
4-851705
63
7-113446
13
4-331880
63
6-351291
H
5-001263
64
7-124186
14
4-4654 1 3
64
6-360880
15
5-138256
65
7^34535
15
4-587728
65
6-370I20
16
5-264151
66
7-144509
16
4700135
66
6-379026
17
5-38oi 9 6
67
7-I54I25
17
4-803746
67
6-387611
18
5-487458
68
7-I63397
18
4-899516
68
6-395890
19
5-586856
69
7-172340
19
4-988264
69
6-403875
20
5-679185
70
7-180967
20
5-070701
70
6-4II577
21
5765138
71
7-189291
21
5'H7445
71
6-419009
22
5-845318
72
7-197324
22
5-219034
72
6-426182
23
5-923829
73
7-205078
23
5-289133
73
6-433106
24
5-990423
74
7-212564
24
5348592
74
6-439790
25
6-056230
75
7-219793
25
5'407349
75
6-446244
26
6-118046
76
7-226775
26
5-462541
76
6-452478
27
6-176198
77
7-2335I9
27
5-514462
77
6-458499
28
6-230979
78
7-240034
28
5-563374
78
6-464316
29
6-282653
79
- 7-246323
29
5-609511
79
6-469932
30
6-33H55
80
7-252412
30
5-653085
80
6-475368
31
6-377600
81
7-258292
31
5-694286
81
6-480618
32
6-421279
82
7-263976
! 32
5733285
82
6-485693
33
6-462668
83
7-269471
33
5770239
83
6-490600
34
6-501925
84
7-274785
i 34
5-805290
84
6-495344
35
6-539196
85
7-279923
35
5-838568
85
6-499932
36
6-574611
86
7-284893
i 36
5-870189
86
6-504369
37
6-608293
87
7-289700
37
5-900261
87
6-508661
38
6-640350
88
7-294350
38
5-928884
88
6-512813
39
6-670886
89
7-298849
39
5-956i49
89
6-516830
40
6-699994
90
7-303203
40
5-982138
90
6-520717
41
6727759
9 1
7-307416
41
6-006928
91
6-524478
42
6754262
92
7'3IH93
42
6-030591
92
6-528118
43
6-779574
93
.7-3I5439
43
6-053191
93
6-531642
44
6-803766
94
7-319259
44
6-074791
94
6-535052
45
6-826899
95
7-322957
45
6-095445
95
6-538354
46
6-849032
96
7-326537
46
6-115207
96
6-541551
47
6-870219
97
7-330003
47
6-134124
97
6-544646
48
6-890512
98
7333360
48
6-152242
98
6-547643
49
6-909956
99
7-336610
49
6-169604
99
6-550545
50
6-928597
100
7J39758
50
6-186248 100
6-553356
TABLE X.
cxli
Present Value (or Years' Purchase) of 1 per Annum in n years, after
years' Deterrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 12 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
j
635518
51
5-537688
I
567427
5"
4'944365
2
I*l6l88o
5 2
5-551364
2
I'037393
52
4-956575
3
1-604806
53
5-564491
3
1-432863
53
4-968296
4
1-982525
54
5-577097
4
I770II2
54
4-97955I
5
2-308317
55
5-589206
5
2-060998
55
4-990363
6
2-592086
56
5-600844
6
2-314362
56
5-000753
7
2-841366
57
5-612031
7
2-536934
57
5-010742
8
3-061995
58
5-622788
8
2733924
58
5-020347
9
3-258562
59
5-633I37
9
2-909430
59
5-029587
10
3-434727
60
5-643095
10
3-066721
60
5-038478
ii
3-593444
61
5-652680
ii
3-208432
6l
5-047035
12
3737I 2 3
62
5-661908
12
3-3367I7
62
5-055275
13
3-867750
63
5-670796
13
3-453348
63
5-063210
14
3-986976
64
5^79357
14
3-559800
64
5-070855
15
4-096186
65
5-687607
15
3-657309
65
5-078221
16
4-196549
66
5^95559
16
3-746919
66
5-085320
i?
4-289059
67
5-703224
17
3-829517
67
5-092165
18
4-374568
68
5-710616
18
3-905864
68
5-098764
1 9
4-453807
69
5717745
19
3-976614
69
5-105130
20
4-527412
70
5724623
20
4-042332
7O
5-III270
21
4'595933
71
5731258
21
4-I035II
71
5-II7I95
22
4-659852
72
5737663
22
4-160582
72
5-122913
2 3
4-722440
73
5-743844
2 3
4-216464
73
5-I28432
24
4775529
74
5749812
24
4-263865
74
5-133761
25
4-827990
75
5755575
25
4-310705
75
5-I38906
26
4-877269
76
5-761141
26
4-354704
76
5-143876
27
4-923627
77
5-766517
27
4-396096
77
5-148676
28
4-967298
78
5771711
28
4-435088
78
5-I533I3
29
5-008492
79
5776725
29
4-47 1 868
79
5-157790
30
5^47397
80
5781579
30
4-506605
80
5-162124
31
5-084184
81
5786266
31
4-539450
8l
5-166309
32
5-119004
82
5790797
32
4-570540
82
. 5-I70355
33
5-151999
83
5795178
33
4-599999
83
5-174266
34
5-183295
84
5-799414
34
4-627942
84
5-178048
35
5-213007
85
5-803510
35
4-654470
85
5-181706
36
5-241240
86
5-807472
36
4-679678
86
5-185243
37
5-268090
87
5-811304
37
4703652
87
5-188664
38
5-293647
88
5-815011
38
4-726470
O O
00
5-191974
39
5-317990
89
5-818598
39
4-748205
89
5-I95I77
40
5-34H94
9O
5-822069
40
4768923
90
5-198275
41
5-3633 2 9
9 1
5-825427
41
4788686
91
5-20I274
42
5-384456
9 2
5-828677
42
4-807550
92
5-204176
43
5-404635
93
5-831823
43
4-825567
93
5-206985
44
5-423920
94
5-834868
44
4-842786
94
5-209704
45
5-442362
95
5-837816
45
4-859252
95
5-2I2336
46
5 -460006
96
5-840670
46
4-875005
96
5-214884
47
5-476897
97
5-843434
47
4-890086
97
5-2I7352
48
5-493074
98
5-846110
48
4-904530
98
5-219741
49
5-508575
99
5-848701
49
4-918370
99
5-222054
50
5-523436
100
5-851211
50
4-931639
100
5-224295
cxlii
THE ENGINEERS VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Kedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 12 per cent.
n
Years
Deferred 5 Years
n
Years
Deferred 5 Years
n
1 Years
Deferred 6 Years
n
Years
Deferred Years
I
506631
51
4-414611
I
452349
51
3-941617
2
926244
52
4-4255t3
2
827003
52
3-95I35I
3
1-279342
53
4-435978
3
1-142269
53
3-960695
4
1-580457
54
4-446028
4
I-4III22
54
3-969667
5
1-840177
55
4-455681
5
1-643015
55
3-978287
6
2-066395
56
4-464958
6
1-844995
56
3-986570
7
2-265120
57
4-473876
7
2-022428
57
3-994532
8
; 2 -44 1 004
58
4-482453
8
2*179467
58
4-002190
9
^2-597706
59
4-490702
9
2-319380
59
4-009556
10
2-738143
60
4-498641
10
2-444771
60
4-016643
ii
2-864672
61
4-506282
n
2-557743
61
4-023466
12
2-979212
62
4-513638
12
2-6600IO
62
4-030034
13
3-083347
63
4-520724
13
2752988
63
4-036360
14
3-I78393
64
4-527549
H
2-837851
64
4-042454
15
3-265454
65
4-534126
15
2-915584
65
4-048327
16
3-345463
66
4-540465
16
2-987021
66
4-053986
17
3-419212
67
4-546576
17
3-052868
67
4-059442
18
3-487379
68
4-552468
18
3-II373I
68
4-064704
19
3-550548
69
4-558151
19
3-170132
69
4-069778
20
3-609225
70
4-563634
20
3-222522
70
4-074673
21
3-663849
71
4-568924
21
3-271294
71
4-079397
22
3-714805
72
4-574030
22
3-3I679I
72
4-083955
23
3-764700
73
4-578957
23
3361340
73
4-088355
24
3-807022
74
4-583715
24
3-399127
74
4-092603
25
3-848844
75
4-588309
25
3-436468
75
4-096705
26
3-888129
76
4-592746
26
3-47I543
76
4-I00666
27
3-925085
77
4-597032
27
3-504540
77
4-104493
28
3-9599oo
78
4-601172
28
3-535625
78
4-108190
29
3-992740
79
4-605170
2 9
3-564946
79
4-III759
30
4-023754
80
4-609039
30
3-592638
8O
4TI52I4
31
4-053080
81
4-612776
31
3-6l882I
81
4-118550
32
4-080839
82
4-616388
32
3-643606
82
4-I2I775
33
4-107142
83
4-619881
33
3-667091
83
4-124893
34
4-132091
84
4-623257
34
3-689367
84
4-127908
35
4-155777
85
4-626523
35
3710515
85
4-130824
36
4-178284
86
4-629681
36
3730611
86
4-133644
37
4-199689
87
4-632736
37
3749723
87
4-136372
38
4-220063
88
4-635691
38
37679U
88
4-I390IO
39
4-239469
89
4-63855I
39
3-785240
89
4-HI56i
40
4-257967
9O
4-641317
40
3-8oi757
90
4-144033
4i
4-275613
91
4-643995
41
3-817511
91
4-146424
42
4-292455
92
4-646586
42
3-832549
92
4-I48737
43
4-308542
93
4-649094
43
3-846913
93
4-150976
44
4-323916
94
4-651521
44
3-860639
94
4-I53H4
45
4-338618
95
4-653871
45
3-873766
95
4-155242
46
4-352683
96
4-656147
46
3-886324
96
4-I57274
47
4-366148
97
4-658350
47
3-898347
97
4-I5924I
48
4-379045
98
4-660483
48
3-909861
98
4-161145
49
4-391402
99
4-662548
49
3-920895
99
4-162990
50
4-403249
100
4-664549
50
3-93H72
100
4-164776
TABLE X.
cxliii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 12 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
I
403883
51
3-519301
I
360610
51
3-I42233
2.
738396
51
3-527992
2
'659282
52
3-149993
3
1-019883
53
3-536335
3
910610
53
3-I57442
4
1-259931
54
3-544346
4
1-124938
54
3-I64595
5
1-466978
55
3-552042
5
1-309801
55
3-171466
6
1-647317
56
3-559437
6
1-470819
56
3-178069
7
1-805740
57
3-566547
7
1-612267
57
3-184417
8
1-945953
58
3-573384
8
1737458
58
3-190521
9
2-070875
59
3-579960
9
I -848996
59
3-196393
10
2-182831
60
3-586289
10
1-948956
60
3*202044
ii
2-283699
61
3-592380
ii
2-039017
6l
3-207482
12
2-375009
6*2
3-598245
12
2-120544
62
3-212718
13
2-458025
63
3-603893
13
2-194665
63
3-217762
14
2*533795
64
3-609334
H
2-262317
64
3-222620
15
2-603200
65
3^14577
15
2-324286
65
3-22730I
16
2-666983
66
3-619631
16
2-381235
66
3-231813
17
2724775
67
3-624502
17
2-433727
67
3-236163
18
2780017
68
3-629200
18
2-482247
68
3-240357
19
2-830475
69
3'63373
19
2-527210
69
3-244402
20
2-877252
70
3-638101
20
2-568975
70
3 248305
21
2-920798
71
3-642318
21
2-607856
71
3-252070
22
2*961420
72
3-646388
22
2-644125
72
3-255704
23
3-001196
73
3-650317
23
2-679639
73
3-259211
24
3-034935
74
3-654110
24
2709763
74
3-262598
25
3-068275
75
3-657772
25
2739531
75
3-265868
26
3-099592
76
3-661309
26
2767493
76
3-269026
27
3-129054
77
3-664726
27
2-793798
77
3-272076
28
3-156808
78
3-668026
28
2-818579
78
3-275024
29
3-182987
79
3-671213
29
2-841953
79
3-277869
30
3-2077I2
80
3-674298
30
2-864029
80
3-280623
31
3'23I09I
81
3-677277
31
2-884902
81
3-283283
33
3-253220
82
3-680156
32
2-904661
82
3-285854
33
3-274189
83
3-682941
33
2-923383
83
3-288340
34
3-294078
84
3-685632
34
2-941141
84
3-290743
35
3-312960
85
3-688236
35
2-958000
85
3-293068
36
3-330903
86
3-690754
36
2-974020
86
3-295316
37
3-347967
87
3-693189
37
2-989256
87
3-297490
38
3-364208
88
3-695545
38
3-003757
88
3-299594
39
3-379679
89
3-697824
39
3-017570
89
3-301629
40
3-394426
90
3-700030
4O
3-030737
90
3-303598
41
3-408492
91
3-702164
41
3-043297
91
3-305504
42
3-421919
92
3-704230
42
3-055285
92
3-307348
43
3'434743
93
3-706229
43
3-066735
93
3-309I33
44
3-447000
94
3-708164
44
3-077678
94
3-310861
45
3-4587I9
95
3-710038
45
3-088142
95
3'3 T 2534
46
3-469933
96
3-711852
46
3-098154
96
3-3I4I53
47
3-480667
97
3-713608
47
3-107738
97
3-315721
48
3-490948
98
3-715308
48
3-II69I7
98
3-317240
49
3-500799
99
3-716955
49
3-125713
99
3-318710
50
3-5I0243
1OO
3-718550
50
3" J 34H6
100
3-320134
cxliv
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years after
t years' Deterrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 12 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
fears
Deferred 10 Years
n
Years
Deferred 10 Years
I
321973
51
2-805565
I
287476
51
2-504969
2
588645
52
2-812494
2
-525575
52
2-511155
3
813045
53
2-819144
3
725933
53
2-517093
4
I '004409
54
2-825531
4
896794
54
2-522795
5
1-169465
55
2-831666
5
1-044166
55
2-528273
6
1-313231
56
2-837562
6
1-172528
56
2-533537
7
I-439524
57
2-843229
7
1-285290
57
2-538598
8
I-55I302
58
2-848680
8
1-385091
58
2-543464
9
1-650889
59
2-853923
9
I -474008
59
2-548145
10
1-740140
60
2-858968
10
1-553696
60
2-552650
ii
1-820551
61
2-863823
ii
1-625492
61
2-556985
12
I-893343
62
2-868499
12
1-690485
62
2-561160
13
r959522
63
2-873002
13
1-749574
63
2-565180
14
2-019926
64
2-877339
H
1-803506
64
2-569053
15
2-075255
65
2-881519
15
1-852907
65
2-572785
16
2-I26I02
66
2-885547
16
1-898306
66
2-576382
17
2-172971
67
2-889431
17
1-940153
67
2-579849
18
2-216292
68
2-893176
18
1-978832
68
2-583193
19
2-256437
69
2-896788
19
2-014676
69
2-586418
20
2-293728
70
2-900272
20
2-047971
70
2-589529
21
2-328443
71
2-963633
21
2-078967
71
2-592530
22
2-360826
72
2-906878
22
2-107880
72
2-595427
23
2-392535
73
2-9IOOIO
23
2-136192
73
2-598223
24
2-419432
74
2-913034
24
2-160206
74
2-600923
25
2-446010
75
2-915954
25
2-183937
75
2-603530
26
2-470976
76
2-918773
26
2-206229
76
2-606047
27
2-494463
77
2-921497
27
2-227199
77
2-608479
28
2-516588
78
2-924128
28
2-246954
78
2-610829
29
2-537458
79
2-926669
29
2-265588
79
2*613097
30
2-557169
80
2-929128
30
2-283186
80
2-615293
31
2-575806
81
2-931503
31
2-299826
81
2-617413
32
2-593447
82
2.933798
32
2-315578
82
2-619463
33
2-610163
83
2-936018
33
2'3353
83
2-621444
34
2-626019
84
2-938164
34
2-344659
84
2-623360
35
2-641071
85
2-940239
35
2-358100
85
2-625213
36
2-655375
86
2-942246
36
2-370871
86
2-627005
37
2-668979
87
2-944188
37
2-383017
87
2-628739
38
2-681926
88
2-946066
38
2-394577
88
2-630416
39
2-694259
89
2-947883
39
2-405589
89
2-632038
40
2-706015
90
2-949641
40
2-416085
90
2-633608
41
2-717229
91
2-95I343
41
2-426097
9 1
2-635127
42
2727933
9 2
2-952989
42
2-435654
92
2-636598
43
2738156
93
2-954583
43
2-444783
93
2-638021
44
2-747927
94
2-956126
44
2-453506
94
2-639398
45
2757270
95
2-957619
45
2-461848
95
2-640732
46
2766209
96
2-959065
46
2-469829
96
3-642023
47
2-774766
97
2-960465
47
2-477470
97
2-643273
48
2*782962
98
2-961821
48
2-484788
98
2-644483
49
2-790816
99
2-963134
49
2-491800
99
2-645655
50
2-798344
100
2-964405
so
2-498522
100
2-646791
TABLE X.
cxlv
Present Value (or Years' Purchase) of .1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 15 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
I
756144
51
5-485046
I
657516
51
4-769605
2
1-353176
52
5-496023
2
1-176674
52
4779150
3
I-836345
53
5-506550
3
1-596822
53
4788304
4
2-235231
54
5-516651
4
1-943679
54
4797087
5
2-569982
55
5-526345
5
2-234767
55
4-805517
6
2-854801
56
5'535654
6
2-482436
56
4-813612
7
3-099984
57
5-544596
7
2-695638
57
4-821387
8
3-313180
58
5-553I88
8
2-88I026
58
4-828859
9
3-500188
59
5-561448
9
3-043642
59
4-836041
10
3-665487
60
5-569390
10
3-187380
60
4-842947
ii
3-812588
61
5-577029
ii
3'3I5293
61
4-849590
12
3-944285
62
5-584380
12
3-429813
62
4-855982
13
4-062828
63
5-59*455
13
3-532894
63
4-862134
H
4-170050
64
5-598266
14
3-626130
64
4-868057
15
4-267458
65
5-604826
15
3710833
65
4-873761
16
4-356303
66
5-611145
16
3-788089
66
4^79256
17
4'437632
67
5-617233
17
3-858810
67
4-884550
18
4-512330
68
5-623101
18
3-923765
68
4-889653
19
4-581147
69
5-628758
19
3-983606
69
4-894572
20
4-644724
70
5-634212
20
4-038890
70
4-8993I5
21
4-703613
71
5-639473
21
4-090098
71
4-903889
22
4-758291
72
5-644547
22
4-I37644
72
4-908301
23
4-809173
73
5-649443
23
4-181889
73
4-912559
34
4-856620
74
5-654168
24
4-223148
74
4-916667
25
4-900951
75
5-658729
25
4-261696
75
4-920633
26
4-942445
76
5-663131
26
4-297778
76
4-924462
27
4-981349
77
5-667383
27
4-331608
77
4-928158
28
5-017884
78
5-671488
28
4-363377
78
4-931729
29
5-052244
79
5-675454
29
4393255
79
4-935I77
30
5-084605
80
5-679285
30
4'42I395
80
4-938509
31
5-115122
81
5-682987
31
4-447932
81
4-941728
32
5-H3938
82
5-686564
32
4-472989
82
4-944838
33
5-171178
83
5-690022
33
4-496676
83
4-947845
34
5-196959
84
5-693364
34
4-519094
84
4-950751
35
5-221382
85
5-696595
35
4-540332
85
4-953560
36
5-244544
86
5-699719
36
4-560473
86
4-956277
37
5-266530
87
5-702740
37
4-57959I
87
4-958904
38
5-287418
88
5-705662
38
4-597755
88
4-961445
39
5-307281
89
5-708488
39
4-615026
89
4-963902
40
5-326183
90
5-711222
40
4-631463
90
4-966280
41
5-344186
91
5-713867
4i
4-647117
9 1
4-968580
42
5'36i344
92
5716426
42
4-662038
92
4-970805
43
5-377708
93
5718903
43
4-676268
93
4-972959
44
5-393327
94
5721300
44
4-689849
94
4-975043
45
5-408243
95
5723619
45
4-702820
95
4-977060
46
5-422497
96
5725865
46
47I52I4
96
4-979012
47
5-436125
97
5728039
47
4-727065
97
4-980903
48
5'449 T 63
98
5730143
48
4-738402
98
4-982733
49
5-461643
99
5732181
49
4-749254
99
4-984505
50
5-473595
100
5734154
50
4-759647
100
4-986220
cxlvi
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 15 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years years
Deferred 4 Years
I
571753
51
4-147482
I
497177
51
3-606506
2
I-023I95
52
4-I55783
2
88 9 735
52
3-613724
3
1-388541
53
4-I63743
3
I-207427
53
3-620646
4
1-690156
54
4-171380
4
1-469701
54
3-627287
5
1-943276
55
4-178711
5
I -689805
55
3-633661
6
2-158640
56
4-185749
6
1-877078
56
3-639782
7
2'344033
57
4-192511
7
2*038290
57
3-645661
8
2*505240
58
4-199008
8
2-178470
58
3-651311
9
2-646645
59
4-205253
9
2-301430
59
3-656742
10
2771634
60
4-211258
10
2-4IOII7
60
3-661964
1 1
2-882864
61
4-217035
ii
2-506838
61
3-666987
12
2-982446
62
4-222593
J2
2-59343I
62
3-671820
13
3-072082
63
4-227943
13
2-671375
63
3-676472
14
3-I53I57
64
4-233093
14
2741875
64
3-680951
IS
3-2268II
65
4-238053
15
2-805923
65
3-685264
16
3-293990
66
4-242831
16
2-864340
66
3-689419
17
3-355487
67
4-247435
17
2-917815
67
3-693422
18
3-411970
68
4-251872
18
2-966930
68
3-697280
19
3-464005
69
4-256149
19
3-012178
69
3700999
20
3-512078
70
4-260273
20
3-053981
70
3-704586
21
3-556607
71
4-264251
21
3-092702
71
3-708044
22
3-59795I
72
4-268088
22
3-128653
72
3711380
23
3-636425
73
4-271790
23
3-162109
73
3-714600
24
3-672302
74
4-275363
24
3-193306
74
3-717707
25
3705823
75
4-278811
25
3-222455
75
3-720706
26
3737198
76
4-282141
26
3-249737
76
3723601
27
3766615
77
4-285355
27
3-275318
77
3-726396
28
3-794241
78
4-288460
28
3-299340
78
3729095
29
3-820222
79
4-291458
29
3-321932
79
3731703
30
3-844691
80
4^94355
3O
3-3432IO
80
3734222
31
3-867767
81
4-297154
31
. 3-363276
81
3736656
32
3-889556
82
4-299859
32
3-382222
82
3739008
33
3-910153
83
4-302474
33
3-400I33
83
374I28I
34
3-929647
84
4-305001
34
3-417084
84
3743479
35
3-948115
85
4-307444
35
3*433*43
85
3-745603
36
3-965628
86
4-309806
36
3-448373
86
3747657
37
3-982253
87
4-312090
37
3-462829
87
3-749644
38
3-998047
88
4-314300
38
3H76563
88
3751565
39
4-013066
89
4'3l6437
39
3-489623
89
3753423
40
4-027359
90
4-318504
4O
3-502051
90
3755221
4i
4-040972
91
4-320504
41
3-513888
91
3756960
42
4-053946
92
4-322439
42
3-525170
92
3758643
43
4-066320
93
4-324312
43
3-535930
93
3-760271
44
4-078130
94
4-326124
44
3-546200
94
3761847
45
4-089408
95
4-327878
45
3-556007
95
3763372
46
4TOOI86
96
4-329576
46
3^65379
96
3-764849
47
4-110491
97
4-33I220
47
3-574340
97
3-766278
48
4-120350
98
4-332811
48
3-582913
98
3-767662
49
4-129786
99
4-334352
49
3-59III9
99
3-769002
50
4-I38823
100
4-335 8 44
50
3-598977
100
3-770299
TABLE X.
cxlvii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 15 per cent.
n
Years
Deferred 5 Years
n
Years
Deferred 5 Years
n
Years
Deferred 6 Years ^
Deferred 6 Years
I
432328
51
3-136093
I
'375937
51
2727037
2
773682
52
3-142369
2
672767
52
2732495
3
1-049936
53
3-148388
3
912988
53
2737729
4
I -278000
54
3-I54I63
4
1-111305
54
2742750
5
1-469396
55
3-159706
5
1-277735
55
2747570
6
1-632242
56
3-165028
6
1-419341
56
2752198
7
1772426
57
3-170140
7
1-541240
57
2756644
8
1-894321
58
3-I75053
8
1-647236
58
2760916
9
2-001244
59
3-I79775
9
1740212
59
2*765022
10
2-095754
60
3-184316
10
1-822395
60
2-768971
ii
2-179859
61
3-188684
ii
1-895530
6]
2-772769
12
2-255158
62
3-192887
12
1-961007
62
2-776423
13
2*322935
63
3-196932
13
2-019944
63
2779941
14
2-384240
64
3-200827
H
2-073252
64
2783328
15
2-439933
65
3-204577
15
2-121681
65
2786589
16
2-490730
66
3-208190
16
2-165852
66
2789730
I?
2-537231
67
3-2II67I
17
2-206287
67
2792758
18
2-579939
68
3-215026
18
2-243425
68
2795675
19
2-619285
69
3-218260
19
2-277640
69
2798487
20
2-655636
70
3-22I379
20
2-309249
70
-2-801199
21
2-689306
71
3-224386
21
2-338527
71
2-803814
22
2720568
72
3-227288
22
2-365711
72
2-806337
23
2749660
73
3-230087
23
2-391009
73
2-808771
24
2776788
74
3-232789
24
2-414598
74
2-8III2I
25
2-802134
75
3-235396
25
2-436639
75
2-813388
26
2-825859
76
3-237914
26
2-457268
76
2-8I5577
27
2-848102
77
3-240344
27
2-476611
77
2*81769 1
28
2-868991
78
3-242692
28
2-494775
78
2-8I9732
29
2-888637
79
3-244959
29
2-511858
79
2-821704
30
2-907139
80
3-247150
30
2-527947
80
2-823608
31
2-924587
81
3-249266
31
2-543120
8l
2-825449
32
2-941063
82
3-251311
32
2-557446
82
2-827227
33
2-956638
83
3-253288
33
2-570989
83
2-828946
34
2-971378
84
3-255199
34
2-583807
8 4
2-830608
35
2-985342
85
3-257046
35
2-595950
85
2-8322I4
36
2-998585
86
3-258833
36
2-607465
86
2-833767
37
3-OIII55
87
3-260560
37
2-618396
87
2-835269
3B
3-023098
88
3-262230
38
2-628781
88
2-836722
39
3-034455
89
3-263846
39
2-638656
89
2-838127
40
3-045262
90
3-265409
40
2-648054
90
2-839486
41
3-055555
91
3-266922
4i
2-657004
91
2-840802
42
3-065365
92
3-268385
42
2-665535
92
2-842074
43
3-074722
93
3-2698,0!
43
2-673671
93
2'843305
44
3-083652
94
3-271171
44
2-681437
94
2-844497
45
3-092180
95
3-272498
45
2-688852
95
2-845650
46
3-100330
96
3-273782
46
2-695939
96
2-846767
47
3-108122
97
3-275024
47
2702715
97
2-847847
48
3-115576
98
3-276228
48
2709197
98
2-848894
49 3-122712
99
3-277393
49
2715402
99
2-849907
50 3-I29545
100
3-278521
SO
2721341
100
2-850888
cxlviii
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 15 per cent.
n
Years
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Year?
Deferred 8 Years
I
326902
51
2-371336
I
284262
51
2-062032
2
585015
52
2-376082
2
508709
52
2-066158
3
793903
53
2-380634
3
690350
53
2-070II6
4
966352
54
2-385000
4
840306
54
2-073913
5
I-III075
55
2-389191
5
966151
55
2-077558
6
1-234209
56
2-393216
6
1-073225
56
2-081057
7
I -340209
57
2-397082
7
1-165399
57
2-084419
8
I-432379
58
2-400796
8
1-245547
58
2-087649
9
i '5 1 3228
59
2-404367
9
1-315850
59
2-090754
10
1-584691
60
2-40780!
10
1-377992
60
2-093740
ii
i -648287
61
2-4III06
ii
I '433293
61
2-096612
12
1-705223
62
2-414281
12
I -482803
62
2-099375
13
1756473
63
2-417340
13
1-527368
63
2-102035
H
1-802828
64
2-420285
14
1-567676
64
2-104595
15
1-844940
65
2-423121
15
I -604295
65
2-107062
16
1-883350
66
2-425853
16
1-637695
66
2-109437
17
1-918511
67
2-428485
17
I -668270
67
2-III726
18
i -950805
68
2*431022
18
1-696352
68
2-II3932
19
1-980556
69
2-433467
19
1722223
69
2-116058
20
2-008042
70
2-435825
20
1746124
70
2-Il8l09
21
2-033502
71
2-438099
21
1768262
71
2-I20086
22
2-057140
72
2-440293
22
1788818
72
2*121994
23
2-079138
73
2-442410
23
I -807946
73
2-123835
24
2-099651
74
2-444453
24
1-825783
74
2-125611
25
2-118816
75
2-446424
25
I -842449
75
2-127325
26
2-136755
76
2-448328
26
1-858048
76
2-128981
27
.2-153575
77
2-450166
27
1-872674
77
2-130579
28
2-169369
78
2-451941
28
1-886408
78
2-I32I22
29
2-184224
79
2-453655
29
1-899325
79
2-133613
30
2-198215
80
2-455312
30
I-9II49I
80
2-135054
31
2-211408
Si
2-456912
31
I -922964
81
2-136445
32
2-223866
82
2-458458
32
1-933797
82
2-137790
33
2-235643
83
2-459953
33
I -944037
83
2-139090
34
2-246788
84
2-461398
34
1-953729
84
2-140346
35
2-257347
85
2-462795
35
1-962911
85
2-141561
36
2-267361
86
2-464146
36
1-971618
86
2-142735
37
2-276866
87
2-465452
37
1-979883
87
2-143871
38
2-285897
88
2-466715
! 38
1-987736
88
2-144969
39
2-294484
89
2-467937
39
1-995203
89
2*146032
40
2-302656
90
2-469119
40
2-002309
90
2*147060
41
2-310439
91
2-470262
4i
2-009077
91
2-148054
42
2-317857
92
2-471369
42
2-015527
9 2
2-149016
43
2-324932
93
2-472439
43
2-02l68o
93
2-149947
44
2-331684
94
2-473475
44
2-02755I
94
2-150848
45
2-338132
95
2-474478
45
2-033159
95
2'I5I720
46
2-344295
96
2-475449
46
2-038517
96
2-152564
47
2-350187
97
2-476389
47
2-043641
97
2-153382
48
2-355823
98
2-477299
48
2-048542
98
2-I54173
49
2-361219
99
2-478180
49
2-053234
99
2-154939
50
2-366386
100 2-479033
SO
2-057727 jioo
2-155681
TABLE X.
cxlix
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Eedemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 15 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
247185
51
1793071
I
214943
51
I-559I92
2
442355
52
1 796660
2
384657
52
1-562313
3
600305
53
I -800IOI
3
522004
53
I'565305
4
730701
54
I '803403
4
635392
54
1-568176
5
840132
55
1-806572
5
730549
55
1-570932
6
933239
56
1-809615
6
811513
56
I-573578
7
1-013390
57
1-812538
7
881209
57
1-576120
8
I -083084
58
1-815347
8
941813
58
1-578563
9
I-I442I8
59
1-818046
9
994972
59
1-580910
10
1-198254
6O
I '820643
10
1-041960
60
1-583168
ii
1-246342
61
1-823141
ii
1-083775
61
1-585340
12
1-289394
62
1-825543
12
I-I2I2I2
62
1-587429
13
1-328146
63
1-827856
13
I-I54909
63
1-589440
14
1-363197
64
1-830083
14
1-185388
64
1-591377
15
I-395039
65
1-832227
15
1-213078
65
1-593241
16
i -424083
66
1-834293
16
I-238333
66
1-595037
17
i -450670
67
1-836283
17
1-261452
67
I -596768
18
1-475089
68
1-838202
18
I-282686
68
1-598436
!9
1-497585
69
I -84005 1
19
1-302248
69
I '600044
20
1-518368
70
1-841834
20
I -320320
70
1-601595
21
1-537619
71
I'843553
21
I -337060
71
I '603090
22
i'555494
72
1-845212
22
1-352603
72
1-604532
23
1-572128
73
1-846813
23
1-367067
73
I -605924
24
1-587638
74
1-848357
24
1-380554
74
1-607267
25
1-602129
75
1-849848
25
I-393I56
75
I -608564
26
1-615694
76
1-851288
26
1-404951
76
1-609815
27
1-628412
77
1-852677
27
I-4I60IO
77
. I-6II024
28
1-640355
78
1-854019
28
I -426396
78
I-6I2I9I
29
1-651587
79
1-855316
29
1-436163
79
1-613318
30
1-662166
80
1-856568
30
I-445362
80
1-614407
3 1
1-672142
81
I-857778
31
I-454037
81
1-615460
32
1-681562
82
1-858948
32
1-462228
82
1-616476
33
i -690467
83
I-860078
33
1-469972
83
1-617459
34
1-698895
84
r86n7I
34
I-477300
84
1-618409
35
1 706879
85
I-862227
35
1-484243
85
1-619328
36
1-714451
86
1-863248
36
I -490827
86
I-6202I6
37
1-721638
87
1-864236
37
I-497076
87
I-62I075
38
1-728466
88
1-865191
38
1-503014
88
1-621905
39
1734959
89
r866ll5
39
I -508660
89
1-622708
40
1-741138
90
1-867008
40
1-514034
90
I -623486
41
1-747024
9 1
1-867873
41
I-5I9I5I
91
1-624237
42
1752633
9 2
1-868710
42
1-524028
92
I -624965
43
1757983
93
1-869519
43
I-528680
93
1-625669
44
1-763088
94
I -870303
44
I-533I20
94
1-626350
45
i -767964
95
1-871061
45
1-537360
95
I-6270IO
46
1-772624
96
1-871795
46
I-54I4I2
96
1-627648
47
1-777079
97
1-872506
47
I-545286
97
1-628266
48
1-781341
98
1-873194
48
I -548992
98
1-628864
49
1-785421
99
1-873860
49
I-552540
99
I -629443
50
1789328
100 1-874505
J50
1-555937
100
I '630004
1 THE ENGINEEE'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent,, with Interest
allowed to a Purchaser at 18 per cent.
n
Years
Deferred 1 Year
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years y^
Deferred 2 Years
I
718184
51
4-494990
I
608631
5i
3-8093I3
2
1-259952
52
4-502552
2
1-067756
52
3-815722
3
1-683032
53
4-509799
3
1-426298
53
3-821864
4
2-02244I
54
4-516749
4
I7I3933
54
3-827753
5
2-300657
55
4-5234I5
5
I-9497IO
55
3-833403
6
2-532767
56
4-529813
6
2-146413
56
3-838824
7
2729276
57
4-535955
7
2-312946
57
3-844030
8
2-897723
58
4-541854
8
2-455698
58
3-849029
9
3-043659
59
4-547522
9
2-579372
59
3-853832
10
3-I7I26I
60
4-552969
10
2-687509
60
3-858448
ii
3-283734
61
4-558207
ii
2782825
61
3-862887
12
3-383577
62
4-563244
12
2-867438
62
3-867156
13
3-472777
63
4-568091
13
2-943022
63
3-871263
H
3-552889
64
4-572755
H
3-010923
64
3-875216
15
3-625230
65
4-577244
15
3-072229
65
3-879021
16
3-690843
66
4-581568 '
16
3-I27833
66
3-882685
17
3-750600
67
4-585732
17
3-178475
67
3-886214
18
3-805229
68
4-589744
18
3-224770
68
3-889614
19
3'855342
69
4-593610
!9
3^67239
69
3-892890
20
3-901456
70
4-597337
20
3-3063I9
70
3-896048
21
3-944016
71
4-600930
21
3-342386
71
3-899094
22
3-983398
72
4-604396
22
3-37576I
72
3-902030
23
4-019932
73
4-607738
23
3-406722
73
3-904863
24
4-05390!
74
4-610963
24
3'4355 10
74
3-907595
25
4-085553
75
4-614074
25
3-462333
75
3-910232
26
4-II5I05
76
4-617078
26
3-487377
76
3-912778
27
4-142746
77
4-619977
27
3-510802
77
3-9I5235
28
4-168647
78
4-622776
28
3-53275I
78
3-917607
29
4-I92955
79
4-625479
2 9
3-55335I
79
3-919898
30
4-215803
80
4-628090
30
3-5727I5
80
3-922110
31
4-23731!
81
4-630612
31
3-590941
81
3-924247
32
4-257584
82
4-633049
32
3-608122
82
3-926313
33
4-276717
83
4-635403
33
3-624336
83
3-928308
34
4-294796
84
4-637679
34
3-639658
84
3-930237 -
35
4-311899
85
4-639879
35
3-654152
85
3-93210!
36
4-328096
86
4-642005
36
3-667878
86
3-933903
37
4-343450
87
4-644061
37
3-680890
87
3'935 6 45
38
4-358020
88
4-646049
38
3-693237
88
3-937330
39
4-37I857
89
4^47972
39
3-704964
89
3-938959
40
4-385011
90
4-64983!
40
3716111
90
3-940535
41
4-397525
91
4-651630
41
3726716
91
3-942060
42
4-409440
92
4-65337I
42
3736813
9 2
3*943534
43
4-420793
93
4-655054
43
3-746435
93
3-944961
44
4-431618
94
4-656684
44
3755608
94
3-946342
45
4-441947
95
4-658260
45
3764362
95
3-947678
46
4-451809
96
4-659786
46
3772719
96
3-948972
47
4-461231
97
4-661264
47
3-780704
97
3-950223
48
4-470237
98
4-662694
48
3788337
98
3'95 H35
49
4-478852
99
4-664078
49
3-795637.
99
3-9152608
50
4-487096 100
4-665418
50
3-802624
100
3-953744
TABLE X.
cli
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 18 per cent.
Years' Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
j
515789
51
3-228232
I
437109
51
2735790
2
904878
5 2
3-233663
2
766846
5 2
2-740392
3
1-208727
53
3-238868
3
1-024345
53
2-744803
4
1-452486
54
3-243859
4
1-230920
54
2749033
5
1-652296
55
3-248646
5
1-400251
55
2753090
6
1-818994
56
3-25324I
6
I-54I520
56
2756984
7
1-961024
57
3-257652
7
I -66II22
57
2760722
8
2-081100
58
3-261889
8
1763644
58
2764313
9
2-185908
59
3-265959
9
1-852465
59
2767762
10
2-277550
60
3-269872
10
I-930I27
60
2771078
ii
2-358326
61
3-273633
ii
1-998582
61
2774265
12
2-430032
62
3-277251
12
2-059349
62
2777331
13
2-494087
63
3-280731
13
2' 1 1 3633
63
2780281
14
2-551630
64
3-284081
H
2*162398
64
2783120
15
2-603584
65
3-287306
15
2'206427
65
2785852
16
2-650706
66
3-290411
16
2*246361
66
2788484
17
2-693623
67
3-293401
17
2-28273I
'67
2791018
18
2-732856
68
3-296283
18
2*315980
68
2-793460
19
2-768846
69
3-299059
19
2-346480
69
2795813
20
2-801965
70
3-301736
zo
2-374547
70
2798081
21
2-832531
71
3-304317
21
2-400450
71
2-800268
22
2-860815
72
3-306805
22
2-424419
72
2-802377
23
2-887053
73
3-309206
23
2-446655
73
2-804412
24
2-911449
74
3-3II522
24
2-467330
74
2-806374
25
2-934181
75
3-3I3756
25
2-486594
75
2-808268
26
2-955404
76
3-3I59I3
26
2-504580
76
2-810096
27
2-975256
77
3317995
27
2-521403
77
2-811861
28
2-993857
78
3-320006
28
2-537167
78
2-813564.
29
3-011315
79
3-32I947
29
2-551962
79
2-815209
30
3-027724
8O
3-323822
3O
2-565868
80
2-816798
31
3-043171
81
3-325633
31
2-578958
81
2-818333
32
3-057730
82
3-327383
32
2-59I297
82
2-819817
33
3-071471
83
3-329075
33
2-602942
83
2-821250
34
3-084456
84
3-330709
34
2*613946
84
2-822635
35
3-096739
85
3-332289
35
2-624355
85
2-823973
36
3-108371
86
3-3338I6
36
2-6342I3
86
2-825268
37
3-119398
87
3335292
37
2-643558
87
2-826519
38
3-129862
oo
oo
3-336720
38
2-652425
88
2-827729
39
3-139800
89
3-338IOI
39
2-660847
89
2-828899
40
3-149247
90
3-339437
40
2-668853
90
2-830031
4i
3-158234
91
3-340728
4i
2-676469
91
2-831126
42
3-166791
92
3'34I978
42
2-683721
92
2-832185
43
3" 1 74945
93
3-343I88
43
2-690631
93
2-833210
44
3-182719
94
3-344358
44
2-697220
94
2-834201
45
3-190137
95
3-345490
45
2-703506
95
2-835161
46
3-197220
96
3-346586
46
2709508
96
2-836090
47
3-203986
97
3-347647
47
2-715243
97
2-836989
48
3-210455
98
3-348674
48
2-720724
98
2-837859
49
3-216642
99
3-349668
49
2725968
99
2-838702
50
3-222563
100
3-35063I
SO
2-730985
100
2-839517
clii
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 18 per cent.
n
Years
Deferred 5 Years years
Deferred 5 Years
n
Years
Deferred 6 Years
n
Years
Deferred 6 Years
I
370432
51
2-318466
!
313925
51
I -964802
2
649869
5 2
2-322366
2
550737
52
1-968107
3
868089
53
2-326104
3
735669
53
I-97I275
4
1*043! 53
54
2-329689
4
884028
54
I-9743I3
5
1-186653
55
2-333127
5
1*005639
55
I-977226
6
I-306373
56
2-336427
6
1-107096
56
I -980023
7
1-407730
57
2*339595
7
1-192992
57
1-982708
8
1-494613
58
2-342638
8
I-26662I
58
1-985286
9
1-569885
59
2-345561
9
I-3304II
59
1-987764
10
1-635701
60
2-348371
10
1-386187
60
1-990145
ii
1-693713
61
2-35I072
ii
i '435350
61
1-992434
12
I7452II
62
2-299824
12
1-478992
62
1-994636
13
1-791214
63
2-356170
13
1-517978
63
1-996754
H
1-832541
64
2-358576
14
1-553001
64
1-998793
15
1-869853
65
2-360892
15
1-584621
65
2-000756
16
I -903696
66
2-363122
16
1-613302
66
2*002646
17
1-934518
67
2-365270
17
1-639422
67
2-004466
18
I -962695
68
2-367339
18
1-663301
68
2-006219
19
1-988542
69
2-369333
19
1-685205
69
2-007909
20
2-012328
70
2-37I255
20
1-705363
70
2-009538
21
2-034279
71
2-373109
21
1-723966
71
2-OIII09
22
2-054593
72
2-374896
22
1741180
72
2-012624
23
2-073436
73
2-376620
23
1-757149
73
2-014085
24
2-Of>0957
74
2-378283
24
1-771998
74
2-015494
25
2-107283
75
2-379888
25
1785833
75
2-016854
26
2-I22525
76
2-381437
26
1-798750
76
2'0l8l67
27
2-136782
77
2-382933
27
1-810833
77
2-019434
28
2-150142
78
2-384376
28
1-822154
78
2-020658
29
2-162679
79
2-385771
29
1-832779
79
2*021840
30
2-174464
80
2-387117
30
1-842766
so
2-022981
31
2-185558
81
2-388418
31
1-852168
81
2-024083
32
2-196014
82
2-389675
32
1-861029
82
2-025148
33
2-205883
83
2-390890
33
1-869392
83
2-026178
34
2-2I5208
84
2-392063
34
1-877295
84
2-027I72
35
2-224030
85
2-393198
35
1-884771
85
2-028I34
36
2-232384
86
2-394295
36
1-891851
86
2-029063
37
2-240303
87
2-395355
37
1-898562
87
2-029962
38
2-247818
88
2-396380
38
1-904931
88
2-030831
39
2-254955
89
2-397372
39
1-910979
89
2-031671
40
2-261740
90
2-398331
40
1-916729
90
2*032484
41
2-268194
91
2-399259
41
1-922199
91
2-033270
42
2-274340
92
2-400157
42
1-927407
92
2-034031
43
2-280196
93
2-401025
43
1-932369
93
2-034767
44
2-285779
94
2-401866
44
1-937101
94
2-035479
45
2-29II07
95
2-402679
45
1-941616
95
2-036169
46
2-296193
96
2-403466
46
1-945927
96
2-036836
47
2-301053
97
2-404228
47
1-950045
97
2-037481
48
2-305699
98
2-404965
48
1-953982
98
2-038106
49
2-310142
99
2-405679
49
1-957747
99
2-038711
SO
2-3H394
100
2-406371
50
1-961351
100
2-039297
TABLE X.
cliii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 18 per cent.
n
Years
Deferred 7 Years Y rg
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
!
266038
5i
1-665086
I
225456
51
1-411090
2
466726
52
1-667887
2
395531
52
1-413464 .
3
623448
53
1-670572
3
528346
53
I-4I5739
4
749176
54
1-673146
4
634895
54
1-417920
852236
55
1-675616
5
722234
55
I-4200I3
6
938217
56
1-677985
6
795099
56
I-422O22
7
I'OIIOIO
57
1-680261
7
856788
57
1-423950
8
1-073408
58
1-682446
8
909668
58
1-425802
9
1-127467
59
1-684545
9
955481
59
1-427581
10
1*174735
60
1-686563
10
995538
60
1-429291
n
1-216399
61
1-688504
ii
I -030846
61
I-430935
12
1-253383
62
1-690369
12
1-062189
62
1-432516
13
1-286422
63
1-692165
13
1-090188
63
1-434038
14
I'3i6io2
64
1-693892
H
I-II534I
64
1-435502
15
1-342900
65
1-695556
15
1-138050
65
. I'4369I2
16
1-367205
66
1-697157
16
1-158648
66
I -438269
17
1-389341
67
I -698700
17
I-I77407
67
1-439576
18
1-409577
68
I*700l86
18
I-I94557
68
I -440836
19
1-428140
69
I70l6l8
19
I-2I0288
69
1-442049
20
1-445223
70
1702999
20
1-224765
70
I-4432I9
21
1*460988
71
1-704330
21
1*238125
71
1-444347
22
1-475576
72
1705613
22
1-250488
72
1-445435
23
1*489110
73
1706851
23
I-26I957
73
1-446484
24
1-501693
74
I -708046
24
1-272621
74
1-447497
25
1-513418
75
1709199
25
1*282557
75
1-448473
26
1-524365
76
I7I03II
26
1-291834
76
1-449416
27
1-534604
77
I7H385
27
I-3005I2
77
1-450326
28
1-544198
78
I7I2422
28
I -308642
78
1-451205
29
i'553i93
79
I7I3423
2 9
1-316273
79
1-452054
3O
1-561666
80
I7I4390
3O
1-323446
30
1-452873
31
1-569634
81
I7I5325
31
1*330198
81
1*453665
3 2
1-577143
82
1716227
32
1-336562
82
1-454430
33
1-584231
83
I7I7IOO
33
1-342568
83
1-455169
34
1-590928
84
I7I7943
34
1-348244
84
1-455884
35
1-597263
85
1718757
35
I-3536I3
85
1-456574
36
i -603263
86
I7I9545
36
1-358698
86
1-457242
37
1-608951
87
1-720307
37
1-363518
87
1-457887
38
1-614348
88
I72I043
38
1-368091
88
1-458511
39
4O
1-619474
1-624346
89
90
I72I755
1722444
39
40
I-372435
1-376565
89
90
1-459115
1-459698
41
1-628982
9 1
I723HI
4i
1-380493
91
1-460263
42
1-633396
92
1723755
42
I-384234
92
i -460809
43
1-637601
93
1724379
43
I-387798
93
1-461338
44
1-641611
94
1724982
44
1-391196
94
1-461850
45
I-645437
95
1725567
45
I'394438
95
1-462345
46
i -649090
96
1726132
46
1*397534
96
1-462824
47
1-652581
97
1726679
47
i -400492
97
1-463287
48
1-655917
98
1727209
48
1-403319
98
i'463736
49
1-659108
99
I72772I
49
i -406024
99
1-464171
50
1-662162
LOO
I7282I8
SO
1-408612
100
1-464591
cliv
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 18 per cent.
n
Years
Deferred 9 Years
n
Years
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
191064
51
1-195839
I
161919
51
1-013423
2
335195
52
I-I9785I
2
284064
52
1-015128
3
'4477 5 1
53
I-I99779
3
379450
53
1-016762
4
538047
54
I-20I628
4
455972
54
1-018328
5
612063
55
I-20340I
5
518697
55
1-019831
6
673813
56
1-205103
6
571028
56
I-O2I274
7
726092
57
1-206737
7
615332
57
1-022659
8
770905
58
I -208306
8
653309
58
1-023989
9
809729
59
1-209814
9
6862II
59
1-025266
10
843676
60
I-2II264
10
714980
60
1-026495
ii
873598
61
1-212657
ii
740338
61
1-027675
12
900160
62
1-213997
12
762848
62
I-0288II
13
923888
63
1-215286
13
782956
63
I -029904
14
945204
64
1-216527
H
80I02O
64
1-030955
15
964450
65
I-2I7722
15
817330
65
1-031968
16
981905
66
I-2I8872
16
832123
66
I "032942
17
997803
67
1-219980
17
845596
67
1-033881
18
1-012336
68
I-22I047
18
857912
68
1-034786
19
1-025668
69
I-222076
19
869210
69
1-035657
2O
1-037936
70
1-223067
20
879607
7O
I -036498
21
1*049259
71
I '224023
21
889202
71
1-037308
22
1-059736
72
I 224945
22
898081
72
I -038089
23
1-069455
73
1-225834
23
906318
73
1-038843
24
1-078493
74
1-226692
24
913977
74
I-039570
25
1-086913
75
I-227520
25
92 1 1 1 3
75
1-040271
26
1-094775
76
1-228319
26
9 2 7775
76
I "040948
27
I'I02I29
77
1-229090
27
934007
77
1-041602
28
I'IO9OI9
78
1-229835
28
939847
78
I-042233
29
I-II5486
79
1-230554
29
945327
79
1-042842
30
I'I2I565
80
I-23I249
30
950478
80
I-04343I
31
I-I27286
81
1-231920
31
955327
81
I '044000
32
1-132680
82
1-232568
32
959898
82
1-044549
33
I-I37770
83
1-233194
33
964212
83
I -045080
34
1-142580
84
1-233800
34
968288
84
1-045593
35
I-I47I30
85
1-234385
35
972144
85
I '046089
36
I-I5I439
86
1-234951
36
975796
86
1-046568
37
I-I55524
87
1-235497
37
979257
87
I -047032
38
I-I59400
88
1-236026
38
982542
88
I '047480
39
I'l63o8l
89
1-236538
39
985662
89
1-047913
40
1-166580
90
1-237033
40
, -988627
90
I-048333
41
1-169909
91
I-2375II
4i
991449
91
I -048738
42
I-I73079
9 2
1-237974
42
994135
92
1-049131
43
I-I76IOO
93
1-238422
43
996695
93
1-049510
44
1-178980
94
1-238856
44
999U5
94
1-049878
45
I-I8I727
95
1-239275
45
1-001464
95
1-050233
46
I-I8435I
96
1-239681
46
i -003687
96
1-050577
47
1-186858
97
I -240074
47
1-005812
97
1-050910
48
I-I89254
98
1-240454
48
1-007842
98
1-051233
49
I-I9I546
99
1-240823
49
1-009784
99
I-05I545
50
I-I93739
100
I-24II79
SO
1-011643
100
I -05 1 847
TABLE X.
civ
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 20 per cent.
n
Years
Deferred 1 Tear
n
Years
Deferred 1 Year
n
Years
Deferred 2 Years
n
Years
Deferred 2 Years
!
694444
51
3-996154
I
578704
51
3-330I29
2
1-203177
52
4-002231
2
I -002647
5 2
3-335I93
3
1-591757
53
4-008054
3
I -326465
53
3-340045
4
1-898137
54
4-OI3635
4
1-581781
54
3-344696
5
2-145805
55
4-018988
5
1788171
55
3-349I56
6
2-350082
56
4-024123
6
1-958402
56
3353436
7
2-521384
57
4-029052
7
2-IOII53
57
3*357543
8
2-667039
58
4-033784
8
2-222532
58
3-361487
9
2792355
59
4-038330
9
2-326963
59
3-365275
10
2-901270
60
4-042698
10
2-417725
60
3-3689I5
ii
2-996767
61
4-046897
ii
2-497306
61
3-3724I4
12
3-081147
62
4-050934
12
2-567622
62
3375779
13
3-156212
63
4-054818
13
2-630177
63
33790I5
14
3-223398
64
4-058555
14
2-686165
64
3382I29
15
3-283858
65
4-062 1 5 1
15
2736548
65
3385I26
16
3-338530
66
4-065614
16
2782108
66
3-388011
17
3-388188
67
4-068948
17
2-823490
67
3-390790
18
3*433471
68
4-072160
18
2-86I226
68
3393467
19
3-4749I7
69
4-075255
19
2-895764
69
3-396046
20
3-512977
70
4-078238
20
2-927481
70
3-39853I
21
3-548035
71
4-081113
21
2-956696
71
3-400927
22
3-580420
72
4-083885
22
2-983683
72
3-403238
23
3'6lO4I2
73
4-086559
23
3-008677
73
3-405366
24
3-638257
74
4-089138
24
3-031881
74
3-4076I5
25
3-664165
75
4-091627
25
3-05347I
75
3-409689
26
3-688323
76
4-094028
26
3-073602
76
3-411690
27
3710891
77
4-096347
27
3-092409
77
3-413622
28
3-732013
78
4-098584
28
3'IIOOH
78
3-415487
29
375l8l6
79
4-100745
29
3-126513
79
3-417288
30
3770410
80
4-102832
3O
3-142009
8O
3-419026
31
3787897
81
4-104847
31
3-156581
81
3-420706
32
3-804365
82
4-106795
32
3-170304
82
3-422329
33
3-819894
83
4-108676
33
3-I83245
83
3-423897
34
3-834556
84
4-110494
34
3-195464
84
3-425412
35
3-848416
85
4-112251
35
3-207014
85
3-426876
36
3-861532
86
4-113950
36
3-217944
86
3-428291
37
3-873958
87
4-115592
37
3-228298
87
3-429660
38
3-885740
88
4-117180
38
3-238117
88
3-430983
39
3-896924
89
4-118715
39
3-247437
89
3-432262
40
3-907550
90
4' 1 2 D2OO
4O
3-256291
90
3-43350
41
3W653
91
4-121636
41
3-264711
91
3-434697
42
3-927267
92
4-I23026
42
3-272722
92
3-435855
43
3-936423
93
4-I24370
43
3-280353
93
3-436975
44
3-945150
94
4-125670
44
3-287625
94
3-438059
45
3-953472
95
4*126929
45
3-294560
95
3-439108
46
3-961415
96
4-I28I47
46
3-30II79
96
3-440123
47
3-969000
97
4-I29326
47
3-307500
97
3-441105
48
3-976249
98
4-130467
48
3-3I3540
98
3-442056
49
3-983I79
99
4-I3I572
49
3-3I93t6
99
3-442976
50
3-989809
100
4-I3264I
50
3-324840
100
3-443868
clvi
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 20 per cent.
n
Years
Deferred 3 Years
n
Years
Deferred 3 Years
n
Years
Deferred 4 Years
n
Years
Deferred 4 Years
I
482253
51
2775107
I
401878
51
2-312589
2
835539
52
2779327
2
696283
52
2-316106
3
1-105387
53
2783371
3
921156
53
2-3I9476
4
1-318150
54
2787247
4
1-098459
54
2-322706
5
1-490143
55
2-790964
5
1-241786
55
2-325803
6
I '632002
56
2794530
6
1-360001
56
2-328775
7
1750961
57
2797952
7
i '459 i 34
57
2-33I627
8
I-852IIO
58
2-80I239
8
I-543425
58
2-334366
9
1-939136
59
2-804396
9
1-615946
59
2-336997
10
2-OI477I
60
2-807429
10
1-678976
60
2339524
ii
2-08I088
6.1
2-810345
ii
1734240
61
2-341954
12
2-139685
62
2-813149
12
1783071
62
2-344291
13
3*191814
63
2-815846
13
1-826512
63
2-346538
14
2-238471
64
2-818441
H
1-865392
64
2-34870!
15
2-280457
65
2-820938
15
1-900381
65
2-350782
16
2-318424
66
2-823343
16
i -932020
66
2-352786
17
2-352908*
67
2-825658
17
1-960757
67
2-3547I5
18
2-384355
68
2-827889
18
1-986963
68
2-356574
19
2-413137
69
2-830038
J 9
2-010947
69
2-358365
20
2-439567
70
2-832110
20
2-032973
70
2360091
21
2-463913
71
2-834106
21
2-053261
71
2-361755
22
2-486402
72
2-836032
22
2-072002
72
2-363360
23
2-507231
73
2-837888
23
2-089359
73
2-364907
24
2-526567
74
2-839679
24
2-105473
74
2-366400
25
2-544559
75
2-841408
25
2*120466
75
2-367840
26
2-56I335
76
2-843075
26
2-134446
76
2-369229
27
2-577008
77
2-844685
27
2-147506
77
2-370571
28
2-591676
78
2-846239
28
2-159730
78
2-371866
29
2-605428
79
2-847740
29
2-171190
79
2-373116
30
2*618341
so
2-849189
3O
2-181951
80
2-374324
31
2*630484
81
2-850588
31
2-192070
81
2'375490
32
2*641920
82
2-851941
32
2-201600
82
2-376617
33
2-652704
83
2-853247
33
2-210587
83
2-377706
34
2-662886
84
2-854510
34
2-219072
84
2-378758
35
2-672511
85
2-855730
35
2-227093
85
2*379775
36
2-68l620
86
2-856910
36
2-234683
86
2-380758
37
2-690248
87
2-858050
37
2-241874
87
2-381708
38
2-698431
88
2-859152
38
2-248692
88
2-382627
39
2706198
89
2-860219
39
2-255165
89
2-383516
40
2713576
90
2-861250
40
2-261313
90
2-384375
41
2720592
91
2*862247
41
2-267160
91
2*385206
42
2727269
92
2-8632I2
42
2-272724
92
2-386010
43
2733627
93
2 864146
43
2-278023
93
2-386788
44
2739687
94
2-865049
44
2-283073
94
2-387541
45
2745467
95
2-865923
45
2-287889
95
2*388269
46
2750983
96
2-866769
46
2-292486
96
2-388974
47
2756250
97
2-867587
47
2-296875
97
2-389656
48
2761284
98
2-868380
48
2-301070
98
2*390317
49
2766096
99
2-869147
49
2*305080
99
2-390956
SO
2-770702
100
2-869890
50
2-308917
100
2-39I575
TABLE X.
clvii
Present Value (or Years* Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 20 per cent.
n
Years
Deferred 5 Years
n
Years
Deferred 5 Years
n
Years
Deferred 6 Years
n
Years
Deferred 6 Years
I
334898
51
1-927158
I
279082
51
1-605965
2
580236
5 2
1-930088
2
483530
52
I '608407
3
767630
53
1-932896
3
639692
53
1-610747
4
915382
54
I-935588
4
762819
54
1-612990
5
1*034821
55
1-938169
5
862351
55
1-615141
6
I-I33334
56
I -940646
6
'944445
56
1-617205
7
1-215945
57
1-943023
7
I-OI3288
57
1-619185
8
I-286I88
58
I "94535
8
1-071823
58
1-621087
9
1-346622
59
I '947497
9
I-I22I85
59
1-622914
10
I-399I47
60
1-949604
10
I-I65955
60
I '624670
ii
I-445200
61
1-951629
ii
1-204333
61
1-626357
12
1-485892
62
1-953576
12
1-238244
62
I '627980
13
I'522093
63
1*955449
13
1-268411
63
I '629540
H
J'554494
64
1-957251
14
I-2954II
64
1-631042
IS
1-583650
65
1-958985
15
1-319709
65
1-632488
16
1-610016
66
1-960655
16
1-341680
66
1-633879
I?
1-633964
67
1-962263
17
1-361637
67
1-635219
18
1-655802
68
1-963812
18
I-379835
68
1-636510
19
1-675789
69
1-965304
19
1-396491
69
1-637754
20
1-694144
70
1-966743
20
I-4II787
70
1-638952
21
1711051
71
1-968129
21
1-425876
71
1-640108
22
1-726668
72
I -969466
22
1-438890
72
I-64I222
23
1741132
73
1-970756
23
1-450944
73
I '642297
24
1754561
74
I-972000
24
1-462134
74
I-643333
25
1767055
75
I-973200
25
1-472546
75
I-644333
26
1778705
76
I-974358
26
1-482254
76
1-645298
27
1789589
77
I-975476
27
1-491324
77
1-646230
28
1799775
78
1-976555
28
I -4998 1 2
78
I '647 1 29
29
1-809325
79
1-977597
29
I-50777I
79
1-647997
30
1-818292
80
I -978603
30
I-5I5243
80
I -648836
31
1-826725
81
1-979575
31
r52227I
81
I -649646
32
1-834667
82
1-980514
32
1-528889
82
1-650429
33
1-842156
83
1-981422
33
I-535I30
83
1-651185
34
1-849227
84
1-982298
34
I-54I022
84
1-651915
35
1-855911
85
1-983146
35
1-546592
85
1-652622
36
1-862236
86
1-983965
36
I-55I863
86
I-6533 4
37
1-868228
87
1-984757
37
I-556857
87
1-653964
38
1-873910
88
1-985523
38
I-56I592
88
1-654602
39
1-879304
89
1-986263
39
1-566087
89
1-655219
40
i -884428
90
1-986979
40
1-570357
90
1-655816
4i
1-889300
9 1
1-987672
41
I-5744I7
91
1-656393
42
i ^93937
9 2
1-988342
42
I-57828I
92
1-656952
43
1-898352
93
I -988990
43
1-581960
93
1-657492
44
1-902561
94
1-989617
44
1-585467
94
1-658014
45
1-906574
95
1-990224 .
45
I-5888I2
95
1*658520
46
1-910405
96
I -9908 1 2
46
I-592004
96
1-659010
47
1-914063
97
1-991380
47
I-595052
97
1-659484
48
1-917558
98
I-99I93I
48
I-597965
98
I -659942
49
i -920900
99
1-992463
49
I-600750
99
1-660386
SO
1-924097
100
1-992979
50
1-603415
100
i -6608 1 6
clviii
THE ENGINEEK'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 20 per cent.
n
Ysars
Deferred 7 Years
n
Years
Deferred 7 Years
n
Years
Deferred 8 Years
n
Years
Deferred 8 Years
I
232568
51
I-338304
I
193807
51
II5253
2
402942
52
I'340339
2
335785
52
116949
3
5330/6
53
1-342289
3
444230
53
118574
4
635682
54
1-344158
4
529735
54
I20I32
5
718626
55
I-34595I
5
598855
55
-121626
6
787038
56
1-347671
6
655865
56
123059
7
'844406
57
I-34932I
7
703672
57
124434
8
893186
58
1-350906
8
744322
58
125755
9
935154
59
1-352429
9
779295
59
127024
10
971630
60
l*3$389*
10
809691
60
128243
ii
I '0036 1 1
61
1-355298
ii
836343
61
129415
12
I '03 1 870
62
1-356650
12
859891
62
130541
13
1-057009
63
I-357950
13
880841
63
131625
H
I '0795 10
64
I-359202
H
899591
64
132668
15
1-099757
65
I -360406
15
916464
65
133672
16
I-Il8o67
66
1-361566
16
931722
66
134638
17
1-134697
67
1-362683
17
9 4558l
67
135569
18
1-149863
68
1-363758
18
958219
68
136465
19
1-163743
69
1-364795
19
969786
69
137329
20
1-176489
70
1-365794
20
980407
70
138161
21
I-I88230
71
1-366757
21
990192
71
138964
22
I-I99075
72
1-367685
22
999229
72
139737
23
I-209I20
73
1-368580
23
I -007600
73
140484
24
I-2I8445
74
1-369444
24
I-OI537I
74
141203
25
I'227I22
75
1-370278
25
I-02260I
75
141898
26
I-2352I2
76
1-371082
26
1-029343
76
142568
27
I-242770
77
1-371858
27
1-035642
77
143215
28
1-249844
78
1-372608
28
1-041536
78
143840
29
1-256476
79
i'37333i
29
1.047063
79
144443
30
1-262703
so
1-374030
30
1-052252
80
145025
31
I-268559
81
1-374705
31
1-057133
81
145588
32
I-274074
82
J'375357
32
1-061729
82
146131
33
I-279275
83
1-375987
33
I -066062
83
146656
34
1-284185
84
1-376596
34
I-070I54
84
147163
35
I-288827
85
1-377185
35
I'074022
85
147654
36
I-2932I9
86
1-377753
36
1-077683
86
148128
37
1-297381
87
1-378303
37
I-08II5I
87
148586
38
1-301327
88
1-378835
38
I -084439
00
OO
149029
39
1-305072
89
1-379349
39
1-087560
89
149458
4O
I -308630
90
1-379847
40
1-090525
90
149872
41
I-3I20I4
91
1-380328
41
1-093345
91
150273
42
i'3 J 5234
92
1-380793
42
I -096028
92
150661
43
1-318300
93
1-381243
43
1-098583
93
151036
44
1-321223
94
1-381679
44
ITOIOI9
94
151399
45
1-324010
95
1-382100
45
1-103342
95
I5I750
46
1-326670
96
1-382508
46
1-105558
96
152090
47
1-329210
97
1-382903
47
I-I07675
97
152419
48
1-331638
98
1-383285
48
1-109698
98
152738
49
i'333959
99
1-383655
49
1-111632
99
153046
50
1-336179
100
1-384013
50
I-II3482
100
'53344
TABLE X.
clix
Present Value (or Years' Purchase) o 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3 per cent., with Interest
allowed to a Purchaser at 20 per cent.
n
Years
Deferred 9 Years
n
Tears
Deferred 9 Years
n
Years
Deferred 10 Years
n
Years
Deferred 10 Years
I
161506
51
929378
I
134588
51
774481
2
279820
52
930791
2
233184
52
775659
3
370192
53
932145
3
308493
53
776788
4
441446
54
'933443
4
367872
54
777869
5
499046
55
934688
5
415871
55
778907
6
546554
56
935882
6
455462
56
779902
7
586393
57
937029
7
488661
57
780857
8
620268
58
938129
8
516890
58
781774
9
649413
59
939186
9
54II77
59
782655
10
674743
60
940202
10
562286
60
783502
ii
696952
61
94II79
ii
580794
61
784316
12
716576
62
942118
12
597H7
62
785098
13
734034
63
943021
13
611695
63
785851
14
749659
64
943890
H
624716
64
786575
IS
763720
65
944727
15
636434
65
787272
16
776435
66
945532
16
'647029
66
787943
17
787984
67
946307
17
656653
67
788589
18
798519
68
947054
18
665430
68
789212
19
808155
69
'947774
19
673462
69
789812
20
817006
70
948468
20
680838
70
790390
21
825160
71
949136
21
687633
71
790947
22
832691
72
949781
22
693909
72
791484
23
839666
73
950403
23
699722
73
792003
24
'846142
74
951003
24
705119
74
792502
25
852168
75
951582
25
7IOI40
75
792985
26
857786
76
952140
26
714822
76
793450
27
863035
77
952679
27
719196
77
793899
28
867947
78
953200
28
723289
78
794333
29
872552
79
953702
29
727127
79
794752
30
876877
80
954188
30
730731
80
795156
31
880944
81
954656
31
734120
81
795547
32
884774
82
955109
32
7373II
82
795924
33
888385
83
'955547
33
740321
83
796289
34
891795
84
955970
34
743163
84
796641
35
895019
85
956378
35
745849
85
796982
36
898069
86
956773
36
748391
86
797311
37
900959
87
957155
37
750799
87
797629
38
903699
88
957524
38
753083
88
797937
39
906300
89
957881
39
755250
89
798235
40
908771
90
958227
4O
757309
90
798522
41
9III2I
91
958561
41
759267
91
798801
42
913357
92
958884
42
76II3I
92
799070
43
915486
93
959197
43
762905
93
799330
44
917516
94
"959499
44
764596
94
799583
45
919451
95
959792
45
766209
95
799826
46
921299
96
960075
46
767749
96
800063
47
923063
97
960349
47
769219
97
800291
48
924748
98
960615
48
770624
98
800512
49
926360
99
960872
49
771967
99
800726
50
927902
100
961120
so
773252
100
800934
TABLE XL
FOE
VALUING MINEEAL AND OTHEE PEOPEETIES,
OB
-.
The Present Value, (or Tears' Purchase) of 1 per annum
in n years, deferred I, 2, 3, 4, 5, 6, 7, 8, 9, and 10 years,
allowing interest to a present purchaser upon his purchase
money, or capital invested, at the rate of 20 per cent, per
annum, and to redeem the capital so invested, by an Annual
Redemption Fund, at the rates of 3^ and 4 per cent, per
annum.
Calculated to 6 places of decimals, and to 100 years
for each percentage.
TABLE XL
clxiii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3^ and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 1 YEAR.
n
Years
Bedemption
3i per cent.
n
Years
Redemption
34 per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
694444
51
4-019519
I
694444
51
4-040229
2
1-205283
52
4-025291
2
1-207386
52
4-045657
3
1-596625
53
4-030807
3
1-601490
53
4-050828
4
1-905846
54
4-036080
4
I-9I3553
54
4-055758
5
2-156206
55
4-041123
5
2-I66600
55
4-060458
6
2-362939
56
4-045948
6
2-375780
56
4-064943
7
2-536440
57
4-050717
7
2-551465
57
4-069221
8
2-684045
58
4-054988
8
2700998
58
4-073305
9
2-8 1 1080
59
4-059224
9
2-829721
59
4-077204
10
2-921502
60
4-063283
10
2-941615
60
4-080928
n
3-018318
61
4-067172
ii
3-039708
61
4-084486
12
3-103848
62
4-070901
12
3-126341
62
4-087885
13
3-179914
63
4-074478
13
3-203356
63
4-091135
H
3-247967
64
4-077908
14
3-272220
64
4-094242
15
3'309 1 75
65
4-081199
15
3-334II8
65
4-0972I3
16
3-36449I
66
4-084358
16
3-3900I3
66
4-100055
17
3-414697
67
4-087392
17
3-440702
67
4-I02774
18
3-460445
68
4-090304
18
3-486846
68
4-105376
19
3-502279
69
4-093101
19
3-528999
69
4-108069
20
3-540659
70
4-095788
20
3-567629
7O
4-II025I
21
3'575976
71
4-098370
21
3-603I33
71
4-II2533
22
3-608565
72
4-100852
22
3-635852
72
4-II47I9
23
3-638711
73
4-103237
23
3-666079
73
4-116813
24
3-666665
74
4-I05530
24
3-694068
74
4-Il88l8
25
3-692642
75
4-107736
25
3-720038
75
4-120739
26-
3-716830
76
4-109857
26
3744183
76
4-I2255I
27
3739396
77
4-111897
27
3-766673
77
4-124345
28
3-760485
78
4-113859
28
3787653
78
4-126036
29
3-780226
79
4-II5565
29
3-807261
79
4-127658
30
379 8 734
80
4-117565
30
3-825610
80
4-129207
3 1
3-816111
81
4-II93I5
31
3-842806
81
4-130702
32
3-832448
82
4-120998
32
3-858942
82
4-132131
33
3-847828
83
4-I22620
33
3-874101
83
4-I33502
34
3-862322
84
4-124181
34
3-888360
84
4-134816
35
3-875999
85
4-125684
35
3-901786
85
4-136077
36
3-888917
86
4-127132
36
3-914440
86
4-137287
37
3-901131
87
4-128527
37
3-926379
87
4-I38447
3*
3-912691
88
4-129870
38
3-937653
88
4-I3956I
39
3-923641
89
4-131164
39
3-948308
89
4-140629
40
3-934023
90
4-132411
40
3-958385
90
4-141654
41
3-943873
91
4-I336I3
4i
3^67924
91
4-142638
42
3-953226
92
4-I3477I
42
3-976960
92
4-I43583
43
3-962115
93
4-135887
43
3-985525
93
4-144490
44
3-970567
94
4-136963
44
3-993649
94
4-145360
45
3-978609
95
4-138000
45
4-001360
95
4-146196
46
3-986267
96
4-138999
46
4'008682
96
4-146998
47
3-993562
97
4-I39963
47
4-015639
97
4-147768
48
4-000516
98
4-140893
48
4-022253
98
4-148508
49
4-007149
99
4-141788
49
4-028543
99
4-149218
50
4-013478
100
4-142653
so
4-034530
100
4-149899
cixiv
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3J and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 2 YEARS.
n
Years
Redemption
3i per cent.
n
Years
Redemption
3i per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
578704
51
3-349599
I
578703
51
3-366857
2
I -004403
52
3-354408
2
1-006155
52
3-37I380
3
1-330521
53
3359005
3
1-334575
53
3-375690
4
1-588205
54
3-363399
4
1-594627
54
3-379798
5
1796838
55
3'36760I
5
1-805500
55
3-3837I5
6
1-969116
56
3-371623
6
I'9798l6
56
3-38745I
7
2-II3700
57
3-375596
7
2-I26220
57
3-391017
8
2-236704
58
3379I56
8
2-250831
58
3-394420
9
2-342566
59
3-382686
9
2'358lOI
59
3-397669
10
2-434585
60
3-386068
10
2-451346
60
3-400772
ii
2-5I5265
61
3389309
ii
2-533089
61
3-403737
12
2^586540
62
33924I7
12
2-605284
62
3-406570
13
2-649929
63
3-395397
13
2-669463
63
3-409278
14
2-706639
64
3398255
14
2726850
64
3-411867
15
2-757646
65
3-400999
15
2778431
65
3-414344
16
2-803742
66
3-403631
16
2-825010
66
3-416712
17
2-845581
67
3-406159
17
2-867251
67
3-418978
18
2-883704
68
3-408586
18
2-905704
68
3-421146
19
2-918566
69
3-410917
19
2-940832
69
3-423390
20
2-950549
70
3-4I3I56
20
2-973023
70
3-425208
21
2-979980
71
3-4I5308
21
3-002610
71
3-427110
22
3-007137
72
3-4I7376
22
3-029876
72
3-428932
23
3-032259
73
3-4I9363
23
3-055065
73
3-430676
24
3-055554
74
3-421274
24
3-078389
74
3-432347
25
3-077201
75
3-423II2
25
3-100031
75
3-433948
26
3-097358
76
3-424880
26
3-120151
76
3-435483
27
3-116163
77
3-426580
27
3-I38893
77
3-436953
28
3'133737
78
3-428215
28
3-156377
78
3-438362
29
3-150188
79
3-429637
29
3-172717
79
3-4397I4
30
3-165612
80
3-43I303
30
3-188008
80
3-441005
31
3-180093
81
3-432762
31
3-202338
81
3-442251
32
3-193707
82
3-434164
32
3-215784
82
3-443442
33
3-206523
83
3-4355I6
33
3-228417
83
3-444584
34
3-218602
84
3-436817
34
3-240299
84
3-445679
35
3-229999
85
3-438069
35
3-251488
85
3-446730
36
3-240764
86
3-439276
36
3-262033
86
3-447738
37
3-250943
87
3-440438
37
3-271982
87
3-448705
38
3-260576
88
3-441558
38
3-281376
88
3-449633
39
3-26970!
89
3-442636
39
3-290256
89
3-450523
40
3-278352
90
3-443675
40
3'298653
90
3-45I378
41
3-286561
91
3-444676
41
3-306603
91
3-452198
42
3-294355
92
3-445642
42
33I4I33
92
3-452985
43
3-301762
93
3-446571
43
3-321270
93
3-45374I
44
3-308806
94
3-447468
44
3-328040
94
3-454466
45
3-3I5508
95
3-448333
45
3-334466
95
3-455I62
46
3-32I889
96
3-449165
46
3-340567
96
3-455830
47
3-327968
97
3-449969
47
3-346365
97
3-456473
48
3333763
98
3-450743
48
3-35I877
98
3-457089
49
333929I
99
3 '45*489
49
3-357II9
99
3-457680
5O
3-344565
100
3^452210
50
3-362108
100
3-458248
TABLE XI.
clxv
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3^ and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 3 YEAKS.
n
Years
Redemption
3i per cent.
n
tears
Redemption
3i per cent.
n
Years
Redemption
4 per cent.
n
Tears
Redemption
4 per cent.
I
482253
51
2791335
I
482253
51
2-805717
2
837003
52
2-795343
2
838463
52
2-809486
3
1-108768
53
2-799174
3
I-II2I47
53
2-813078
4
1-323505
54
2-802836
4
1-328857
54
2-816501
5
1-497366
55
2-806338
5
1-504585
55
2-819765
6
I '640930
56
2-809689
6
1-649849
56
2-822879
7
1761418
57
2*813000
7
1771852
57
2-825850
8
1-863921
58
2-815967
8
I-875695
58
2-828687
9
I-952I40
59
2-818908
9
1-965086
59
2-831394
10
2-028822
60
2-821727
10
2-042790
60
2-833980
ii
2-096055
61
2-824427
ii
2-II09IO
6l
2-836451
12
2-155451
62
2-827017
12
2-I7I072
62
2-838812
13
2-208275
63
2-829501
13
2-224555
63
2-841069
2-255534
64
2-831883
14
2-272377
64
2-843226
15
2*298040
65
2-834169
15
' 2-315362
65
2-845290
16
2*336453
66
2-836363
16
2-354178
66
2-847263
17
2-371318
67
2-838469
17
2-389379
67
2-849151
18
2-403088
68
2-840492
18
2-421423
68
2-850958
19
2-432139
69
2-842434
19
2-450696
69
2-852828
20
2-458792
70
2-844300
20
2-477522
70
'2-854343
21
2-483318
71
2-846093
21
2-502I78
71
2-855929
22
2-505949
72
2-847816
22
2-524899
72
2-857446
23
2-526884
73
2-849473
23
2'54589I
73
2-858900
24
2-546296
74
2-851065
24
2-565327
74
2-860293
25
2-564336
75
2-852597
25
2-583362
75
2-86l627
26
2-58II33
76
2-854070
26
2-600I29
76
2-862906
27
2-596804
77
2-855486
27
2-6I5747
77
2-864131
28
2-6II449
78
2-856849
28
2-630317
78
2-865305
29
2-625158
79
2-858034
29
2-643934
79
2-866431
3O
2*638011
80
2-859423
30
2-656676
80
2-867507
31
2-650078
81
2-860638
31
2-6686I8
8l
2-868545
32
2-661424
82
2-861807
32
2-679823
82
2-869538
33
2-672I04
83
2-862933
33
2-690350
83
2-870490
34
2-682I70
84
2-864017
34
2700253
84
2-871403
35
2-691667
85
2-865061
35
2-709576
85
2-872278
36
2-700638
86
2-866066
36
2-718364
86
2-873118
37
2709I2I
87
2-867035
37
2726655
87
2-873924
38
2-717148
88
2-867968
38
2734483
88
2-874698
39
2-724752
89
2-868867
39
2-741883
89
2-875440
40
2-731961
90
2-869732
2-748881
90
2-876151
41
2-738802
91
2-870567
4i
2755505
9 1
2-876835
42
2745298
92
2-871371
42
2761780
92
2-877491
43
2751470
93
2-872146
43
2-767728
93
2-878121
44
2-757339
94
2-872893
44
2773370
94
2-878725-
45
2-762924
95
2-873614
45
2-778725
95
2-879305
46
2-768242
96
2-874308
46
2-783809
96
2-879862
47
2-773308
97
2-874977
47
2-788641
97
2-880397
48
2-778137
98
2-875622
48
2-793234
98
2-880911
49
2-782744
99
2-876245
49
2-797602
99
2-881404
so
2787139
100
2-876845
50
2*801760
100
2-881877
clxvi
THE ENGINEEK'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Eedemption of Capital being at 3J and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 4 YEARS.
n
Years
Redemption
3i per cent.
n
Years
Redemption
3i per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
401877
51
2-326III
I
401877
51
2-338096
2
697502
52
2-329451
2
698719
52
2-341237
3
923973
53
2-332643
3
926789
53
2-344230
4
1-102920
54
2-335695
4
1-107380
54
2-347083
5
I '247804
55
2-338613
5
1-253820
55
2-349803
6
1-367441
56
2-341406
6
1-374873
56
2-352398
7
1-467847
57
2-344165
7
1-476542
57
2-354874
8
1-553267
58
2-346637
8
1-563078
58
2-357237
9
1-626782
59
2-349089
9
1-637571
59
2-359494
10
1-690684
60
2-35H37
10
1-702324
60
2-361648
ii
I7467I2
61
2-353688
ii
1759091
61
2-363708
12
I -796208
62
2-355846
12
1-809226
62
2-365675
13
1-840228
63
2-357916
13
I-853795
63
2-367556
H
1-879610
64
2-359901
H
I '893646
64
2-369353
15
1-915032.
65
2-361806
15
1-929467
65
2-371073
16
1-947043
66
2-363634
16
1-961813
66
2-372718
17
1-976097
67
2-365389
17
I-99II47
67
2-374291
18
2-002572
68
2-367075
18
2-017851
68
2-375797
19
2-026781
69
2-368693
19
2-042245
69
2-377355
20
2-048992
70
2-370248
20
2*064600
70
2-378618
21
2-069431
71
2-371742
21
2-085147
71
2-379939
22
2-088290
72
2-373179
22
2-104081
72
2-381204
23
2-105736
73
2-374559
23
2-I2I574
73
2-382415
24
2-I2I9I2
74
2-375886
24
2-I3777I
74
2383575
25
2-136945
75
2-377162
25
2-152800
75
2-384688
26
2-150943
76
2-378390
26
2-166773
76
2-385753
27
2-164002
77
2-379570
27
2-179788
77
2-386774
28
2-176206
78
2-380706
28
2-191930
78
2-387753
29
2-187630
79
2-381693
29
2-203277
79
2-388691
3O
2-198341
80
2-382851
30
2-213895
80
2-389588
31
2-208397
81
2-383863
31
2-223847
81
2-390453
32
2-217852
82
2-384838
32
2-233184
82
2-391280
33
2-226752
83
2-385776
33
2-241957
83
2-392073
34
2-235140
84
2-386679
34
2-250209
84
2-392834
35
2-243055
85
2-387549
35
2-257978
85
2-393563
36
2-250530
86
2-388387
36
2-265301
86
2-394264
37
2-257599
87
2-389194
37
2-2722II
87
2-394935
38
2-264288
88
2-389972
38
2-278735
88
2-395580
39
2-270625
89
2-390721
39
2-284901
89
2-396198
40
2-276633
90
2-391442
40
2-290733
90
2-396791
41
2-282334
91
2'392I37
41
2-296253
91
2-397361
42
2-287747
92
2-392808
42
2-301482
92
2-397908
43
2-292890
93
2-393453
43
2-306439
93
2-398432
44
2-297781
94
2-394076
44
2-311140
94
2-398936
45
2-302435
95
2-394676
45
2-315602
95
2-399419
46
2-306867
96
2-395255
46
2-319839
96
2-399883
47
2-31 1089
97
2-395813
47
2-323866
97
2-400329
48
2-315113
98
2-396350
48
2-327693
98
2-400757
49
2-318952
99
2-396869
49
2-33I333
99
2-401168
50
2-322614
100
2-397369
50
2334798
100
2-401563
TABLE XI.
clxvii
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3^ and 4 per cent, with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 5 YEARS.
n
Years
Redemption
3| per cent.
n
Years
Redemption
3 per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
334898
51
1-938428
I
334898
51
1-948416
2
581252
52
I-94I2I2
2
582267
52
1-951033
3
769978
53
1-943872
3
772325
53
I-953527
4
919101
54
1-946415
4
922818
54
1-955905
5
I -039838
55
1-948847
5
1-044851
55
1-958171
6
1-139536
56
I-95II74
6
I-I45729
56
1-960334
7
1-223207
57
1-953473
7
1-230454
57
1-962397
8
1-294390
58
1-955534
8
1-302567
58
1-964367
9
I-355653
59
I-957576
9
1-364644
59
1-966247
10
I -408905
60
1*959533
10
1-418605
60
I -968043
n
1-455595
61
1-961409
ii
1-465911
61
I-969759
12
i -496842
62
1-963207
12
1-507690
62
1-971398
13
I-533525
63
1-964932
J 3
1-544831
63
1-972965
14
1-566344
64
1-966586
H
1-578041
64
1-974464
15
1-595862
65
1-968174
15
1-607891
65
1-975897
16
1-622538
66
1-969697
16
1-634847
66
I-977267
17
i -646750
67
I-97Il6o
17
1-659292
67
1-978578
18
1-668812
68
1-972565
18
1-681545
68
I-979833
19
1-688986
69
I-9739I3
19
1701873
69
1-981132
20
1-707496
7O
1-975209
20
1-720502
70
1-982184
21
1-724528
71
1-976454
21
1-737624
71
1-983285
22
1-740243
72
1-977651
22
1753403
72
I-984339
23
1-754782
73
1-978801
23
1767981
73
1-985348
24
1-768262
74
1-979907
24
1781478
74
1-986315
25
1-780790
75
1-980971
25
1794002
75
1-987242
26
1-792455
76
1-981994
26
1-805646
76
1-988130
27
1-803337
77
1-982978
27
1-816492
77
1-988981
28
1-813507
78
1-983924
28
1-826610
78
1-989796
29
1-823028
79
1-984747
29
1-836066
79
1-990578
30
1-831953
80
I-9857II
30
1-844915
80
1-991326
3 1
i-84 333
81
1-986555
31
1-853208
81
1-992047
32
1-848212
82
1-987367
32
I -860989
82
1-992736
33
1-855629
83
1-988149
33
1-868300
83
1*993397
34
1-862619
84
I -988902
34
1-875176
84
1-994031
35
1-869215
85
I -989627
35
1-881651
85
1-994639
36
1-875444
86
1-990325
36
1-887754
86
I-995222
37
1-881335
87
1-990998
37
1-893511
87
I-995782
38
i -886909
88
1-991645
38
1-898948
88
1-996319
39
1-892190
89
1-992270
39
I -904086
89
1-996834
40
1-897197
90
I-99287I
40
I -908946
90
I-997328
41
1-901947
91
I-993450
41
I-9I3547
91
1-997803
42
i -906458
92
1-994009
42
1-917904
92
1-998259
43
1-910744
93
1-944547
43
1-922035
93
I -998696
44
1-914820
94
I -995066
44
1-925952
94
1-999116
45
1-918699
95
1-995566
45
1-929671
95
I-9995I9
46
1-922391
96
I -996048
46
I-933202
96
1-999905
47
1-925909
97
1-996513
47
1-936557
97
2-000277
48
1-929263
98
1-996961
48
1-939747
98
2*000633
49
1-932462
99
1-997393
49
1-942780
99
2-000976
50
I-9355H
zoo
1-997810
SO
1-945667
100
2'OOI3O5
clxviii
THE ENGINEERS VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Def errence. Kedemption of Capital being at 3J and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 6 YEARS.
n
Years
Redemption
Si per cent.
n
Years
Redemption
3| per cent.
n
Years
Redeiiiption
4 per cent.
n
Years
Redemption
4 per cent.
I
279082
51
I'6l5355
I
279082
51
1-623678
2
484376
52
1-617675
2
485222
52
1-625859
3
641648
53
1-619892
3
643603
53
1*627938
4
765917
54
I-6220II
4
769014
54
1-629919
5
866531
55
1-624037
5
870708
55
1-631808
6
949612
56
1-625977
6
'954773
56
1-633610
7
1-019338
57
1-627893
7
1-025377
57
1-635329
8
1-078658
58
1-629610
8
1-085471
58
1-636971
9
I-I297IO
59
1-631312
9
I-I37202
59
1-638538
10
1-174086
60
1-632943
10
I-I82I7O
60
I '640034
ii
I-2I2995
61
1-634506
ii
I-22I59I
61
1-641464
12
1-247367
62
I '636005
12
1-256407
62
1-642830
13
1-277936
63
1-637442
13
I-287358
63
1-644136
14
305285
64
1-638820
H
I-3I5033
64
1-645385
15
329884
65
1-640143
15
I-339908
65
1-646579
16
352II4
66
1-641413
16
1-362371
66
1.647721
17
372290
67
I -642632
17
1-382742
67
1-648814
18
390675
68
1*643802
18
1-401286
68
1-649859
19
407487
69
I -644926
19
1-418226
6 9
I '650942
20
422912
70
I '646006
20
I-43375I
70
1-651809
21
I-437I04
71
1-647044
21
1-448019
71
1-652736
22
I-45020I
72
1-648041
22
1-461168
72
1-653614
23
462317
73
I -649000
23
1-473316
73
1-654455
24
473551
74
1-649921
24
1-484564
74
1-655261
25
483990
75
1-650808
25
I-495000
75
1-656033
26
4937II
76
1-651660
26
1-504704
76
1-656774
27
502779
77
1-652480
27
I-5I3742
77
1-657483
28
5H255
78
1-653269
28
I-522I74
78
1-658162
29
519188
79
I-653954
29
1-530054
79
1-658814
30
526626
80
1-654758
30
I-537428
80
1-659436
31
1-533609
81
1-655461
31
I-544338
81
1-660037
32
1-540175
82
1-656138
32
1-550823
82
I -6606 1 1
33
1-546356
83
1-656789
33
1-556915
83
I-66ll62
34
1-552181
84
I-6574I7
34
1-562645
84
1-661691
35
1-557677
85
1-658021
35
1-568041
85
1-662197
36
1-562868
86
1-658602
36
I-573I26
86
1-662684
37
1-567777
87
1-659163
37
1-577925
87
1-663150
38
1-572423
88
1-659703
38
1-582455
QO
oo
1-663597
39
1-576823
89
I-660223
39
1-586737
89
I -664027
40
1-580996
90
1-660724
40
1-590787
90
1-664439
41
584954
9 1
I-66I207
41
I-59462I
91
1-664834
42
588713
9 2
1-661672
42
1-598252
92
1-665214
43
592285
93
I-662I2I
43
1-601694
93
1-665578
44
595682
94
1-662553
44
1-604959
94
1-665928
45
598914
95
I -662970
45
1-608058
95
I -666264
46
1-601991
96
1-663372
46
1*61 looo
96
1-666586
47
I '604923
97
1-663759
47
1-613796
97
I -666896
48
1-607718
98
1-664133
48
1-616454
98
1-667193
49
1-610383
99
1-664493
49
1-618982
99
I-667478
50
1-612927
100
1 -664840
50
1-621388
1OO
I-667752
TABLE XI.
clxix
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Eedemption of Capital being at 3^ and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 7 YEARS.
n
Years
Redemption
3i per cent.
n
Years
Redemption
3i per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
232568
51
1-346131
I
232568
51
1-353067
2
403647
52
1-348064
2
404352
52
1-354885
3
534707
53
I-3499II
3
536337
53
1-356616
4
638265
54
1-351677
4
640846
54
1-358268
5
722IIO
55
I'353366
5
725591
55
I'359843
6
791344
56
I-354982
6
795645
56
1-361342
7
849450
57
1-356579
7
854482
57
1-362776
8
898882
58
I-3580IO
8
904560
58
1-364144
9
941426
59
I-359428
9
947670
59
1-365450.
10
978407
60
1-360787
10
985H3
60
I -366697
n
1-010830
61
I -362090
ii
I-OI7994
61
1-367888
12
1-039474
62
I\363339
12
I -047007
62
1-369027
13
I -0.64948
63
I-364537
13
1-072799
63
I-370II5
H
1-087739
64
1-365685
H
1-095862
64
1-371156
15
1-108238
6 5
1^366788
15
1-116591
65
I-372I5I
16
1-126763
66
1-367846
16
I-I353IO,
66
I-373I02
17
I-I43576
67
I-36886I
17
J-I52286
67
1-374013
18
.1-158997
68
1-369837
18
1-167740
68
1-374884
19
1-172907
69
. I-370773
19.
1-181857
69
I-375786,
20
1-185761
70
1-371674
20
I-I94794
70
1-376517
21
1-197589
71
1-372538
21
1-206684
71
I-37728I
22
1-208503
72
I'373369
22
1-217641
72
1-378013:
23
1-218599
73
1-374168
23
1-227765
73
1-378714
24
I -227.960
74
I'374936
24
1-237138
74
I-379386
25
1-236660
75
1-375675
25
1-245835
75
1.380030
26
1-244760
76
1-376385
26
1-253921
76
1-380646.
27
1-252318
77
1-377068
27
1-261453
77
1-381237
28
1-259380
78
I-377725
28
I -268480
78
1-381803
29
1-26.5992
79
1-378297
29
1-275046
79
1*382346
30
1-272190
80
1-378966
30
1-281191
80
1-382865
31
1-278009
81
1-379553
31
1-286950
81
1-383366.
32
1-283481
82
1-380116
32
1-292354
82
I-383845
33
1-288631
83
1-380659
33
1-297431
83
1-384304
34
1-293486
84
1-381182
34
1-302206
84
1-384744
35
1-298066
85
1-381686
35
I -306702
85
1-385166
36
1-302392
86
1-382170
36
1-3.10940
86
1-385571
37
1-306483
87
1-382638
37
I-3I4939
87
I-385960
38
I-3I0354
88
I --383087
38
1-318714
88
1386333
39
1-314021
89
1-383521
39
1-322282
89-
1-386691
40
1-317498
90
I-383938
40
1-325657
90
1-387034
41
1-320797
91
1-384341
41
1-328852
91
1-387364
42
1-323929
92
1-384729
42
1-331878
92
1-387680
43
I -326906
93
1-385102
43
1-334747
93
1-387984
44
1-329736
94
^385463
44
I-337467
94
1-388275
45
I-332430
95
1-385810
45
1-340050
95
1-388555
46
1-334994
96
I-386I45
46
I-342502
96
1-388823
47
1-337437
97
1-386568
47
1-344832
97
1-389082
48
1-339766
98
1-386779
48
1-347047
98
1-389329
49
1-341988
99
1-387079
49
I-349I53
99
1-389567
50
1-344107
100
1-387368
so
I-35II58
100
I-38979S
clxx
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capita,! being at 3^ and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 8 YEARS.
n
Years
Redemption
3 per cent.
n
Years
Redemption
3J per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
193807
51
PI2I774
I
193807
51
1-127544
2
336372
52
1-123385
2
336959
52
1-129069
3
445589
53
1-124924
3
446947
53
1-130512
4
531887
54
1-126396
4
534038
54
I-I3I888
5
601757
55
1-127803
5
604658
55
I-I33200
6
659453
56
1-129150
6
663037
56
i '1 3445 i
7
707874
57
1-130481
7
712067
57
1-135645
8
749068
58
1-131673
8
753799
58
1-136785
9
784521
59
1-132855
9
789723
59
1-137873
10
815338
60
I-I33988
10
820951
60
1-138912
ii
842357
61
1-135073
ii
848327
61
1-139905
12
866227
62
1-136114
12
872505
62
1-140854
13
887456
63
I-I37H2
13
893998
63
1-141761
14
906448
64
1-138069
14
913217
64
1-142628
15
923530
65
1-138988
15
930491
65
I-H3457
16
938967
66
1-139870
16
946091
66
1*144250
17
952979
67
1-140716
17
960237
67
1*145009
18
965747
68
1-141528
18
973115
68
I-H5735
19
'977421
69
1-142310
'9
984879
69
1*146487
20
938133
70
1-143060
20
995660
70
1-147096
21
997989
71
1-I43780
21
1*005568
71
I-H7733
22
I -007084
72
I-I44473
22
1-014700
72
1-148343
23
1-015497
73
I-I45I38
23
1-023136
73
1-148927
24
1-023299
74
I'145778
24
1-030947
74
1-149487
25
1-030548
75
1-146394
25
1-038194
75
1-150023
26
1-037299
76
1-146986
26
1-044933
76
1*150537
27
1-043597
77
I-I47555
27
1-051209
77
1*151029
28
1-049482
78
1-148103
28
1-057065
78
1*151501
29
1-054991
79
1-148579
29
1-062537
79
1*151954
3O
1-060157
BO
I-I49I37
30
1-067658
8O
1*152386
31
I -065006
Si
1-149625
31
1-072457
81
1*152803
32
1-069566
82
1*150095
32
i -076960
82
1*153202
33
1-073858
83
1-150548
33
1-081191
83
1*153585
34
1-077903
84
1-150983
34
1-085170
84
1-153951
35
I-08I720
85
1-151403
35
1-088917
85
I-I54303
36
1-085325
86
1-151807
36
1-092449
86
1-154641
37
1-088734
87-
1-152196
37
1-095781
87
1*154965
38
1-091960
88
I-I5257I
38
098927
88
1-155276
39
1-095016
89
1-152932
39
101900
89
I-I55574
40
1-097913
90
I-I53280
40
104713
90
1-155860
41
I-I00662
91
1-153616
4i
107375
91
1-156135
42
1-103273
92
I-I53939
42
109897
92
1*156398
43
1-105753
93
I-I54250
43
112287
93
1-156651
44
1-108112
94
I-I5455I
44
114554
94
1*156894
45
1-110357
95
1-154840
45
116706
95
1-157127
46
1-112494
96
I-I55II9
46
118750
96
1-157351
47
1-114530
97
I-I55388
47
120691
97
1-157566
48
1-116470
98
1-155647
48
122537
98
1-157773
49
1-118322
99
1-155897
49
1-124293
99
1-157971
50 ,
r i 20088
100
1-156139 |
50
1-125964
100
1-158161
TABLE XI.
clxxi
Present Value (or Years' Purcba.se) of ^1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3J and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 9 YEARS.
n
Years
Eedemption
3i per cent.
n
Years
Redemption
3i per cent.
n
Years
Eedemption
4 per cent.
n
Years
Redemption
4 per cent.
I
2
161506
2803 1 1
51
52
934814
936156
I
2
161506
-280800
51
52
939630
940892
3
371325
53
'937439
3
372456
53
942095
4
443240
54
938665
4
445032
54
943242
5
501465
55
939838
5
503883
55
944335
6
549545
56
940960
6
552532
56
945378
7
589896
57
942069
7
'59339
57
946373
8
624224
58
943163
8
628167
58
9473 2 2
9
653768
59
944048
9
658104
59
948229
10
679449
60
944991
10
684127
60
949095
ii
701965
61
945896
ii
706940
61
949923
12
721857
62
946763
12
727088
62
-950713
13
739548
63
'947595
13
745000
63
951469
H
755375
64
948393
H
761015
64
952192
15
769610
65
949158
15
7754II
65
952883
16
782474
66
949893
16
788410
66
'953544
17
794151
67
950599
17
800199
67
954176
18
804790
68
951276
18
810931
68
954781
19
814519
69
951926
19
820734
69
955407
20
-823445
70
952551
zo
829718
70
955915
21
831659
71
953152
21
837975
71
956446
22
839238
72
-953729
22
-845585
72
956954
23
846249
73
-954284
23
852615
73
957441
24
852750
74
954817
24
859124
74
957907
25
858792
75
955330
25
865164
75
958354
26
864417
76
955823
26
-870779
76
958782
27
869665
77
956298
27
876009
77
959193
28
874570
78
956754
28
880889
78
959586
29
879161
79
957151
29
885449
79
959963
30
883466
80
957616
30
889716
80
960323
31
887507
81
958023
31
893716
81
960671
32
891306
82
958414
32
897468
82
961003
33
894883
83
958792
33
900994
83
961322
34
898254
84
959155
34
904310
84
961628
35
901435
85
-959504
35
907432
85
961921
36
904439
86
959841
36
910375
86
962203
37
907280
87
960165
37
913152
87
962472
38
909968
88
960478
38
915774
88
962731
39
912515
89
960779
39
918252
89
962980
10
914929
90
961069
40
920596
90
-963218
4i
917220
9 1
-961348
41
922814
91
963447
42
919396
92
961617
42
924916
92
963667
43
921463
93
961877
43
926908
93
963878
44
923428
94
962127
44
928797
94
964080
45
925299
95
962368
45
930590
95
964275
46
927080
96
962601
46
932293
96
964461
47
928776
97
962825
47
9339H
97
964640
48
930394
98
963041
48
935449
98
964812
49
931936
99
963249
49
936912
99
964977
50
933408
100
963450
SO
938305
100
965136
clxxii
THE ENGINEER'S VALUING ASSISTANT.
Present Value (or Years' Purchase) of 1 per Annum in n years, after
t years' Deferrence. Redemption of Capital being at 3J and 4 per cent., with
Interest allowed to a Purchaser at 20 per cent.
DEFERRED 1O YEAES.
n
Years
Redemption
3$ per cent.
n
Years
Redemption
3J per cent.
n
Years
Redemption
4 per cent.
n
Years
Redemption
4 per cent.
I
134588
51
779012
I
134588
51
783026
2
233593
52
780131
2
234000
52
784078
3
309437
53
781200
3
310380
53
785080
4
369367
54
782222
4
370860
54
786035
5
417888
55
783199
5
419903
55
786946
6
'457954
56
784134
6
460443
56
787815
7
491580
57
785058
7
494492
57
788645
8
520187
58
785886
8
523473
58
789436
9
544808
59
786707
9
548421
59
790192
10
566208
60
787494
10
570106
60
790913
ii
584972
61
788247
ii
589118
61
791603
12
601548
62
788970
12
605908
62
792262
13
'616290
63
789663
13
620834
63
792892
H
629479
64
790328
H
634180
64
793494
15
641342
65
790966
15
646176
65
794070
16
652063
66
791578
16
657009
66
794621
17
661793
67
792166
17
666833
67
795147
18
670659
68
792731
18
675776
68
795652
19
678767
69
793273
19
683946
69
796174
20
686205
70
793794
20
691432
70
796597
21
693050
71
794294
21
698313
71
797039
22
609366
72
794775
22
704655
72
797463
23
705209
73
795237
23
710513
73
797868
24
710626
74
795682
24
715937
74
798257
25
715661
75
796109
25
720970
75
798629
26
720348
76
796520
26
725650
76
798986
27
724722
77
796916
27
730009
77
799328
28
728809
78
797296
28
734075
78
799656
29
732635
79
797626
29
737875
79
799970
3O
!.;; 736222
so
798014
3O
74I43I
so
800270
31
739590
81
798353
31
744764
81
800560
32
742756
82
798679
32
747891
82
800837
33
745737
83
798994
33
750829
83
80 1 103
34
748546
84
799296
34
753592
84
801357
35
751197
85
799588
35
756195
85
801602
36
753700
86
799868
36
758647
86
801836
37
756067
87
800139
37
760961
87
802061
38
758308
88
800399
38
763146
88
802277
39
760430
89
800650
39
765211
89
802484
40
762442
90
800891
4O
767164
90
802683
41
764351
91
801124
41
769013
9 1
802873
42
766164
92
801349
42
770764
92
803057
43
767886
93
801565
43
772424
93
803232
44
769524
94
801773
44
773998
94
803401
45
771083
95
801975
45
775493
95
803563
46
772567
96
802168
46
776912
96
803718
47
773981
97
802355
47
778260
97
803868
48
775329
98
802535
48
779542
98
80401 1
49
776614
99
802709
49
780761
99
804149
50
777841
100'
802876
50
781921
100
804281
TABLE XII.
Comparison of the Difference in Value between the OLD
or ordinary TABLES of the Present Value of 1 per annum,
and a portion of the NEW TABLES in this work, ivhich allow
a purchaser interest on his purchase money, or capital in-
vested, at one rate per cent., and redeem the capital so
invested at another rate per cent.
The Difference in Value is shewn in decimals of a ,
and in . s. d., for the rates of 4, 5, 8, 10, 12, 15, 18, and 20
per cent, per annum. Also the rate per cent, lost on the
purchase of every 1 Annuity by the use of the OLD TABLES.
NOTICE.
The words ' every 1 Annuity,' nsed above, and in the
headings of the third, fourth, and fifth columns all through the
Table, must be taken to mean every \ of the first year's income
purchased.
The reference made to the same Table, and to the rate per
cent, lost on every 1 Annuity, on pp. 52, 54, 56, and 57, must
also be taken in the same sense ; the rate per cent, lost on the
Capital being a distinct question. For example : an Annuity
of 1 for 21 years, at 15 per cent, on the Capital, and the same
rate for redemption, is \vorth 6'31246. But if we can redeem
the Capital at only 3 per cent, the value is ^5*40915, showing
a difference of '90331 ; and this is the loss, or 9O331 per cent.,
on the first year's Annuity, or income. For the loss on Capital
we have '^|l2i^=14'31 per cent, lost by the use of the OLD
TABLES ; and ' 90 ^ 9 X J 00 = 16-69 per cent, gained by the use of the
NEW TABLES.
TABLE XII.
clxxv
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Kedemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
nterest on Capital
and for Redemp-
tion being
4 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
4 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
fable, in Decimals
of a Pound
Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
n Pounds, Shillings,
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
*. d.
I
96154
96154
00000
000
ooo
I
2
I-886IO
1-87754
00856
O O 2
856
2
3
277509
2-75080
02429
005|
2-429
3
4
3-62990
3-58388
04602
II
4-602
4
5
4-45I82
4379J5
07267
o i 5i
7-267
5
6
5-242I4
5-I388I
10333
2 Of
10-333
6
7
6-00206
5-86488
I37I8
2 8|
13-718
7
8
6-73275
6-55925
17350
035*
17-350
8
9
7*43533
7-22367
2Il66
042f
21-166
9
10
8- 1 1090
7^5975
25II5
o 5 of
25-115
10
ii
8-76048
8-46902
29146
o 5 9i
29-146
ii
12
9-38507
9-05288
33219
o 6 7$
33-219
12
13
9-98565
9-61265
37300
o 7 5r
37-300
13
14
10-56312
10-14957
41355
o 8 3;
4I-355
H
15
11-11839
10-66478
45361
o 9 oi
45-36i
15
16
11-65230
II-I5936
49294
o 9 io ;
49-294
16
17
18
12-16567
12-65930
II'63433
12-09063
53134
56867
o 10 7 r
II 4;
53-134
56-867
17
18
19
I3'i3394
12-52915
60479
12 I
60-479
19
20
I3-59033
I2-95073
63960
12 9
63-960
20
21
14-02916
13-35617
67299
o 13 5*
67-299
21
22
14-45112
13-74620
70492
o 14 i
70-492
22
23
14-85684
14-12152
73532
o 14 8
73-532
23
24
15-24696
14-48280
76416
o 15 3?
76-416
24
2 5
15-62208
14-83066
79H2
o 15 9|
79-142
25
26
15-98277
15-16570
81707
o 16 4
81707
26
27
16-32959
15-48846
84113
o 16 9f
84-113
27
28
16-66306
1579948
86358
o 17 3i
86-358
28
29
16-98371
16*09926
88445
o 17 8
88-445
29
30
17-29203
16-38827
90376
o 18 of
90-376
30
3 1
17-58849
16-66696
92153
o 18 5
92-153
31
3 2
I7-87355
I6-93577
93778
o 18 9
93778
32
33
18-14765
17-19509
95256
o 19 o
95-256
33
34
18-41120
I7-44532
96588
o 19 af
96-588
34
35
18-66461
I7-68682
'97779
o 19 6
97779
35
36
18-90828
17-91993
98835
o 19 9
98-835
36
37
19-14258
18-14499
'99759
o 19 ii
99759
37
38
19-36786
18-36232
1-00554
o *4
100-554
38
39
19-58448
18-57222
I'OI226
2}
101-226
39
40
19-79277
1877498
I-OI779
o 4i
101779
40
41
19-99305
18-97087
I-022I8
o 5i
102-218
41
42
20-18563
19-16014
1-02549
o 6
102-549
42
43
20-37079
I9'34307
I'02772
o 6
102772
43
44
20-54884
19-51987
I -02897
o 6|
102-897
44
45
20-72004
19-69079
I-02925
o 7
102-925
45
46
20-88465
19-85603
I-02862
o 6|
102-862
46
47
21-04294
20-01581
I-027I3
o 6
102713
47
48
21-19513
20-17033
I -02480
o 5f
102-480
48
49
21-34147
20-31978
I-02I69
o 5
102-169
49
50
21-48218
20-46434
I-OI784
o 4*
101784
50
clxxvi
THE ENGINEER'S VALUING ASSISTANT.
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
interest on Capital
and for Redemp-
tion being
5 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
5 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings,
and Pence
Rate per Cent.
lo*t on the Pur-
chase of every
i Annuity
by the old Table
Years
s. d.
I
95238
95238
ooooo
O
ooo
I
2
1-85941
I -84294
01647
004
1-647
2
3
272325
2-67716
04609
Il
4-609
3
4
3-54595
3-45988
08607
I 8f
8-607
4
5
4-32948
4-I9543
13405
028
13-405
5
6
5-07569
4-88765
18804
3 9i
18*804
6
7
578637
5-53997
24640
o 4 ii|
24*640
7
8
6-46321
6-15550
30771
o 6 if
30771
8
9
7-10782
673701
37081
o 7 5
37-081
9
10
772174
7-28701
'43473
o 8 Si
43-473
10
ii
8-30641
7-80778
49863
o 9 n|
49-863
ii
12
8-86325
8-30137
56188
II 2f
56-188
12
13
9-39357
8-76966
62391
12 5f
62-391
13
H
9-89864
9-21435
68429
o 13 8i
68-429
H
15
10-37966
9-63701
74265
o 14 10
74-265
15
16
10-83777
10-03907
79870
o 15 n
79-870
16
17
11-27407
10-42182
85225
o 17 oj
85-225
17
18
11-68959
1078647
90312
o 18 of
90-312
18
19
12-08532
II-I34I4
95II8
o 19 o
95-118
19
20
I2-4622I
11-46582
99639
o 19 ii
99-639
20
21
I2-82II5
1178248
1/03867
o 9
103-867
21
22
13-16300
12-08497
I -07803
i 6|
107-803
22
23
13-48857
I2-374II
I-II446
2 3l
1 1 1 -446
23
24
13-79864
12*65063
IT480I
2 Ii}
114-861
24
25
14-09395
12-91525
1-17870
3 6f
117-870
'25
26
I4375I9
13-16859
I -20660
4 i*
120-660
26
27
14-64303
13-41126
1-23177
4 7i
123-177
27
28
14-89813
13-64382
I-2543I
5 i
125-431
28
29
I5'I4I07
13-86680
I-27427
5 5l
127-427
29
30
I5-37245
14-08069
1-29176
5 10
129-176
30
31
I5-5928I
14-28593
I-30688
6 i$
130-688
31
32
15-80268
14-48297
I-3I97I
6 4f
131-971
32
33
16-00255
14-67220
1-33035
6 7i
133-035
33
34
16-19290
I4-85399
.I-3389I
6 9*
133-891
34
35
16-37419
15-02871
I-34548
6 ii
134-548
35
36
16-54685
15-19669
I-350I6
7 o
135-016
36
37
16-71129
15-35824
I-35305
7 of
135-305
37
38
16-86789
15-51366
I-35423
7 i
135-423
38
39
17-01704
15-66322
I-35382
7 of
135-382
39
4O
17-15909
15-80718
I-35I9I
7 oj
135-191
40
41
17-29437
15-94581
1-34856
6 11$
134-856
4i
42
17-42321
16-07932
I-34389
6 ioi
134-389
42
43
I7-5459I
16-20795
1-33796
6 9
133796
43
44
17-66277
16-33190
1-33087
6 7i
133-087
44
45
1777407
16-45138
I-32269
6 5].
132-269
45
46
17-88007
16-56657
I-3I350
6 31
131-350
46
47
17-98101
16-67764
I-30337
6 oi-
130-337
47
48
18-07716
1678478
1-29238
5 i;
129-238
48
49
18-16872
16-88814
1-28058
5 6j-
128-058
49
50
J8-25593
16-98788
I-26805
5 4*
126-805
50
TABLE XII.
clxxvii
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capital
and for Redemp-
tion being
8 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
8 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings.
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
*. d.
I
92593
92593
ooooo
000
ooo
I
2
178327
174639
03688
009
3-688
2
3
2-577IO
2-47813
09897
1 Ilf
9-897
3 .
4
3-3I2I3
3'i3453
17760
o 3 6|
17760
4
5
3-99271
372641
26630
054
26-630
5
6
4-62288
4-26262
36026
o 7 2 |
36*026
6
7
5'20637
47545
45592
o 9 i
45-592
7
8
5-74664
5-19598
55066
II 0|
55-066
8
9
6-24689
5-60432
64257
12 10^
64-257
9
10
671008
5-97977
73031
o 14 7i
73-031
10
ii
7-I3896
6-32601
81295
o 16 3
81-295
ii
12
7-53608
6-64619
88989
o 17 9i
88-989
12
1 3
7-90378
6-94302
96076
o 19 2
96-076
13
14
8-24424
7-21884
I'02540
o 6
102-540
14
15
8-55948
7-47571
1-08377
i 8
108-377
15
16
8-85137
771540
I-I3597
2 8
113-597
16
17
9-12164
7-93950
I-I82I4
3 7f
118-214
17
18
9-37189
8-14938
I-2225I
4 5i
122-251
18
19
9-60360
8-34628
I-25732
5 1%
125732
19
20
9-8l8l5
8-53128
1-28687
5 8|
128-687
20
21
I0'0l68o
870536
i'3 II 44
6 2|
131-144
21
22
IO-2OO74
8-86938
1-33136
6 7
133-136
22
23
10-37106
9-02414
1-34692
6 n|
134-692
23
24
10-52876
9-17032
I-35844
7 2
I35-844
24
25
10-67478
9-30857
1-36621
7 4
136-621
25
26
10-80998
9-43946
1-37052
7 5
137-052
26
27
10-93517
9-56350
1-37167
7 Si
137-167
27
28
II-05I08
9-68118
1-36990
7 4f
136-990
28
29
11-15841
979291
1-36550
7 31
136-550
29
30
11-25778
9-89910
135868
7 2
135-868
30
31
1 1 '34980
1 0-000 1 1
1-34969
6 iif
134-969
31
32
II-43500
10-09626
I-33874
6 9i
I33-874
32
33
11-51389
10-18785
i -32604
6 6
132-604
33
34
11-58693
10-27517
1-31176
6 2f
131-176
34
35
II-65457
10-35848
i -29609
5 ii
129-609
35
36
II7I7I9
10-43800
27919
5 7
127-919
36
37
II775I8
10-51396
26122
5 2f
126-122
37
38
11-82887
10-58657
24230
4 ioi
124-230
38
39
11-87858
10-65600
22258
4 5*
122-258
39
40
11-92461
1072244
20217
4 o
120-217
40
41
11-96724
1078604
18120
3 7i
118-120
41
42
12-00670
10-84697
1-15973
3 2
115-973
42
43
12-04324
10-90535
1-13789
2 9
113789
43
*44
12-07707
10-96132
1-11575
2 32
111-575
44
45
I2-I0840
11-01501
1-09339
i io
109-339
45
46
I2-I374I
11-06653
1-07088
i 5
107-088
46
47
12-16427
11-11599
1-04828
Hi
104-828
47
48
12-18914
11-16348
1-02566
o 6"
102-566
48
49
I2-2I2I6
11-20911
i -00305
o ok
100-305
49
50
12-23349
11-25296
98053.
o 19 7i
98-053
50
z
clxxviii
THE ENGINEER'S VALUING ASSISTANT.
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capital
and for Redemp-
tion being
10 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
10 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings,
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
*. d.
I
90909
90909
ooooo
000
ooo
I
2
1*73554
1-68745
04809
Il
4-809
2
3
2-48685
2-36111
12574
2 6
12-574
3
4
3-I6987
2-94962
22025
o 4 4|
22-025
4
5
379079
3^795
32284
o 6 5
32-284
5
6
435526 '
3-92777
42749
o 8 6
42749
6
7
4-86842
4-33828
53014
o 10 7i
53-014
7
8
5-33493
470685
62808
12 6|
62-808
8
9
575902
5-03946
71956
o 14 4f
71-956
9
10
6-14457
5-34IOI
80356
o 16 i
80-356
10
ii
6-49506
5-6I553
87953
o 17 7i
87-953
ii
12
6-81369
5-86641
94728
o 18 ii
94-728
12
13
7-10336
6-09646
00690
l
100-690
13
14
7-36669
6-30810
05859
I 2
105-859
H
15
7-60608
6-50336
10272
2 Of
110-272
15
16
7-82371
6-68401
13970
2 9
113-970
16
17
8-02I55
6-85154
I700I
3 4|
H7'ooi
17
18
8-20I4I
7-00728
I94I3
119-413
18
19
8-36492
7-15237
21255
4 3
121-255
19
20
8-51356
7-28780
22576
4 6
122-576
20
21
8-64869
7 4H45
23424
4 8
123-424
21
22
877154
7'533 10
23844
4 9i
123-844
22
23
8-88322
7-64445
23877
4 9i
123-877
23
24
8-98474
7-74909
23565
4 8
123-565
24
25
9-07704
7-84758
22946
4 7i
122-946
25
26
9-16095
7-94040
22055
4 5
122-055
26
27
9-23722
8-02799
20923
4 2i
120-923
27
28
9-30657
8-11075
19582
3 ii
119-582
28
29
9-36961
8-18902
18059
3 7i
118-059
29
30
9-42691
8-26315
16376
3 3i
116-376
30
3 1
9-4790I
8-3334I
14560
2 II
114-560
31
32
9-52638
8-40007
12631.
2 6
112-631
32
33
9-56943
8-46338
I-I0605
2 I*
1 10-605
33
34
9-60858
8-52355
1-08503
i 8i
108-503
34
35
9-64416
8-58080
1-06336
i 3i
106-336
35
36
9-67651
8-63530
I'04I2I
O IO
104-121
36
37
970592
8-68722
roi87o
o 4i
101-870
37
38
973265
8-73673
99592
o 19 ii
99-592
38
39
975696
878396
97300
o 19 Si
97-300
39
40
9-77905
8-82906
94999
o 19 o
94-999
4O
41
979914
8-87214
92710
o 18 6
92-710
41
42
9-81740
8-91332
90408
o 18 i
90-408
42
43
9*83400
8-95270
88130
o 17 7i
88-130
43
44
9-84909
8-99039
85870
17 2i-
85-870
44
45
9-86281
9-02648
83633
o 16 8i
83-633
45
46
9-87528
9-06105
81423
o 16 3r
81-423
46
47
9-88662
9-09417
79245
15 10;
79-245
47
48
9-89693
9-12594
77099
o 15 5
77-099
48
49
9-90630
9-15641
74989
o 14 iif
74'989
49
so
9-91481
9-18565
72916
o 14 7
72-916
50
TABLE XII.
clxxix
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capita
and for Redemp-
tion being
12 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
12 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
Difference in
Excesses of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
*. d.
I
89286
89286
00000
000
ooo
I
2
1-69005
1-63236
05769
I I
I-
5-769
2
3
2-40183
2*25464
I47I9
2 II
14-719
3
4
3-03735
278531
25204
050
25-204
4
5
3-60478
3-24302
36176
072
36-176
5
6
4-06131
3-64169
41962
o 8 4
41-962
6
7
4-56376
3-99191
57185
II 5;
57-185
7
8
4-96764
4-30188
66576
o 13 3
66-576
8
9
5-32825
4-57804
75021
o 15 o
75-021
9
10
5-65022
4-82554
82468
o 16 6
82-468
10
ii
5-93770
5-04853
88917
o 17 9i
88-917
ii
12
6-19437
5-25039
94398
18 10;
r
94-398
12
13
6-42355
5-4339I
98964
o 19 9\
!
98-964
13
6-62817
5-60141
I '02676
O 61
102-676
14
15
6-8I086
575485
I-0560I
i ii
t'
105-601
15
16
6-97399
5-89585
1-07814
i 6|
I
107-814
16
17
7-11963
6-02582
I-0938I
i io
109-381
17
18
7-24967
6-14595
I-I0372
2 Of
110-372
18
19
7-36578
6-25728
I-I0850
2 2
110-850
19
20
7-46944
6-36069
I-I0875
2 2:
110-875
20
21
7-56200
6-45695
I-I0505
2 Ii
110-505
21
22
7-64465
6-54676
I -09789
I IlJ
109-789
22
23
771843
6-63469
I-08374
i 8
108-374
23
24
778432
6-70927
I-07505
i 6
107-505
24
25
7-843I4
678298
i -060 1 6
I 2^
106-016
25
26
7-89566
6-85221
1-04345
I0j
104-345
26
27
7-94255
6-91734
1-02521
o 6
102-521
27
28
7-98442
6-97870
1-00572
I;j
100-572
28
29
8-02181
7-03657
98524
o 19 8^
98-524
29
30
8-05518
7-09123
96395
o 19 3^
96-395
30
31
8-08499
7-14291
94208
o 18 10
94-208
31
3 2
8-11159
7-19183
91976
o 1 8 43
91-976
32
33
8-13535
7-23819
89716
o 17 iii
89-716
33
34
8-15656
7-282I6
87440
o 17 5^
87-440
34
35
8-17550
7-32390
85160
o 17 o^
85-160
35
36
8-19241
7-36356
82885
o 16 6|
82-885
36
37
8-20751
7-40129
80622
o 16 iJ
80-622
37
38
8-22099
7-437I9
78380
o 15 8
78-380
38
39
8-23303
7-47I39
76164
o 15 2|
76-164
39
40
8-24378
7-50399
73979
o 14 9;
73-979
40
41
8-25337
7-53509
71828
o 14 4 :
71-828
4i
42
8-26194
7-56477
69717
13 11;
69-717
42
43
8-26959
7-59312
67647
13 6;
67-647
43
44
8-27642
7-020I8
65624
o 13 i.
65-624
44
45
8-28252
7-64613
63639
12 8;
63-639
45
46
8-28796
7-67092
61704
o 12 4
61-704
46
47
8-29282
7-69465
59817
II IlJ
59-817
47
48
8-29716
771737
'57979
o ii 7
57-979
48
49
8-30104
773915
56189
II 2f
56-189
49
so
8-30450
7-76003
'54447
O IO 10^
54-447
50
clxxx
THE ENGINEER'S VALUING ASSISTANT.
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capita'
and for Redernp
tion being
15 per cent.
The new Table o
Present Values,
Interest for Re-
demption being
3 per cent.
and on Capital
15 per cent.
Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
& s. d.
I
86957
86957
ooooo
O O O
ooo
I
2
I-6257I
1-55615
06956
o i 4
6-956
2
3
2-28323
2-11180
I7H3
o 3 5
17*143
3
4
2-85498
2-57052
28446
o 5 8
28-446
4
3-35216
2-95548
39668
o 7 ii
39-668
5
6
3-78448
3-28302
50146
o 10 o
50-146
6
7
4-16042
3-56498
"59544
II lOf
59-544
7
8
4-48732
3-81016
67716
o 13 6
67-716
8
9
4 76287
4-02522
73765
o 14 9
73-765
9
10
5-01877
4-21531
'80346
o 16 9f
80-346
10
ii
5-2337I
4-38448
84923
o 16 nf
84-923
ii
12
5-42062
4-53593
88469
o 17 8
88-469
12
13
5-583I5
4-67225
91090
l8 2
91-090
13
H
5-72448
479556
92892
o 18 6|
92-892
H
15
5-84737
4-90758
'93979
o 18 9!
93-979
15
16
5-95423
5-00975
94448
o 18 io
94-448
16
17
6-04716
5-10328
943 88
o i 8 io
94-388
17
18
6-12797
5-18918
93879
o 18 9
93-879
18
!9
6-19631
5-26832
92799
o 18 6
92-799
19
20
6-25933
5-34I43
91790
o 18 4i
91-790
20
21
6-31246
5-40915
90331
o 18 o ; f
90-331
21
22
6-35866
5-47203
88663
o 17 8}
88-663
22
23
6-39884
5-53055
86829
o 17 4
86-829
23
24
6*43377
5-58511
84866
o 16 n|
84-866
24
25
6-46415
5-63609
82806
o 16 6f
82-806
25
26
6-49056
5-68381
80675
o 16 i^
80-675
26
27
6-5I353
572855
78498
o 15 8i
78-498
27
28
6-5335I
577057
76294
o 15 3
76-294
28
29
6-55088
5-81008
74080
o 14 9l
74-080
29
30
6-56684
5-84729
71955
o 14 4b
71-955
30
3 1
6-57911
5-88239
69672
o 13 ii
69-672
31
32
6-59053
5-91528
67525
o 13 6
67-525
32
33
6-60046
5-94685
65761
o 13 if
65-761
33
34
6-60910
5-97650
63260
12 7f
63-260
34
35
6-61661
6-00459
6l2O2
12 2f
6l'2O2
35
36
6-62314
6-03123
59I9I
II 10
59-I9I
36
37
6-62881
6-05651
57230
on 5i
57-230
37
38
6-63375
608053
55322
II Of
55-322
38
39
6-63805
6-10337
53468
o 10 8
53-468
39
4O
6-64178
6-12511
51667
o 10 4
5I-667
40
41
6-64502
6-14581
49921
o 9 uf
49-92I
41
42
6-64785
6-16554
48231
o 9 7f
48-231
42
43
6-65030
6-18436
46544
o 9 3$
46-594
43
44
6-65244
6-20233
4501 1
090
45-011
44
45
6-65429
6-21948
43481
o 8 8
43-48I
45
46
6-65591
6-23587
42004
o 8 4|
42-OO4
46
47
6-65731
6-25154
40577
o 8 i
40-577
47
48
6-65853
6-26654
39199
o 7 10
39-199
48
49
6-65959
6-28089
37870
076!
37-870
49
50
6-6605 1
6-29463
36588
o 7 3f
36-588
50
TABLE XII.
clxxxi
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capital
and for Redemp-
tion being
1 8 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
1 8 per cent.
The Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
The Difference in
Excess of True
Value on every j
Annuity purchased
by old Table,
in Pounds, Shillings,
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
s. d.
I
84746
84746
00000
O O
*ooo
I
2
1-56564
I -48674
07890
O I 6i
t
7-890
2
3
2-I7427
1-98598
18829
039
18-829
3
4
2-65006
2-38648
26358
o 5 3i
26-358
4
5
3-I27I7
27H78
41239
8 2|
41-239
5
6
3-49760
2-98867 .
50893
10 2
50-893
6
7
3-8II53
3-22055
59098
o ii 9:
|
59-098
7
8
4-07757
3-4I93I
65826
o 13 I;
65-826
8
9
4-30302
3-59152
7II50
14 2i
P
71-150
9
10
4-49409
3-74209
7520O
o 15 o^
75-200
10
ii
4-65601
3-8748I
78120
o 15 7i
78-120
ii
12
4-79322
3-99262
80060
o 16 o
80-060
12
I 3
4-90951
4-09786
8ll65
o 16 2*
I
81-165
13
14
5-00806
4-19241
81565
o 16 33
!
81-565
14
15
5-09158
4-27777
81381
o 16 3^
f
81-381
15
16
5-16235
4-355I9
80716
o 16 i^
1
80-716
16
17
5-22233
4-42571
79662
o 15 ii
79-662
17
18
5-27I77
4-49017
78l6o
o 15 7j
78-160
18
I 9
5-31624
4-54930
76694
o 15 4
76-694
19
20
535275
4-60372
74903
o 14 ii^
L
i
74-903
20
21
538368
4^5394
72974
o 14 7
72-974
21
22
2 3
5-40990
5-432I2
4-70041
70949
68860
o 14 2
o 13 9i
70-949
68-860
22
23
24
5-45095
4-78360
66735
o 13 4
66-735
24
2 5
5-46691
4-82095
64596
12 II
64-596
25
26
5-48043
4-85582
62461
o 12 53
62-461
26
27
5-49189
4-88844
60345
o 12 o;
60-345
27
28
5-50160
4-91900
58260
o ii ji
58-260
28
29
5-50983
4-94769
56214
II 2':
56-214
29
30
5-51681
4-97465
54216
o 10 10
54-216
30
31
5-52272
5-00003
52269
I0 5^
52-269
31
3 2
5-52773
5-02395
50378
o 10 of
50-378
32
33
34
5-53I97
5-53557
5-04653
5-06786
48544
46771
098.
o g 4i
48-544
46-771
33
34
35
5-53862
5-08804
45058
090
45-058
35
36
5-54089
5-10715
'43374
088
43'374
36
37
5-54327
5-12527
41800
084:
41-800
37
38
5-54525
5-14246
40279
o 8 01
r
40-279
38
39
5-54682
5-15879
38803
079
38-803
39
40
5-548I5
5- 1 743 I
37384
o 7 5i
37384
40
4*
5-54928
5-18908
36020
072;
36-020
41
42
5-55024
5-20314
34710
6 II:
34-710
42
43
5-55I05
5-21654
33451
068:
33-45I
43
44
S'SSW
5-22931
32243
065;
32-243
44
45
5-55232
5-24150
31082
6 2.
31-082
45
46
5-55281
5-253I3
29978
o 5 iii
29-978
46
47
5-55322
5-26425
28897
059:
28-897
47
48
5-55359
5-27488
27871
056^
;
,
27-871
48
49
5-28505
26884
o 5 4i
26-884
49
50
5'554!4
5-29477
25937
o 5 2\
i
25-937
50
clxxxii
THE ENGINEEK'S VALUING ASSISTANT.
Comparison of the Difference in Value between the old or ordinary
Table of Present Values, and those calculated at one rate of interest on Capital,
and at another rate for its Redemption, at the following rates.
Years
The ordinary or
old Table of
Present Values,
Interest on Capital
and for Redemp-
tion being
20 per cent.
The new Table of
Present Values,
Interest for Re-
demption being
3 per cent,
and on Capital
20 per cent.
The Difference in
Excess of True
Value on every
i Annuity
purchased by old
Table, in Decimals
of a Pound
The Difference in
Excess of True
Value on every i
Annuity purchased
by old Table,
in Pounds, Shillings,
and Pence
Rate per Cent,
lost on the Pur-
chase of every
i Annuity
by the old Table
Years
s. d.
I
83333
83333
00000
000
ooo
I
2
1-52778
I-4438I
08397
I 8
8-397
2
3
2-10648
I-9IOII
19637
o 3 ii
19-637
3
4
2-58873
2-27776
31097
o 6 2*
31-097
4
5
2-99061
2-57497
41564
o 8 3f
41-564
5
6
3-3255I
2-82010
50541
10 l
50-541
6
7
3-60459
3-02566
57893
o ii 6|
57-893
7
8
3-83716
3 -20045
63671
12 8|
63-671
8
9
4'03097
3-35083
68014
o 13 7
68-014
9
10
4-I9247
3-48152
71095
14 2
71-095
10
ii
4-32706
3-59612
73094
o H 7i
73-094
ii
12
4-43922
3-69738
74184
o 14 10
74-184
12
13
4-53268
378745
74523
o 14 lof
74-523
13
H
4-61057
3-86808
74249
o 14 10
74-249
H
15
4-67547
3-94063
73484
o 14 8
IS
16
472956
4-00624
72332
c H sl
72-332
16
17
4-77463
4-06583
70880
14 2
70-880
17
18
4-81219
4-12017
69202
o 13 10
69-202
18
19
4-84584
4-16990
67594
o 13 6
67-594
19
20
4-86887
4-21557
65330
o 13 of
65330
20
21
4-89132
4-25764
63368
12 8
21
22
4-90943
4-29650
61293
o 12 3
61-293
22
23
4^453
4-33249
59204
II 10
59-204
23
24
4-937IO
4-36591
57II9
o ii 5
57-119
24
25
4-94759
4-397oo
55059
II
55-059
25
26
4-95632
4-42599
53033
o 10 j\
53'033
26
27
4-96360
4-45307
51053
10 2
27
28
4-96967
4-47842
49125
o 9 9f
49-125
28
29
4-97472
4-50218
47254
9 Si
29
30
4-97894
4-52449
'45445
091
45*445
30
31
4-98245
4-54548
43697
o 8 8|
31
32
4-56524
42013
084!
42-013
32
33
4-98784
4-58387
40397
o 8 of
40-397
33
34
4-98984
4-60147
38837
079
38-837
34
35
4-99154
4-61810
'37344
o 7 Si
37*344
35
36
4-99295
4-63384
359H
072
36
37
4-994I2
4-64875
'34537
o 6 iof
34*537
37
38
4-995IO
4-66289
33221
o 6 7^
33-221
38
39
4-99592
4-67631
31961
064!
31-961
39
40
4-99660
4-68906
30754
o 6 if
30-754
40
41
4-997I7
4-70118
29597
o 5 ii
29-597
41
42
4-99764
4-71272
28492
5 8
28-492
42
43
4-99803
4-72371
27432
o 5 5l
27-432
43
44
4-99836
4-73418
26418
o 5 3i
26-418
44
45
4-99863
474417
25446
o 5 i
25-446
45
46
4-99886
475370
24516
o 4 io|
24-516
46
47
4-99905
4-76280
23625
o 4 8
23-625
47
48
4-9992I
477150
22771
o 4 6
22771
48
49
4-99934
477981
21953
044}
21-953
49
50
4-99945
478777
21168
o 4 2|
21-618
50
TABLE XIII.
The Present Value (or Tears' Purchase) of 1 per
annum in n years; Redemption of Capital being at 2,
2^, 3, and 3^ per cent., with interest allowed to a present
purchaser upon his purchase money, or capital invested,
at the same rates per cent.
Calculated to 5 places of decimals, and to 100 years for
each percentage.
TABLE XIII.
clxxxv
Present Value of 1 per Annum in n years, Redemption of Capital
being at 2 and 2^ per cent., with Interest allowed to a Purchaser at the
same rates per cent.
n
Years
2 per cent.
n
Years
2 per cent.
n
Years
2i per cent.
n
Years
2J per cent.
I
98039
51
3178785
I
97561
51
28-64616
2
I-94I5 6
52
32-14495
2
1-92742
52
28-92308
3
2-88388
53
32-49505
3
2-85602
53
29-19325
4
3-80773
54
32-83828
4
376197
54
29-45683
5
471346
55
33-17479
5
4-64583
55
2971398
6
5-60143
56
33-50469
6
5-50813
56
29-96456
7
6-47I99
57
33-82813
7
6-34939
57
30-20962
8
7-32548
58
34-I5523
8
7-17014
58
30-44841
9
8-16224
59
34-45610
9
7-97087
59
30-68137
10
8-98259
60
34-76089
10
8-75206
60
30-90866
ii
978685
61
35-05969
ii
9-51421
61
31-13040
12
10-57534
62
35-35264
12
10-25777
62
31-34673
13
II-34837
63
35^3984
13
10-98319
63
3I-55778
H
12-10625
64
35-92142
H
1 1 '6909 1
64
3176369
15
12-84926
65
36-19747
J 5
12-38138
65
31-96458
1 6
I3-5777I
66
36-46810
16
13-05500
66
32-16056
17
14-29187
67
3673344
17
13-71220
67
32-35I77
18
14-99203
68
36-99356
18
I4-35336
68
32-5383I
*9
15-67846
69
37-24859
19
14-97889
69
3272031
20
16-35143
7O
37-49862
20
15-58916
70
32-89786
21
17-01121
71
3774374
21
16-18455
71
33-07I08
22
17-65805
72
37-98406
22
1676541
72
33-24008
23
18-29220
73
38-21967
23
17-32211
73
33-40495
24
18-91393
74
38-45066
24
17-88499
74
33-5658I
25
19-52346
75
38-67711
25
18-42438
75
3372274
26
20-12104
76
38-89913
26
18-95061
76
33^7584
27
20-70690
77
39-11680
27
19-46401
77
34-0252I
28
21-28127
78
39'33 OI 9
28
19-96489
78
34-17094
2 9
21-84439
79
39-53940
29
20-45355
79
34-3I3II
30
22-39646
80
39-7445I
3O
20-93029
so
34-45182
3 1
22-93770
8l
39-94560
31
21-39541
81
34-587I4
32
23-46834
82
40-14275
32
21-84918
82
3471916
33
23-98856
83
40-33603
33
22-29188
83
34-84796
34
24-49859
84
40-52552
34
2272379
84
34-97362
35
24-99862
85
40-71129
35
23-14516
85
35-09622
36
25-48884
86
40-89342
36
23-55625
86
35-2I582
37
25-96945
87
41-07198
37
23-95732
87
353325I
38
26-44064
88
41-24704
38
24-34860
88
35-44635
39
26-90259
89
41-41867
39
24-73034
89
35-55741
40
27-35548
90
41-58693
40
25-10278
90
35-66577
4i
2779949
91
4175189
41
25-46612
91
3577148
4 2
28-23479
92
41-91362
42
25-82061
92
35-87462
43
28-66156
93
42-07218
43
26-16645
93
35-97524
44
29-07996
94
42-22762
44
26-50385
94
36-07340
45
29-49016
95
42-38002
45
26-83302
95
36-16917
46
29-89231
96
42-52943
46
27-15417
96
36-26261
47
30-28658
97
42-67592
47
27-46748
97
36-35376
48
30-67312
98
42-81953
48
27-773 1 5
98
36-44269
49
31-05208
99
42-96032
49
28-07137
99
36-52946
50
31-42361
100
43-09835
50
28-36231
100
36-61411
a a
clxxxvi
THE ENGINEERS VALUING ASSISTANT,
Present Value of 1 per Annum in n years, Redemption of Capital
being at 3 and 3J per cent., with Interest allowed to a Purchaser at the
same rates per cent.
n
Years
3 per cent.
n
Years
3 per cent. ]
n
Years
3i per cent.
n
Years
3i per cent.
I
97087
51
25-95123
I
96618
51
23-62862
2
1-91347
52
26-16624
2
I -89969
52
23-79577
3
2'8286l
53
26-37499
3
2-80164
53
23-95726
4
37I7IO
54
26-57766
4
3-67308
54
24-11330
5
4-5797I
55
26-77443
5
4-51505
55
24-26405
6
5-41719
56
26-96546
6
5-32855
56
24-40971
7
6-23028
57
27-15094
7
6-11454
57
24-55045
8
7-01969
58
27-33101
8
6-87396
58
24-68642
9
7786II
59
27-50583
9
7-60769
59
24-81780
10
8-53020
60
27-67556
10
8-31661
60
24-94473
ii
9-25262
61
27-84035
ii
9-00155
61
25-06738
12
9-95400
62
28*00034
12
9-66333
62
25-18587
13
10-63496
63
28-15567
13
10-30274
63
25-30036
14
1 1 -29607
64
28-30648
14
10-92052
64
25-41097
15
11-93794
65
28-45289
15
II-5I74I
65
25-51785
16
12-56100
66
28-59504
16
12-09412
66
25-62111
17
I3-l66l2
67
2873305
17
12-65132
67
2572088
18
I37535 1
68
28-86704
18
13-18968
68
25-81726
19
14-32380
69
28-99712
19
1370984
69
25-91041
20
14-87748
70
29-12342
20
14-21240
70
26*00040
21
15*41502
71
29-24604
21
14-69797
71
26-08734
22
15-93692
72
29-36509
22
15-16713
72
26-17134
23
16-44361
73
29-48067
23
15-62041
73
26*25251
24
16-93554
74
29-59288
24
16-05837
74
26-33092
25
17-41315
75
29-70183
25
16-48152
75
26-40669
26
17-87684
76
29-80760
26
16-89035
76
26-47989
27
18-32703
77
29-91029
27
17-28537
77
26-55062
28
18*76412
78
30-OIOOO
28
17-66702
78
26-61896
29
19-18856
79
30-10679
29
18^3577
79
26-68498
30
19-60044
80
30-20076
30
18-39205
80
26-74878
3 1
20-00043
81
30-29200
31
1873628
81
26-81041
32
20-38877
82
30-38059
32
19-06887
82
26-86996
33
20-76579
83
30-46659
33
19-39021
83
26-92750
34
21-13184
84
30-55009
34
19-70068
84
26-98309
35
21-48722
85
30-63115
35
20-00066
85
27-03680
36
21-83225
86
30-70986
36
20-29049
86
27-08870
37
22-16724
87
3078627
37
20-57053
87
27-13884
38
22-49246
88
30-86045
38
20-84109
88
27-18729
39
22-80822
89
30-93248
39
21-10258
89
27-23409
40
23-11477
90
31-00241
40
21-35507
90
27-27932
41
23-41240
91
31-07030
41
21^59910
91
27-32301
42
23-70136
92
31-13621
42
21-83488
92
27-36523
43
23-98190.
93
31-20021
43
22-06269
93
27-40602
44
24-25427
94
31-26234
44
22-28279
94
27'45543
45
24-51871
95
31'32266
45
22-49545
95
27-48350
46
2477545
96
31-38122
46
22-70092
96
27-52029
47
25-02471
97
31-43808
47
22-89944
97
27-55584
48
25-26671
98
31-49328
48
23-09124
98
27-59018
49
25-50166
99
31-54687
49
23-27656
99
27-62337
SO
2572976
100
3I-5989I
SO
23-45562
100
27'65543
TABLE XIV.
Multiples of the Present Value of 1 per annum m
n years. Available Interest on Capital, 21 per cent.,
Redemption being at the rate of 3 per cent.
Calculated to 9 places of decimals.
TABLE XIV.
clxxxix
Multiples of the Present Value of 1 per Annum in n years. Interest on Capital
21 per cent., Redemption 3 per cent.
Years
Annuity i,
10, 100, 1000 or
106,000,000
Years
Annuity i,
10, 100, 1000 or
100,000,000
Years
Annuity 2,
20, 200, 2000 or.
200,000,000
Years
Annuity 2,
20, 200, 2000 or
200,000,000
I
826446280
51
4-575950694
I
1-652892560
51
9-151901388
2
1-423262988
52
4-582590532
2
2-846525976
52
9-165181064
3
1-874304059
53
4-588951424
3
3748608118
53
9-177902848
4
2-227037348
54
4-595047977
4
4-454074696
54
9-190095954
5
2-510326407
55
4-600893831
5
5-020652814
55
9-201787662
6
2742750563
56
4-606501736
6
5-485501126
56
9-213003472
7
2-936802761
57
4-611883630
7
5-873605522
57
9-223767260
8
3-101194563
58
4-617050690
8
6-202389126
58
9-234101380
9
3-242186216
59
4-622013405
9
6-484372432
59
9-244026810
10
3-364392206
60
4-626781616
10
6728784412
60
9-253563232
ii
3-47I288737
61
4-631364575
ii
6-942577474
61
9-262729150
12
3'5 6 5544335
62
4-635770791
12
7-131088670
62
9-271541582
13
3-649241557
63
4-640009037
13
7-298483114
63
9-280018074
H
3-724029470
64
4-644086453
H
7-448058940
64
9-288172906
15
3791230860
65
4-648010514
15
7-582461720
65
9-296021028
16
3-851919142
66
4-651788088
16
7703838284
66
9-303576176
17
3-906974478
67
4-655425670
17
7-813948956
67
9-310851340
18
3-957125402
68
4-658929397
18
7-914250804
68
9-317858794
19
4-002980129
69
4-662305077
19
8-005960258
69
9-324610154
20
4-045050412
70
4-665558205
20
8-090100824
70
9-33III64IO
21
4-083769939
71
4-668693992
21
8-167539879
71
9-337387984
22
4-119508680
72
4-671717378
22
8-239017360
72
9-343434756
23
4-152584168
73
4-674633046
23
8-305168336
73
9-349266092
24
4-183270487
74
4-677445445
24
8-366540974
74
9-354890890
25
4-211805445
75
4-680158806
25
8-423610890
75
9-360317612
26
4-238396399
76
4-682777136
26
8-476792798
76
9-365554272
27
4-263224976
77
4-685304265
27
8-526449952
77
9-370608530
28
4-286450941
78
4-687743826
28
8-572901882
78
9375487652
29
4-308215397
79
4-690099281
2 9
8-616430794
79
9-380198562
30
4-328643434
80
4-692373931
30
8-657286868
80
9-384747862
31
4-347846336
81
4-694570917
31
8*695692672
81
9-389141834
32
4-365923441
82
4-696693240
32
8731846882
82
9-393386480
33
4-382963699
83
4-698743762
33
8765927398
83
9-397487524
34
4-399046995
84
4700725212
34
8-798093990
84
9-401450424
35
4-414245285
85
4-702640204
35
8-828490570
85
9-405280408
36
4-428623547
86
4704491229
36
8-857247094
86
9-408982458
37
4-442240611
87
4-706280668
37
8-884481222
87
9-412561336
38
4-455149870
88
4-708010803
38
8-910299740
88
9-416021606
39
40
4'467399898
4-479034978
89
90
4709683816
47II30I793
39
40
8'934799796
8-958069956
89
90
9-419367632
9-422603586
41
4-490095567
91
4712866734
41
8-980191134
91
9-425733468
42
4-500618704
92
4-714380553
42
9-001237408
92
9-428761 106
43
4-510638357
93
4715845084
43
9-021276714
93
9-431693168
44
4-520185743
94
4717262091
44
9-040371486
94
9-434524182
45
4-529289599
95
4718633256
45
9-058579198
95
9-437266512
46
4-5379764I8
96
4719960199
46
9-075952836
96
9-439920398
47
4-546270673
97
4721244475
47
9-092541346
97
9-442488950
48
4-554I95002
98
4722487574
48
9-108390004
98
9-444975148
49
4-561770374
99
4-723690927
49
9-123540748
99
9-447381854
50
4-569016247
100
4-724855909
SO
9-138032494
100
9-449711818
cxc
THE ENGINEER'S VALUING ASSISTANT.
Multiples of the Present Value of 1 per Annum in n years. Interest on Capital
21 per cent., Redemption 3 per cent.
Years
Annuity 3,
30, 300, 3000 or
300,000,000
Years
Annuity 3,
30, 300, 3000 or
300,000,000
Years
Annuity 4,
40, 400, 4000 or
400,000,000
Years
Annuity 4,
40, 400, 4000 or
400,000,000
I
2-479338840
51
13-727852082
!
3-305785120
51
18-303802776
2.
4-269788964
52
I374777I596
2
5-693051952
52
18-330362128
3
5-622912177
53
13766854272
3
7-497216236
53
18-355805696
4
6*681112044
54
I3785I4393I
4
8-908149392
54
18-380191908
5
7-530979221
55
13-802681493
5
10-041305628
55
18-403575324
6
8-228251689
56
13-819505208
6
10-971002252
56
18-426006944
7
8-810408283
57
13-835650890
7
II7472II044
57
18-447534520
8
9-303583689
58
13-851152070
8
12-404778252
58
18-468202760
9
9726558648
59
13-866040215
9
12-968744864
59
18-488053620
10
10-093176618
60
13-880344848
10
13-457568824
60
18-507126464
ii
10-413866211
61
13-894093725
ii
13-885154948
61
18-525458300
12
10-696633005
62
13-907312373
12
14-262177340
62
18-543083164
13
10-947724671
63
13-920027111
13
14-596966228
63
18-560036148
H
11-172088410
64
13-932259359
14
14-896117880
64
18-576345812
15
11-373692580
65
13-944031542
15
15-164923440
65
18*592042056
16
II'555757426
66
I3-955364264
16
15-407676568
66
18-607152352
17
11720923434
67
13-966277010
17
15-627897912
67
18-621702680
18
11-871376206
68
13-976788191
18
15-828501608
68
18-635717588
19
12*008940387
69
13-986915231
19
16-011920516
69
18-649220308
20
12-135151236
70
13-996674615
20
16-180201648
70
18-662232820
21
12-251309817
71
14-006081976
21
16-335079756
71
18-674775968
22
12-358526040
72
14-015152134
22
16-478034720
72
18-686869512
23
12-457752504
73
14-023899138
23
16-610336672
73
18-698532184
24
12-549811461
74
14-032336335
24
16733081948
74
18709781780
25
12-635416335
75
14-040476418
25
16-847221780
75
18720635224
26
12715189197
76
14-048331408
26
I6-953585596
76
18731108544
27
12-789674928
.77
14-055912795
27
17-052899904
77
18741217060
28
12-859352823
78
14-063231478
28
17-145803764
78
18750975304
29
12-924646191
79
14-070297843
29
17-232861588
79
18760397124
30
12-985930302
so
14-077121793
3O
17-314573736
80
18-769495724
31
i3-o435398
81
14-083712751
31
I7-39I385344
81
18778288668
32
13-097770323
82
14-090079720
32
17-463693764
82
18786772960
33
13-148891097
83
14-096231286
33
17-531854796
83
18-794975048
34
13-197140985
84
14-102175636
34
17-596187980
84
18-802900848
35
13-242735855
85
14-107920612
35
17-656981140
85
18-810560816
36
13-285870641
86
14-113473687
36
I77I4494I88
86
18-817964916
37
13-326721833
87
14-118842004
37
17-768962444
87
18-825122672
38
13-365449610
88
14-124032409
38
17-820599480
88
18-832043212
39
13-402199694
89
14-129051448
39
17-869599592
89
18-838735264
4O
13-437104934
90
14-133905379
40
17-916139912
90
18*845207172
41
13-470286701
91
I4-I386002O2
41
17-960382268
91
18-851466936
42
13-501856112
92
14-143141659
42
18-002474816
92
18-857522212
43
i3'53 I 9 I 57l
93
I4-I47535252
43
18-042553428
93
18-863380336
44
13-560557229
94
14-151786273
44
18-080742972
94
18-869048364
45
13-587868797
95
14-155899768
45
18-117158396
95
18-874533024
46
13-613929254
96
14-159880597
46
18-151905672
96
18-879840796
47
13-638812019
97
I4-I63733425
47
18-185082692
97
18-884977900
48
13-662585006
98
14-167462722
48
18-216780008
98
18-889950296
49
13-685311122
99
14-171072781
49
18-247081496
99
18-894763708
50
13-707048741
100
14-174567727
50
18-276064988
LOO
18-899423636
TABLE XIV.
cxci
Multiples of the Present Value of 1 per Annum in n years. Interest on Capital
21 per cent., Redemption 3 per cent.
Years
Annuity 5,
50, 500, 5000 or
500,000,000
Years
Annuity 5,
50, 500, 5000 or
500,000,000
Years
Annuity 6,
60, 600, 6000 or
600,000,000
Years
Annuity 6,
60, 600, 6000 or
600,000,000
I
4-132231400
51
22-879753470
I
4-958677680
51
27-455704164
2
7-116314940
52
22-912952660
2
8-539577928 '
52
27-495543I92
3
9-371520295
53
22-944757I20
3
11-245824354
53
27-533708544
4
11-135186740
54
22-975239885
4
13-362224088
54
27-570287862
5
12-551632035
55
23-004469155
5
15-061958442
55
27-605362986
6
13713752815
56
23-032508680
6
16-456503378
56
27-639010416
7
14-684013805
57
23-059418150
7
17-620816566
57
27-671301780
8
15-505972815
58
23-085253450
8
18-607167378
58
27-702304140
9
16-210931080
59
23-110067025
9
19-453117296
59
27-732080430
10
16-821961030
60
23-133908080
10
20-186353236
60
27-760689696
ii
17-356443685
61
23-156822875
ii
20-827732422
61
27788187450
12
17-827721675
62
23-I78853955
12
21-393266010
62
27-814624746
13
18-246207785
63
23-200045185
13
21-895449342
63
27-840054222
14
18-620147350
64
23-220432265
H
22-344176820
64
27-864518718
15
18-956154300
65
23-240052570
15
22747385160
65
27-888063084
16
19-259595710
66
23-258940440
16
23-111514852
66
27-910728528
17
19-534872390
67
23-277128350
17
23-441846868
67
27-932554020
18
19-785627010
68
23-294646985
18
23742752412
68
27-953576382
19
20-014900645
69
23-311525385
19
24-017880774
69
27-973830462
20
20-225252060
70
23-327791025
20
24-270302472
7O
27-993349230
21
20-418849695
71
23-343469960
21
24-502619634
71
28-012163952
22
20-597543400
72
23-358586890
22
24717052080
72
28-030304268
23
20762920840
73
23-373165230
23
24-915505008
73
28-047798276
24
20-916352435
74
23-387227225
24
25-099622922
74
28-064672670
25
21-059027225
75
23-400794030
25
25-270832670
75
28-080952836
26
21-191981995
76
23-413885680
26
25-43 378394
76
28-096662816
27
21-316124880
77
23-426521325
27
25-579349856
77
28-111825590
28
21-432254705
78
23-438719130
28
25718705645
78
28-126462956
29
21-541076985
79
23-450496405
29
25-849292382
79
28-140595686
30
21-643217170
80
23-461869655
3O
25-971860604
80
28-154243586
31
21-739231680
8l
23-472854585
31
26-087078016
81
28-167425502
32
21-829617205
82
23-483466200
32
26-195540646
82
28-180159440
33
21-914818495
83
23-4937I88IO
33
26-297782194
83
28-192462572
34
21-995234975
8 4
23-503626060
34
26-394281970
84
28-204351272
35
22-071226425
85
23-513201020
35
26-485471710
85
28-215841224
36
22-143117735
86
23-522456146
36
26-571741282
86
28-226947374
37
22-211203055
87
23-531403340
37
26-653443666
87
28-237684008
38
22-275749350
88
23-540054015
38
26730899220
88
28-248064818
39
22-336999490
89
23-548419080
39
26-804399388
89
28.258102896
40
22-395174890
90
23-556508965
40
26-874209868
90
28-267810758
41
22-450477835
91
23-564333670
41
26-940573402
91
28-277200404
42
22-503093520
92
23-571902765
42
27-003712224
92
28-286283318
43
22-553191785
93
23-579225420
43
27-063830142
93
28-295070504
44
22-600928715
94
23-586310455
44
27-121114458
94
28-303572546
45
22-646447995
95
23-593I66280
45
27'175737594
95
28-311799536
46
22-689882090
96
23-599800995
46
27-227858508
96
28-319761194
47
22731353365
97
23-606222375
47
27-277624038
97
28-327466850
48
22770975010
98
23-612437870
48
27-325170012
98
28-334925444
49
22-808851870
99
23-618454635
49
27-370622244
99
28-342145562
50
22-845081235 -loo
23-624279545
so
27-414097482
100
28-3491 35454
CXC11
THE ENGINEER'S VALUING ASSISTANT.
Multiples of the Present Value of 1 per Annum in n years.
21 per cent., Redemption 3 per cent.
Interest on Capital
Years
Annuity 7,
70, 700, 7000 or
700,000,000
Years
Annuity 7,
70, 700, 7000 or
700,000,000
Years
Annuity 8,
80, 800, 8000 or
800,000,000
Years
Annuity 8,
80, 800, 8000 or
800,000,000
I
5785123960
51
32-031654858
I
6*611570240
51
36-607605552
2
9-962840916
52
32-078133724
2
11-386103904
S 2
36*660724256
3
13-120128413
53
32-122659968
3
14-994432472
53
36711611392
4
15-589261436
54
32-165335839
4
17-816298784
54
36760383816
5
17-572284849
55
32-206256817
5
20*082611256
55
36-807150648
6
19-199253941
56
32-245512152
6
21-942004504
56
36-852013888
7
20-557619327
57
32-283185410
7
23-494422088
57
36-895069040
8
21708361941
58
32-319354830
8
24-809556504
58
36-936405520
9
22-695303512
59
32-354093835
9
25'937489728
59
36-976107240
10
23-550745442
60
32-387471312
10
26-915137648
60
37-014252928
ii
24-299021159
61
32-419552025
ii
27-770309896
61
37-050916600
12
24-958810345
62
32-450395537
12
28-524354680
62
37-086166328
13
25-544690899
63
32-480063259
13
29-193932456
63
37-120072296
H
26-068206290
64
32-508605171
H
29-792235760
64
37-152691624
15
26-538616020
65
32-536073598
15
30-329846880
65
37-184084112
16
26-963433994
66
32-562516616
16
30-815353136
66
37-214304704
17
27-348821346
67
32-587979690
17
31-255795824
67
37-243405360
18
27-699877814
68
32-612505779
18
31-657003216
68
37-271435176
19
28-020860903
69
32-636135539
19
32*023841032
69
37-298440616
20
28-315352884
70
32-658907435
20
32-360403296
70
37-324465640
21
28-586389573
71
32-680857944
21
32-670159512
71
37'34955I936
22
28-836560760
72
32702021646
22
32-956069440
72
37-373739024
23
29-068089176
73
32722431322
23
33-220673343
73
37-397064368
24
29-282893409
74
32742118115
24
33-466163896
74
37-419563560
25
29-482638115
75
32-761111642
25
33-694443560
75
37-441270448
26
29-668774793
76
32779439952
26
33-907171192
76
37-462217088
27
29-842574832
77
32797129855
27
34-105799808
77
37-482434120
28
30-005156587
78
32-814206782
28
34-291607528
78
37-501970608
29
30-157507779
79
32-830694967
29
34-465723176
79
37-520794248
30
30-300504038
80
32-846617517
30
34-629147472
80
37-538991448
3 1
30-434924352
8 1
32-861996419
31
34782770688
81
37-556567336
32
30-561464087
82
32-876852680
32
34-927387528
82
37-573545920
33
30-680745893
83
32*891206334
33
35-063709592
83
37-589950096
34
30-793328965
84
32-905076484
34
35-192375960
84
37-605801696
35
30-899716995
85
32-918481428
35
35-313962280
85
37-621121632
36
31-000364829
86
32-931438603
36
35-428988376
86
37-635929832
37
31-095684277
87
32-943964676
37
35-537924888
87
37-650245344
38
31-186049090
88
32-956075621
38
35-641198960
88
37^664086424
39
31-271799286
89
32-967786712
39
35739 I 99 J 84
89
37-677470528
40
31-353244846
90
32-979112551
40
35-832279824
90
37-690414344
41
31-430668969
91
32-990067138
41
35-920764536
91
37-702933872
42
31-504330928
92
33-000663871
4 2
36-004949632
92
37715044424
43
31-574468499
93
33-010915588
43
36-085106856
93
37726760672
44
31-641300201
94
33-020834637
44
36-161485944
94
37738096728
45
31-705027193
95
33-030432792
45
36-234316792
95
37-749066048
46
31-765834926
96
33-039721393
46
36-303811344
96
37759681592
47
31-823894711
97
33-048711325
47
36-370165384
97
37769955800
48
31-879635014
98
33-057413018
48
36-433560016
98
37-779900592
49
31-932392618
99
33-065836489
49
36-494162992
99
37789527416
50
31-983113729
100
33-073991363
50
36-552129976
100
37-798847272
TABLE XIV.
BBS*
CXClll
Multiples of the Present Value of 1 per Annum in n years. Interest on Capital
21 per cent., Redemption 3 per cent.
Year
Annuity q,
90, 900, 9000 o
900,000.000
Years
Annuity 9,
90, 900, 9000 or
900,000,000
Year=
Annuity 10,
100, 1000, io,ooc
or 1000,000,000
Years
Annuity 10,
100, 1000, 10,000
or 1000,000,000
I
7-438016520
51
41-183556246
I
8-264462800
51
45-759506940
2
12-809366892
5 2
41-243314788
2
14-232629880
52
45-825905320
3
16-868736531
53
41-300562816
3
18-743040590
53
45-889514240
4
20-043336132
54
4I-35543I793
4
22-270373480
54
45-950479770
5
22-592937663
55
41-408044479
5
25-103264070
55
46-008938310
6
24-684755067
56
41-458515624
6
27-427505630
56
46-065017360
7
26-431224849
57
41-506952670
7
29-368027610
57
46-118836300
8
27-910751067
58
4I-5534562IO
8
31-011945630
58
46-170506900
9
29-179675944
59
41-598120645
9
32-421862160
59
46*220134050
10
30-279529854
60
41-641034544
10
33- 6 43922o6o
60
46-267816160
ii
31-241598633
61
4I-68228II75
ii
34-7I2887370
61
46-313645750
12
32-089899015
62
4I72I937II9
12
35-655443350
62
46-357707910
13
32-843174013
63
41760081333
13
36-492415570
63
46*400090370
14
33-516265230
64
41796778077
H
37-240294700
64
46-440864530
15
34-I2I077740
65
41-832094626
15
37-912308600
65
46-480105140
1 6
34-667272278
66
41-866092792
16
38-519191420
66
46-517880880
17
35-162770302
67
41-898831030
57
39-069744780
67
46-554256700
18
35-614128618
68
41-930964573
iS
39-57I254020
68
46-589293970
19
36-02682Il6l
69
41-960745693
19
40-029861290
69
46-623050770
20
36-405453708
70
41-990023845
20
40-450504120
70
46-655582050
21
36753929451
71
42-018245928
21
40-837699390
71
46-686939920
22
37-075578120
72
42-045456402
22
4I-I95086800
72
46717173780
23
373732575I2
73
42-071697414
23
41-525841680
73
46746330460
24
37-649434383 .
74
42-097009005
24
41-832704870
74
46-774454450
25
37-906249005
75
42-121429254
25
42-118054450
75
46-801588060
26
38-145567591
76
42-144994224
26
42-383963990
76
46-827771360
27
38-369024784
77
42-167738385
27
42-632249760
77
46-853042650
28
38-578058469
78.
42-189694434
28
42-864509410
78
46-877438260
29
38773938573
79
42-210893529
29
43-082153970
79
46-900992810
30
38-957790906
80
42-231365379
30
43-286434340
80
46-923739310
31
39-130617024
81
42-251138253
31
43-478463360
81
46-945709170
32
39-293310969
82
42-270239160
32
43-659234410
82
46-966932400
33
39-446673291
83
42-288693858
33
43-829636990
83
46-987437620
34
39-591422955
84
42-306526908
34
43-990469950
84
47-007252120
35
39-728207565
85
42-323761836
35
44-143452850
85
47-026402040
36
39-857611923
86
42-340421061
36
44-286235470
86
47-044912290
37
39-980165499
87
42-356526012
37
44-422406110
87
47-062806680
38
40-096348830
88
42-372097227
38
44-551498700
88
47-080108030
39
40*206599082
89
42-387154344
39
44-673998980
89
47-096838160
40
40-311314802
90
42-401716137
40
44-790349780
90
47-113017930
41
40-410860103
91
42-415800606
4i
44-900955670
91
47-128667340
42
40-505568336
92
42-429424977
42
45-006187040
92
47-143805530
43
40-5957452I3
93
42-442605756
43
45-106383570
93
47-158450840
44
40-681671687
94
42-455358819
44
45-20I857430
94
47-172620910
45
40763606391
95
42-467699304
45
45-292895990
95
47-186332560
46
40-841787762
96
42-479641791
46
45'379764l8o
96
47-199601990
47
40-916436057
97
42-491200275
47
45-462706730
97
47-212444750
48
40-987755018
98
42-502388166
48
45'54I950020
98 47-224875740
49
4I-055933366
99
42-513218343
49
45-617703740
99
47-236909270
50
41-121146223
LOO
42-523703181
50
45-690162470
oo
47-248559090
bb
TABLE XV.
MULTIPLES OF KEDEMPTION FUNDS,
At the rate of 3 per cent, per annum, necessary to
produce i, 2, 3, 4, 5, 6, 7, 8, 9, and 10;
or from i to 100,000,000, 2 to 200,000,000, 3 to
300,000,000, etc., up to 10 or 1,000,000,000; and by
employing the decimal system of notation for any
intermediate sum.
Calculated to 10 places of decimals.
TABLE XV.
cxcvn
Multiples of Redemption Funds, at 3 per cent, per Annum, necessary to produce
the following sums in n years.
Years
Sum to produce i,
10, 100, 1000, or
100,000,000
Years
Sum to produce i,
10, 100, 1000, or
100,000,000
Years
Sum to produce 2,
20, 200, 2000, or
200,000,000
Years
Sum to produce 2,
20, 200. 2000, or
200,000,000
I
I -CXDOOOOOOOO
51
0085338232
I
2*0000000000
51
0170676464
2
4926108374
5 2
0082171837
2
9852216748
52
0164343674
3
3235303633
53
0079147059
3
6470607266
53
0158294118
4
2390270452
54
0076255841
4
4780540904
54
0152511682
5
1883545714
55
0073490710
5
3767091428
55
0146981420
6
1545975005
56
0070844726
6
309I9500IO
56
0141689452
7
1305063538
57
0068311432
7
26IOI27076
57
0136622864
8
1124563888
58
0065884819
8
2249127776
58
0131769638
9
0984338570
59
0063559281
9
1968677140
59
0127118562
10
0872305066
60
0061329587
10
I7446IOI32
60
0122659174
ii
0780774478
61
0059190847
ii
1561548956
61
0118381694
12
0704620855
62
0057138575
12
1409241710
62
0114277150
13
0640295440
63
0055168216
13
1280590880
63
oi 10336432
14
0585263390
64
0053276021
H
1170526780
64
0106552042
15
0537665805
65
0051458128
15
I07533l6lO
65
0102916256
16
0496108493
66
0049710995
16
0992216986
66
0099421990
17
0459525294
67
0048031288
17
0919050588
67
0096062576
18
0427086959
68
0046415871
18
0854173918
68
0092831742
19
0398138806
69
0044861787
19
0796277612
69
0089723574
20
0372157076
70
0043366251
20
07443I4I52
70
0086732502
21
0348717765
71
0041926632
21
0697435530
71
0083853264
22
0327473948
72
0040540446
22
0654947896
72
0081080892
23
0308139027
73
0039205345
23
0616278054
73
0078410690
24
0290474159
74
0037919109
24
0580948318
74
0075838218
25
0274278710
75
0036679633
25
0548557420
75
0073359266
26
0259382903
76
-0035484929
26
0518765806
76
0070969858
27
0245642103
77
0034333105
27
0491284206
77
00686662IO
28
0232932334
78
0033222371
28
0465864668
78
0066444742
29
0221146711
79
0032151027
29
0442293422
79
0064302054
30
0210192593
80
0031117457
30
0420385186
80
0062234914
31
0199989288
81
0030I20I27
31
0399978576
81
0060240254
32
0190466183
82
0029157577
32
0380932366
82
0058315154
33
0181561219
83
0028228417
33
0363122438
83
0056456834
34
0173219634
84
0027331326
34
9346439268
84
0054662652
35
0165392916
85
0026465042
35
0330785832
85
0052930084
36
0158037942
86
0025628365
36
0316075884
86
0051256730
37
0151116244
87
0024820151
37
0302232488
87
0049640302
38
0144593401
00
OO
0024039306
38
0289186802
88
0048078612
39
0138438516
8 9
0023284787
39
0276877032
89
0046569574
40
0132623779
90
0022555599
40
0265247558
90
0045111198
41
0127124089
91
0021850789
4i
0254248178
91
0043701578
42
0121916731
92
0021169449
42
0243833462
92
0042338898
43
0116981103
93
0020510708
43
0233962206
93
004I02I4I6
44
0112298469
94
0019873733
44
0224596938
94
0039747464
45
0107851757
95
0019257729
45
0215703514
95
0038515458
46
0103625378
96
0018661933
46
0207250756
96
0037323866
47
0099605065
97
0018085613
47
OI992IOI30
97
0036171226
48
0095777738
98
0017528070
48
0191555476
98
0035056140
49
0092131383
99
0016988633
49
0184262766
99
0033977266
50
0088654944
100
0016466659
50
0177309888
100
0032933318
CXCV111
THE ENGINEER'S VALUING ASSISTANT.
Multiples of Redemption Funds, at 3 per cent, per Annum, necessary to produce
the following sums in n years.
Years
Sum to produce 3,
30, 300, 3000, or
300.000,000
Years
Sum to produce 3,
30, 300, 3000, or
300,000,000
Years
Sum to produce 4,
40, 400, 4000, or
400,000,000
Years
Sum to produce 4,
40, 400, 4000, or
400,000,000
I
3 0000000000
51
0256014696
I
4-0000000000
51
0341352928
2
1-4778325122
52
0246515511
2
1-9704433496
52
0328687348
3
9705910899
53
0237441177
3
1-2941214532
53
0316588236
4
7170811356
54
0228767523
4
9561081808
54
0305023364
5
5650637142
55
0220472130
5
7534182856
55
0293962840
6
4637925015
56
0212534178
6
'6183900020
56
0283378904
7
3915190614
57
0204934296
7
5220254152
57
0273245728
8
3373691664
58
0197654457
8
4498255552
58
0263539276
9
2953015710
59
0190677843
9
3937354280
59
0254237124
10
2616915198
60
0183988761
10
3489220264
60
0245318348
ii
2342323434
61
0177572541
ii
3123097912
61
0236763388
12
2113862565
62
0171415725
12
2818483420
62
0228554300
13
1920886320
63
0165504648
13
2561181760
63
0220672864
14
1755790170
64
0159828063
14
2341053560
64
0213104084
15
1612997415
65
0154374384
15
2150663220
65
0205832512
16
1488325479
66
0149132985
16
1984433972
66
0198843980
17
1375575882
67
0144093864
17
1838101176
67
0192125152
18
1281260877
68
0139247613
18
1708347836
68
0185663484
19
1194416418
69
0134585361
19
1592555224
69
0179447148
20
1116471228
70
0130098753
20
1488628304
7O
0173465004
21
1046153295
71
0125779896
21
1394871060
71
0167706528
22
0982421844
72
0121621338
22
1309895792
72
0162161784
23
0924417081
73
0117616035
23
1232556108
73
0156821380
24
0871422477
74
OII3757327
24
1161896636
74
0151676436
25
0822836130
75
0110038899
2 5
1097114840
75
0146718532
26
0778148709
76
0106454787
26
1037531612
76
0141939716
27
0736926309
77
0102999315
27
0982568412
77
0137332420
28
0698797002
78
0099667113
28
0931729336
78
0132889484
29
0663440133
79
0096453081
29
0884586844
79
0128604108
3O
0630577779
80
0093352371
30
0840770372
80
0124469828
3-1
0599967864
81
0090360381
31
0799957152
81
0120480508
32
0571398549
82
' -0087472731
32
0761864732
82
0116630308
33
0544683657
83
0084685251
33
0726244876
83
0112913668
34
0519658902
84
0081993978
34
0692878536
84
0109325304
35
0496178748
85
0079395126
35
0661571664
85
0105860168
36
0474113826
86
0076885095
36
0632151768
86
0102513460
37
0453348732
87
0074460453
37
0604464976
87
0099280604
38
0433780203
88
0072117918
38
0578373604
88
0096157224
39
0415315548
89
0069854361
39
0553754064
89
0095139148
40
0397871337
9O
0067666797
40
0530495116
90
0090222396
41
0381372267
91
0065552367
41
0508496356
91
0087403156
42
0365750193
92
0063508347
42
0487666924
92
0084677796
43
-0350943309
93
0061532124
43
0467924412
93
0082042832
44
0336895407
94
0059621199
44
0449193876
94
0079494933
45
0323555271
95
0057773187
45
0431407028
95
0077030916
46
0310876134
96
0055985799
46
0414501512
96
0074667732
47
0298815195
97
0054256839
47
0398420260
97
0072342452
48
0287333214
98
0052584210
48
0383110952
98
0070II2280
49
0276394149
99
0050965899
49
0368525532
99
0067954532
50
0265964832
100
0049399777
50
0354619776
100
0065866636
TABLE XV.
cxcix
Multiples of Redemption Funds, at 3 per cent, per Annum, necessary to produce
the following sums in n years.
Years
Suni to produce 5,
50, 500, 5000, or
500,000,000
ears
um to produce 5,
50, 500, 5000, or
500,000,000
ears
Sum to produce 6,
60, 600, 6000, or
600,000,000
fears
Sum to produce 6,
60, 600, 6000, or
600,000,000
I
5-OOOOOOOOOO
5 1
0426691160
I
6-0000000000
51
0512029392
2
2-4630541870
52
0410859185
2
2-9556550244
52
0493031022
3
1-6176518165
53
0395735295
3
1-9411821798
53
0474882354
4
1-1951352260
54
0381279205
4
1-4341622712
54
0457535046
5
9417728570
55
0367453550
5
1-1301274284
55
0440944260
6
7729875025
56
0354223630
6
9275850030
56
0425068356
7
6525317690
57
0341557160
7
7830381228
57
0409868592
8
5622819440
58
0329424095
8
6747383328
58
0395308914
9
4921692850
59
0317796405
9
5906031420
59
0381355686
10
4361525330
60
0306647935
10
5233830396
60
0367977522
ii
3903872390
61
0295954235
ii
4684646868
61
0355145082
12
3523104275
62
0285692875
12
4227725130
62
0342831450
13
3201477200
63
0275841080
13
3841772640
63
0331009296
14
2926316950
64
0266380105
14
3511580340
64
0319656126
15
2688329025
65
0257290640
15
3225994830
65
0308748768
16
2480542465
66
0248554975
16
2976650958
66
0298265970
17
2297626470
67
0240156440
17
2751151764
67
0288187728
18
2135434795
68
0232079355
18
2562521754
68
0278495226
19
1 990694030
69
0224308935
19
2388832836
69
0269170722
20
1860785380
70
0216831255
20
2232942446
70
0260197506
21
1743588825
71
0209633160
21
2092306590
71
0251559792
22
1637369740
72
0202702230
22
1964843688
72
0243242676
23
1540695135
73
0196026725
23
1848834162
73
0235232070
24
1452370795
74
.0189595545
24
1742844954
74
0227514654
25
I37I393550
75
0183398165
25
1645672260
75
0220077798
26
1296914515
76
0177424645
26
1556297418
76
0212909574
27
1228210515
77
0171665525
27
1473852618
77
0205998630
28
1164661670
78
0166111855
28
1397594004
78
0199334226
29
H05733555
79
0160755135
29
1226880266
79
0192906162
30
1050962965
80
0155587285
30
1261155558
80
0186704742
31
0999946440
81
0150600635
31
1199935728
81
0180720762
32
0952330915
82
0145787885
32
1142797098
82
0174945462
33
0907806095
83
0141142085
33
1089367314
83
0169370502
34
0866098170
84
0136656630
34
1039317804
84
0163987956
35
0826964580
85
0132325210
35
0992357496
85
0158790252
36
0790189710
86
0128141825
36
0948227652
86
0153770190
37
0755581220
87
0124100755
37
0906697464
87
0148920906
38
0722967005
88
0120196530
38
0867560406
88
0144235836
39
0692192580
89
0116423935
39
0830631096
89
0139708722
&o
0663118895
90
0112777995
4O
0795742674
90
0135333594
4i
0635620445
91
0109253945
41
0762744534
91
0131104734
42
0609583655
92
0105847245
42
0731500386
92
0127016694
43
0584905515
93
0102553540
43
0701886618
93
0123064248
44
0561492345
94
0099368665
44
0673790814
94
0119242398
45
0539258785
95
0096288645
45
0647110542
95
0115546374
46
0518126890
96
0093309665
46
0621752268
96
0111971598
47
0498025325
97
0090428065
47
0597630390
97
0108513678
48 -0478888690
98
0087640350
48
0574666428
98
0105168420
49 | -0460656915
99
0084943165
49
0552788298
99
-0101931798
50 I -0443274320
100
0082333295
50
0531929664
100
0098799954
cc
THE ENGINEER'S VALUING ASSISTANT.
Multiples of Redemption Funds, at 3 per cent, ppr Annum, necessary to produce
the following sums in n years.
| Sum to produce 7
Years 70, 700, 7000, o
00,000,000
Years
Sum to produce 7
70, 700, 7000, o
700 ooo.ooo
Years
Sum to produce 8
80, 800, 8000, o
800,000,000
Year
Sum to produce 8,
80, 800, 8000, or
800,000,000
I
7'OOOOOOOOOO
51
0597367624
I
8-OOOOOOOOOO
51
0682705856
2
3-4482758618
52
0575202859
2
3-9408866992
52
0657374696
3
2-2647125431
53
0554029413
3
2-5882429064
53
0633176472
4
1-6731893164
54
0533790887
4
1-9122163616
54
0610046728
5
1-3184819998
55
0514434970
5
1-5068365712
55
0587925680
6
1-0821825035
56
0495913082
6
I -2367800040
56
0566757808
7
9135444766
57
0478180024
7
I -0440508304
57
0546491456
8
7871947216
58
0461183733
8
8996511104
58
0527078552
9
6890369990
59
0444914967
9
7874708560
59
0508474248
10
6106135462
60
0429307109
10
6978440528
60
0490636696
n
5465421346
61
0414335929
ii
6246195824
61
0473526776
12
4932345985
62
0399970025
12
5636966840
62
0457108600
13
4482068080
63
0386I775I2
13
5122363520
63
0441345728
H
4096843730
64
0372932147
14
4682107120
64
0426208 1 68
15
3763660635
65
0360206896
15
4301326440
65
041 1665024
16
3472759451
66
0347976965
16
3968867944
66
0397687960
17
3216677058
67
03362,19016
17
3676202352
67
0384250304
18
2989608713
68
03249II097
18
3416695672
68
0371326968
19
2786971642
69
0314032509
19
3185110448
69
0358894296
20
2605099532
70
0303563757
20
2977256608
70
0346930008
21
2441024355
71
0293486424
21
2789742120
71
0335413056
22
2292317636
72
0283783122
22
2619791584
72
0324323568
23
2156973189
73
0274437415
23
2465112216
73
0313542760
24
2033319113
74
0265433763
24
2323793272
74
0303352872
25
1919950970
75
0256757431
25
2194229680
75
0293437064
26
1815680321
76
0248394503
26
2075063224
76
0283879432
27
I7I949472I
77
0240431735
27
1965136824
77
0274664840
28
1630526338
78
0232556597
28
1863458672
78
0265778968
2 9
1548026977
79
0225057189
2 9
1769173688
79
0257208216
30
1471348151
so
02I7822I99
3O
1681540744
80
0248939656
31
1399925016
81
0210840889
31
1599914304
81
0240961016
32
1333263281
82
0204103039
32
1523729464
82
0233260616
33
1270928533
83
0197598919
33
1452489752
83
0225827336
34
1212537438
84
0191319282
34
1385757072
84
0218650608
35
II577504I2
85
0185255294
35
1323143328
85
0211720336
36
1106265594
86
0179398555
36
1264303536
86
0205026920
37
1057813708
87
OI7374I059
37
1208929952
87
0198561208
38
1012153807
88
OI68275I42
38
1156747208
88
0192314448
39
0969069612
89
0162993509
39
1107508128
89
0186278296
40
0928366453
90
0157889193
10
1060990232
90
0180444792
4i
0889868623
91
0152955523
4i
1016992712
91
0174806312
42
0853417117
92
0148186143
42
0975333848
92
0169355592
43
0818867721
93
0143574956
43
0935848824
93
0164085664
44
0786089283
94
0139116131
44
0898387752
94
0158989864
45
0754962299
95
0134804103
45
0862814056
95
0154061832
46
0725377646
96
OI3063353I
46
0829003024
96
0149295464
47
0697235455
97
0126599291
47
0796840520
97
0144684904
48
0670444166
98
0122696490
48
0766221904
98
0140224560
49
0644919681
99
OII892043I
49
0737051064
99
0135909064
5O
0620584608
LOO
OII52666I3
SO
0709239552
1OO
0131733272
TABLE XV.
CC1
Multiples of Redemption Funds, at 3 per cent, per Annum, necessary to produce
the following sums in n years.
Years
Sum to produce 9,
90, 900, 9000, 01
900,000,000
Years
Sum to produce 9,
90, 900, 9000, o
900,000,000
Years
Sum to produce 10
100, 1000, 10,000
or 1000,000,000
Years
Sum to produce 10,
100, 1000, 10,000,
or 1000,000,000
I
8-0000000000
51
0768044088
I
lO'OOOOOOOOOO
51
0853382320
2
4-4334975366
52
0739546533
2
4-9261083740
52
0821718370
3
2-9117732697
53
0712323531
3
3-2353036330
53
0791470590
4
2-1512434068
54
0686302569
4
2-3902704520
54
0762558410
5
1-6951911426
55
0661416390
5
1-8835457140
55
0734907100
6
1-3913775045
56
0637602534
6
I '5459750050
56
0708447260
7
1-1745571842
57
0614802888
7
1-3050635380
57
0683114320
8
1-0121074992
58
0592963371
8
1-1245638880
58
0658848190
9
8859047130
59
0572033529
9
9843385700
59
0635592810
10
7850745594
60
0551966283
10
8723050660
60
0613295870
ii
7026970302
61
0532717623
ii
7807744780
61
0591908470
12
6341587695
62
0514247175
12
7046208550
62
0571385750
!3
5762658960
63
'0496513944
13
6402954400
63
0551682160
14
15
5267370510
4838992245
64
65
0479484189
0463123152
H
15
5852633900
5376658050
64
65
05,32760210
0514581280
16
4464976437
66
0447398955
16
4961084930
66
0497109950
17
4135727646
67
0432281592
17
4595252940
67
0480312880
18
3843782631
68
0417742839
18
4270869590
68
0464158710
19
3583249254
69
0403756083
19
3981388060
69
0448617870
20
3349413684
70
0390296259
20
3721570760
70
0433662510
21
3138459885
7i
0377339688
21
3487177650
71
0419266320
22
2947265532
72
0364864014
22
3274739480
72
0405404460
23
2773251243
73
0352848105
23
3081390270
73
0392053450
24
2614267431
74
0341271981
24
2904741590
74
0379191020
2 5
2468508390
75
0330116697
25
2742787100
75
0366796330
26
2334446127
76
0319364361
26
2593829030
76
0354849290
27
2210778927
77
0308997945
27
2456421030
77
0343331050
28
2096391006
78
-0299001339
28
2329323340
78
0332223710
29
1990320399
79
0289359243
29
2211467110
79
0321510270
30
1891733337
80
0280057113
30
2101925930
80
0311174570
31
1799903592
81
0271081143
31
1999892880
81
030I20I270
32
1714195647
82
0262418193
32
1904661830
82
0291575770
33
1634050971
83
0254055755
33
1815612190
83
0282284170
34
1558976706
84
0245981934
34
1732196340
84
0273313260
35
1488536244
85
0238185378
35
1653929160
85
0264650420
36
1422341478
86
0230655285
36
1580379420
86
0256283650
37
1360046196
87
0223381359
37
1511162440
87
0248201510
38
1301340609
88
0216353754
38
1445934010
88
0240393060
39
1245946644
89
0209563083
39
1384385160
89
0232847870
40
1193614011
90
0203000391
40
1326237790
90
0225555990
41
1144116801
91
0196657101
41
1271240890
91
0218507890
42
1097250579
92
0190525041
42
1219167310
92
O2 1 1 694490
43
1052829927
93
0184596372
43
1169811030
93
0205107080
44
1010686221
94
0178863597
44
1122984690
94
0198737330
45
0970665813
95
0173319561
45
1078517570
95
0192577290
46
0932628402
96
0167957397
46
1036253780
96
0186619330
47
0896445585
97
0162770517
47
0996050650
97
0180856130
48
0861999642
98
0157752630
48
0957777380
98
0175280700
49
0829182447
99
0152897697
49
0921313830
99
0169886330
0797894496
100
0148199931
50
0886549440
100
0164666590
c c
TABLE XVI.
Present Value of a Perpetuity of 1, receivable once
in every nth year, the first payment due n years hence ;
also of a Perpetuity of 1 deferred n years, at the rates
of 3> 3i 4> 4i> 5> 6, 7, and 8 per cent.
Calculated to 4 places of decimals.
TABLE XVI.
CCV
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
3 PER CENT.
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
,
32-3625
51
7-382I
I
33-3333
51
2845
2
31-4199
52
7-1671
2
16-4204
52
2739
3
30-5047
53
6-9583
3
10-7843
53
2638
4
29-6162
54
6-7557
4
7-9676
54
2542
5
287536
55
6-5589
5
6-2785
55
'2450
6
27-9161
=56
6-3679
6
5-I533
56
2361
7
27-I03I
57
6-1824
7
4-3502
57
2277
8
26-3136
58
6-0023
8
3-7485
58
2196
9
25-5472
59
5-8275
9
3-28II
59
2119
10
24-8031
60
5-6578
10
2-0077
60
2044
ii
24-0807
6!
5-4930
ii
2-6026
61
1973
12
23*3793
62
5-3330
12
2-3487
62
1005
13
22-6984
63
5-1777
13
2-1343
63
1839
H
22-0373
64
5-0269
H
1*9509
64
1776
15
21-3954
65
4-8804
15
I-7922
65
1715
16
20-7722
66
4-7383
16
1-6537
66
1657
17
20-1672
67
4-6003
17
1-5318
67
1601
18
19-5798
68
4-4663
18
1-4236
68
1547
19
19-0095
69
4-3362
19
I-327I
69
1495
20
18-4559
70
4-2099
20
1-2405
70
1446
21
17-9183
71
4-0873
21
1-1624
71
1398
22
17-3964
72
3-9682
22
1-0916
72
I35i
23
16-8897
73
3-8527
23
I-027I
73
1307
24
16-3978
74
3-7405
24
9682
74
1264
25
15-9202
75
3-6315
25
9H3
75
1223
26
I5-4565
76
3-5257
26
8646
76
1183
27
15-0063
77
3-4230
27
8l88
77
1144
28
14-5692
78
3-3233
28
7764
78
1107
29
I4-I449
79
3-2265
29
7372
79
1072
30
13-7329
80
3-1326
30
7006
80
1037
31
I3-3329
81
3-0413
31
6666
81
1004
32
12-9446
82
2-9527
32
6349
82
0972
33
12-5675
83
2-8667
33
6052
83
0941
34
I2-20I5
84
27832
34
'5774
84
0911
35
11-8461
85
2-7022
35
5513
85
0882
36
II-50II
86
2-6235
36
5268
86
0854
37
. 11-1661
87
2-5471
37
5037
87
0827
38
10-8409
QQ
OO
2-4729
38
4820
88
0801
39
10-5251
8 9
2-4009
39
4615
89
0776
40
10-2186
90
2-3309
40
4421
90
0752
41
9-9209
91
2-2630
41
4237
91
0728
42
9-6320
92
2-1971
42
4064
92
0706
43
93514
93
2-1331
43
3899
93
0684
44
9-0791
94
2-0710
44
'3743
94
0662
45
8-8146
95
2-0107
45
'3595
95
0642
46
8-5579
96
1-9521
46
'3454
96
0622
47
8-3086
97
I-8953
47
3320
97
0603
48
8-0666
98
1-8401
48
3193
98
0584
49
7-8317
99
1-7865
49
3071
99
0566
50
7-6036
100
17344
50
2955
100
0549
CCV1
THE ENGINEER'S VALUING ASSISTANT.
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
3 PER CENT.
Years
Present Values
of a Perpetuity of i
Deferred n Years
rears
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of 1
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
I
27'6052
51
4-9428
I
28-5714
51
2092
2
26-6717
52
47757
2
14-0400
52
2007
3
257698
53
4-6142
3
9-1981
53
1926
4
24-8983
54
4-4581
4
67786
54
1849
5
24-0564
55
43074
5
5'3280
55
-1775
6
23-2429
56
4-1617
6
4-3619
56
1705
7
22-4569
57
4-0210
7
3-6727
57
1638
8
2I-6975
58
3-8850
8
3-I565
58
1574
9
20-9637
59
37536
9
27556
59
1512
10
20-2548
60
3-6267
10
2'4355
60
1454
ii
19-5699
61
3-5041
ii
2-1741
61
1398
12
18-9081
62
33856
12
1-9567
62
1344
13
18-2687
63
3-2711
13
17732
63
1293
H
17-6509
64
3-1605
14
1-6163
64
1244
15
17-0540
65
3-0536
15
i -4807
65
1197
16
16-4773
66
2-9503
16
1-3624
66
1152
17
15-9201
67
2-8505
17
1-2584
67
1108
18
15-3817
68
2-7542
18
1-1662
68
1067
19
I4-86l6
69
2-6610
19
i -0840
69
1027
20
I4-3590
70
2-5710
20
1-0103
70
0989
21
I3*8735
71
2-4841
21
'9439
71
0952
22
13*4043
72
2-4001
22
8838
72
0917
23
I2-95IO
73
2-3189
23
8291
73
0883
24
I2-5I3I
74
2-2405
24
7792
74
0851
25
12-0899
75
2-1647
25
7335
75
0820
26
II-68II
76
2-0915
26
6916
76
0790
27
II-286I
77
2-0208
27
6529
77
0761
28
29
10-9044
10-5357
78
79
1-9525
1-8864
28
29
6172
5842
78
79
0733
0707
30
10-1794
80
1-8227
3O
'5535
80
0681
31
9-8352
81
1-7610
31
5249
81
0657
32
9-5026
82
1-7015
32
4983
82
0633
33
9-l8l2
83
1-6439
33
'4735
83
06 1 1
34
8-8707
84
1-5883
34
4503
84
0589
35
8-5708
85
I-5346
35
4285
85
0568
36
8-2809
86
1-4827
36
4081
86
0547
37
8-OOO9
87
1-4326
37
3890
87
0528
38
77303
88
1-3841
38
3709
88
0509
39
7'4689
89
1-3373
39
'3539
89
0491
40
7-2164
90
1-2921
40
3379
90
0474
41
6-9723
91
i -2484
41
3228
91
0457
42
6-7365
92
i -2062
42
3085
92
0441
43
6-5087
93
1-1654
43
2950
93
0425
44
6-2886
94
1-1260
44
2822
94
0410
45
6-0760
95
i -0879
45
2701
95
0396
46
5'8705
96
i -05 1 1
46
2586
96
0382
47
5-6720
97
1-0156
47
2477
97
0369
48
5-4802
98
9812
48
2373
98
0356
49
5-2949
99
9481
49
2275
99
0343
50
5-II58
100
9160
50
2181
100
0331
TABLE XVI.
CCVll
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
4 PER CENT.
Present Value of i
Present Value of i
Present Values
Present Values
receivable once
receivable once
Years
of a Perpetuity of i
Years
of a Perpetuity of i
Years
in every nth Year,
Years
in every nth Year,
Deferred n Years
Deferred n Years
the first due
the first due
n Years hence
n Years hence
I
24-0385
51
3-3825
I
25-OOOO
51
1565
2
23-1139
52
3-2524
2
12-2549
52
1496
3
22-2249
53
3-1273
3
8-0087
53
1430
4
2I-370I
54
3-0070
4
5-8873
54
1367
5
20-5482
55
2-8914
5
4-6I57
55
1308
6
197579
56
2-7802
6
37690
56
1251
7
18-9979
57
2-6733
7
3-1652
57
1197
8
18-2673
58
2-5704
8
27132
58
1146
9
17-5647
59
2-4716
9
2-3623
59
1097
10
16-8891
60
2-3765
10
2*0823
60
IOCJO
ii
16-2395
61
2-2851
n
1-8537
61
I006
12
I5-6I49
62
2-I972
12
1-6638
62
0964
13
15-0144
63
2-II27
13
1-5036
63
0923
H
14-4369
64
2-0315
H
1-3667
64
0884
15
I3-88I6
65
1-9533
15
1-2485
65
0848
16
133477
66
1-8782
16
I-I455
66
O8l2
17
12-8343
67
i -8060
17
1-0550
67
'0779
18
12-3407
68
1-7365
18
9748
68
0746
19
II-866I
69
1-6697
19
9045
69
0716
20
II-4097
70
1-6055
20
8395
70
0686
21
10-9708
71
1-5437
21
7820
71
0658
22
10-5489
72
1-4844
22
7300
72
0631
23
IO-I432
73
i -4273
23
6827
73
0605
24
97530
74
1-3724
24
6397
74
0581
2 l
9-3779
75
1-3196
25
6003
75
0557
26
9-OI72
76
1-2688
26
5642
76
"535
27
8-6704
77
I'2200
27
5310
77
0513
28
8-3369
78
I-I73I
28
5003
78
0492
29
8-0163
79
I-I280
29
4720
79
'0473
30
7-7080
80
I -0846
30
4458
80
0454
31
7-4II5
81
I -0429
3 1
4214
81
"435
32
7-1264
82
I -0028
32
3987
82
0418
33
6-8524
83
9642
33
3776
83
0401
34
6-5888
84
9271
34
'3579
84
0385
35
6-3354
85
8 9 I5
35
'3394
85
0370
36
6-0917
86
8572
36
3222
86
"355
3 l
5-8574
87
8242
37
3060
87
0341
38
5-632I
88
7925
38
2908
88
0327
39
5-4I55
89
7620
39
2765
89
0314
&o
5-2072
90
7327
40
2631
90
0302
4i
5-0069
9 1
7045
4i
2504
9 1
0290
42
4-8144
92
6774
42
2385
92
0279
43
4-6292
93
6514
43
2272
93
0268
44
4-45I2
94
6263
44
2166
94
0257
45
4-2800
95
6022
45
2066
95
0247
46
4-II53
96
5791
46
1971
96
0237
47
3-957I
97
5568
47
1880
97
0228
48
3-8049
98
'5354
48
1795
98
0219
49
3-6585
99
5H8
49
1714
99
0210
50
3-5I78
100 '495^
SO
1638
100
0202
CCV111
THE ENGINEER'S VALUING ASSISTANT.
Present Value of a Perpetuity of jl, receivable once in every nth Year,
'the first payment due n years hence ; also Present Value of a Perpetuity ol 1
Deferred n Years.
* PER CENT.
Years
Present Values
,of a Perpetuity of i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Year
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
I
21-2653
51
2-3543
I
22-2222
51
1185
2
20-3496
52
2-2529
2
10-8666
52
1128
3
19-4733
53
2-1559
3
7-0839
53
1074
4
18-6347
54
2-0630
4
5-I943
54
1023
5
17-8322
55
I-9742
5
4-0620
55
0975
6
17-0643
56
1-8892
6
3'3084
56
0929
7
16-3295
57
1-8078
7
277II
57
0886
8
15-6263
58
1-7300
8
2-3691
58
0844
9
H'9534
59
1-6555
9
2-0572
59
0805
10
14-3095
60
1-5842
10
I -8084
60
0770
ii
I3-6933
61
1-5160
ii
I-6055
61
0732
12
13-1036
62
I-4507
12
I-4370
62
0698
13
12-5394
63
1-3882
13
r2950
63
0666
H
11*9994
64
I-3284
H
I-I738
64
06 3 6
15
11-4827
65
I-27I2
15
I -0692
65
0607
16
10-9882
66
1-2165
16
978l
66
0579
17
10-5150
67
1-1641
17
8982
67
0553
18
IO-0622
68
riI40
18
8275
68
0528
19
9-6289
69
I -0660
19
7646
69
0504
30
9-2143
70
I -020 1
20
7084
70
0481
21
8-8I75
71
9762
21
6578
71
0459
22
8-4378
72
9341
22
6121
72
0439
23
8-0744
73
8938
23
5707
73
0419
24
77267
74
8554
24
5330
74
0400
25
7-3940
75
8l88
25
4986
75
0382
26
7-0756
76
7833
26
4672
76
0365
2?
6-7709
77
7496
27
4382
77
0349
28
6-4793
78
7173
28
4116
78
0334
29
6-2003
79
6864
29
3870
79
0319
30
5-9333
80
6569
30
3643
80
0305
31
5-6778
81
6286
31
3432
81
0291
32
5-4333
82
6015
32
3236
82
0278
33
5-I994
83
5756
33
3054
83
0266
34
4-9755
84
5508
34
2885
84
0254
35
4-7612
85
5271
35
2727
85
0243
36
4-5562
86
5044
36
2579
86
0232
37
4-3600
87
4827
37
2441
87
0222
38
4-I722
88
4619
38
2312
88
0212
39
3-9926
89
4420
39
2190
89
0203
40
3-8206
90
4230
40
2076
90
0194
41
3-6561
91
4048
41
1969
91
0186
42
3H987
92
3873
42
1869
92
0177
43
3-3480
93
3707
43
1774
93
0170
44
3-2038
94
'3547
44
1685
94
Ol62
45
3-0659
95
'3394
45
1600
95
0155
46
2*9339
96
3248
46
1521
96
0148
47
2-8075
97
3108
47
1446
97
OI42
48
2-6866
98
2974
48
1375
98
0136
49
2-5709
99
2846
49
1308
99
0130
50
2-4602
100
2724
50
1245
LOO
0124
TABLE XVI.
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
5 PEE CENT.
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
, receivable once
in every nth Year,
the first due
n Years hence
I
19-0476
51
I -66lO
I
2O-OOOO
51
0906
2
18-1406
52
1-5819
2
97561
52
0859
3
17-2768
53
I -5066
3
6-3442
53
0815
4
164540
54
14349
4
4-6402
54
0773
5
15-6705
55
I-3665
5
3-6I95
55
0733
6
14-9243
56
I-30I5
6
2-9403
56
0696
7
14-2136
57
1-2395
7
24564
57
0661
8
I3-5368
58
1-1805
8
2-0944
58
0627
9
12-8922
59
I-I242
9
1-8138
59
0596
10
12-2783
60
1-0707
10
I-590I
60
"0566
ii
1 1 -6936
61
I-OI97
ii
1 4078
61
0537
12
11-1367
62
9712
12
1-2565
62
0510
13
10*6064
63
9249
13
I-I29I
63
0485
10-1014
64
8809
14
I -0205
64
0461
15
9-6203
65
8389
15
9268
65
0438
16
9-1622
66
7990
16
8454
66
0416
17
87259
67
7609
17
7740
67
0396
18
8-3104
68
7247
18
7109
68
0376
19
7-9147
69
6902
19
6549
69
0357
20
7-5378
70
6573
20
6049
70
0340
21
7-1788
71
6260
21
"5599
71
0323
22
6-8370
72
5962
22
5194
72
0307
23
6-5114
73
5678
23
4827
73
0292
24
6-2014
74
5408
24
'4494
74
0278
25
5-9061
75
5150
25
4190
75
0264
26
5-6248
76
4905
26
3913
76
0251
27
53570
77
4671
27
3658
77
0238
28
5-IOI9
78
4449
28
3425
78
0228
29
4-8589
79
4237
29
3209
79
02l6
3O
4-6275
80
4035
30
3010
80
0206
31
44072
81
3843
31
2.826
81
0196
32
4-I973
82
3660
32
2656
82
Ol86
33
3-9975
83
3486
33
2498
83
0177
34
3-8071
84
3320
34
2351
84
0169
35
3-6258
85
3162
35
2214
85
0161
36
34531
86
3011
36
2087
86
0153
37
3-2887
87
2868
37
1968
87
0145
38
3-I32I
88
2731
38
1857
88
0138
39
2-9830
89
2601
39
1753
89
0132
40
2-8409
90
2477
40
1656
90
0125
41
27056
91
2359
41
1564
91
0119
42
2-5768
92
2247
42
1479
92
0114
43
24541
93
2140
43
1399
93
0108
44
2-3372
94
2038
44
1323
94
0103
45
2-2259
95
1941
45
1252
95
0098
46
2-1199'
96
1849
46
1186
96
0093
47
2-0190
97
1761
47
1123
97
0089
48
1-9228
98
1677
48
1064
98
0085
49
1-8313
99
1597
49
1008
99
0080
SO
17441
100
1521
so
-t
0955
100
0077
ccx
THE ENGINEER'S VALUING ASSISTANT.
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
6 PER CENT.
Years
Present Values
of a Perpetuityof i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferre 1 n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
I
157233
51
8536
I
16-6667
51
0540
2
I4-8333
52
8053
2
8-0906
52
0508
3
I3-9937
53
7597
3
5-2352
53
0478
4
I3-20I6
54
7167
4
3-8099
54
0449
5
I2-5432
55
6761
5
2-8233
55
0423
6
II7493
56
6379
6
2-3894
56
0398
7
1 1 -0843
57
6017
7
1-9856
57
0375
8
10-4569
58
5677
8
1-6839
58
0353
9
9-8650
59
5356
9
I-4504
59
0332
10
9-3066
60
5052
10
1-2645
6O
0313
ii
87798
61
4766
ii
I-II32
61
0294
12
8-2828
62
'4497
12
9880
62
0277
13
7-8140
63
4242
13
8827
63
026l
14
7-37I7
64
4002
14
7931
64
0246
15
6-9544
65
3775
15
7160
65
0232
16
6-5608
66
3562
16
6492
66
0218
17
6-1894
67
3360
17
5907
67
0206
18
5^391
68
3170
18
'5393
68
0194
19
5-5086
69
2991
19
'4937
69
0183
20
5-I 9 67
70
2821
20
453i
70
0172
21
4-9026
71
2662
21
4167
71
Ol62
22
4-625I
72
2511
22
3841
72
0153
23
4-3633
73
2369
23
3546
73
0144
24
4-1163
74
2235
24
3280
74
0136
25
3'8833
75
2108
25
3038
75
0128
2O
3-6635
76
1989
26
2817
76
01 2 1
27
3-456I
77
1876
27
2616
77
0114
28
3-2605
78
1770
28
2432
78
0107
29
3-0759
79
1670
29
2263
79
oioi
30
2-9018
80
1575
30
2108
30
0095
31
32
27376
2-5826
81
82
1486
1402
31
32
1965
1834
81
82
0090
0085
33
2-4364
83
1323
33
1712
83
OO8O
34
2-2985
84
1248
34
1600
84
0075
35
2-1684
85
1177
35
1496
85
0071
36
2-0457
86
mi
36
1399
86
0067
37
1-9299
87
1048
37
1310
87
0063
3*
I-8206
88
0988
38
1226
88
0060
39
I7I76
89
0932
39
1149
89
0056
40
I '6204
9O
0880
40
1077
9O
0053
41
1-5287
91
0830
4i
1010
91
OO5O
42
I-442I
92
0783
42
0947
92
0047
43
1-3605
93
0739
43
0888
93
0045
44
I'2835
94
0697
44
0834
94
0042
45
I-2IOS
95
0657
45
0783
95
OO4O
46
I-I423
96
0620
46
0736
96
0037
47
1-0776
97
0585
47
0691
97
0035
48
i -oi 66
98
0552
48
0650
98
0033
49
9591
99
0521
49
06 1 1
99
0031
50
9048 100
0491
50
0574
100
0030
TABLE XVI.
Present Value of a Perpetuity of 1, receivable once in every ntli Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Yearn.
7 PER CENT.
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
I
I3'35II
51
4532
I
14-2857
51
0328
2
12-4777
52
4236
2
6-9013
52
0306
3
11-6614
53
'3959
3
4-4436
53
0285
4
10-8985
54
3700
4
3-2175
54
0266
5
10-1855
55
3458
5
2-4842
55
0248
6
9-5192
56
3232
6
I-997I
56
0231
7
8-8964
57
-3020
7
I -6508
57
02l6
8
8-3I44
58
2823
8
1-3924
58
0202
9
77705
59
2638
9
1-1927
59
0188
10
7-2621
60
2465
10
I '0340
60
0176
ii
6-7870
61
2304
ii
9051
61
0164
12
6-3430
62
2153
12
7986
62
0153
13
5-9281
63
2012
13
7093
63
0143
14
5-5402
64
1881
14
6335
64
0133
i5
5-1778
65
1758
15
5685
65
0125
16
4-8391
66
1643
16
5123
66
oi 1 6
17
4-5225
67
1535
17
4632
67
0109
18
4-2266
68
1435
18
4202
68
oioi
19
3-9501
69
1341
1 9
3822
69
0095
20
3-6917
70
1253
20
3485
70
0089
21
3-4502
71
1171
21
3184
71
0083
22
3-2245
72
1095
22
2915
72
0077
23
3-0135
73
1023
23
2673
73
0072
24
2-8164
74
0956
24
2456
74
0067
25
2-6321
75
0894
2 5
2259
75
0063
26
2-4599
76
0835
26
2080
76
0059
27
2-2990
77
0780
27
1918
77
0055
28
2-1486
78
0729
28
1770
78
0051
29
2-0080
79
0682
29
1636
79
0048
30
1-8767
80
0637
30
1512
80
0045
31
17539
81
0595
31
1400
81
0042
32
1-6392
82
0556
32
1296
82
0039
33
5319
83
0520
33
1201
83
0037
34
4317
84
0486
34
III4
84
0034
35
338o
85
0454
35
1033
85
0032
36
2505
86
0425
36
0959
86
0030
37
1687
87
0397
37
0891
87
0028
38
1-0922
88
0371
38
0828
88
0026
39
1-0208
89
0347
39
0770
89
0024
40
9540
9O
0324
40
07l6
90
0023
41
8916
91
0303
41
0666
9 1
0021
42
8333
92
0283
42
0619
92
0020
43
7788
93
0264
43
0577
93
0019
44
7278
94
0247
44
0537
94
0017
45
6802
95
0231
45
O5OO
95
00l6
46
6357
96
0216
46
0466
96
0015
47
'5941
97
0202
47
0434
97
0014
48
5552
98
0188
48
0404
98
0013
49
5189
99
0176
49
0307
99
0012
50
4850
100
0165
50
0351
100
0012
ccxii
THE ENGINEER'S VALUING ASSISTANT.
Present Value of a Perpetuity of 1, receivable once in every nth Year,
the first payment due n years hence ; also Present Value of a Perpetuity of 1
Deferred n Years.
8 PER CENT.
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Values
of a Perpetuity of i
Deferred n Years
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
Years
Present Value of i
receivable once
in every nth Year,
the first due
n Years hence
I
H'5741
51
2468
I
12-5000
51
0201
2
107167
52
2285
2
6-0096
52
0186
3
9-9229
53
2116
3
3-8504
53
0172
4
9-1879
54
1959
4
2-7740
54
0159
5
8-5073
55
I8l4
5
2'1307
55
0147
6
7-877I
56
1680
6
17039
56
0136
7
7-2936
57
1555
7
1-4009
57
OI26
8
67534
58
1440
8
I-I752
58
0117
9
6-2531
59
1333
9
rooio
59
OI08
10
5-7899
60
1234
10
8629
60
oioo
ii
5-36IO
61
1143
ii
7510
61
0092
12
4-9639
62
1058
12
6587
62
0085
13
4*5962
63
-0980
13
5815
63
0079
H
4-2558
64
0907
14
5162
64
0073
15
3-9405
65
0840
15
4604
65
0068
16
3-6486
66
0778
16
4122
66
0063
17
33784
67
072O
17
3704
67
0058
18
3-I28I
68
0667
18
3338
68
0054
19
2-8964
69
O6l8
19
3016
69
0050
20
2-68I9
70
0572
20
2732
70
0046
21
2-4832
71
0529
21
2479
71
0043
22
2-2993
72
0490
22
2254
72
0039
23
2'1289
73
0454
23
2053
73
0036
24
I-97I2
74
0420
24
1872
74
0034
25
I-8259
75
0389
25
1710
75
0031
26
1-6900
76
0360
26
1563
76
0029
27
I-5643
77
0334
27
1431
77
0027
28
1-4489
78
0309
28
1311
78
0025
29
I-34I6
79
0286
29
1202
79
0023
30
I-2422
80
0265
30
IIO3
80
0021
31
I-I5O2
81
0245
31
1013
81
002O
32
I -0650
82
O227
32
0931
82
00l8
33
9861
83
02 1 o
33
0856
83
0017
34
OI3I
84
0195
34
0788
84
O0l6
35
8454 .
85
0180
35
0725
85
0014
36
7828
86
0167
36
0668
86
0013
37
7248
87
0155
37
O6l6
87
0012
38
6711
88
0143
38
0567
88
001 1
39
6214
89
0132
39
0523
89
001 1
40
'5754
90
0123
40
0483
90
ooio
41
5328
91
0114
41
0445
91
0009
42
"4933
92
0105
42
0411
92
0008
43
4568
93
0097
43
0379
93
0008
44
-4229
94
0090
44
0350
94
OO07
45
39i6
95
0083
45
0323
95
0007
46
3626
96
0077
46
0299
96
0006
47
'3357
97
0072
47
0276
97
O006
48
3109
98
0066
48
0255
98
O005
49
2878
99
0061
49
0236
99
O005
SO
2665
100
0057
so
0218
100
0005
TABLE XVII.
SINGLE LIFE ANNUITIES (CAELISLE).
Available Interest on Capital being at the rates 0/4, 5, 6,
8, and 10 per cent, per annum, Redemption of Capital
being at the rate of 3 per cent.
Calculated to 3 places of decimals.
TABLE XVII.
ccxv
Single Life Annuities (Carlisle). Available Interest on Capital at the following
rates, Redemption being at 3 per cent.
Age
4 Per Cent.
Age
4 Per Cent.
Age
5 Per Cent.
Age
5 Per Cent.
14763
52
11-939
O
12-864
52
10-666
I
16725
53
II-645
I
14-329
53
10-430
2
17-696
54
II-346
2
I5'035
54
10-190
3
' 18-489
55
11-039
3
15-604
55
9-941
4
18-887
56
10726
4
15-886
56
9-687
I9'I54
57
10-406
5
16-075
57
9-425
6
19-254
58
10-086
6
16-146
58
9-162
7
19-268
59
9781
7
16-155
59
8-909
8
19-225
60
9-495
8
16-125
60
8-672
9
19-144
61
9-240
9
16-068
61
8-458
10
19-036
62
8-988
10
15-990
62
8-247
ii
18-914
63
8-731
ii
15-906
63
8-030
12
18-793
64
8-463
12
I5'820
64
7-803
13
18-671
65
8-187
13
15733
65
7-568
14
18-546
66
7-90I ,
14
15-645
66
7-322
15
18-422
67
7-602
15
15-556
67
7-065
16
18-304
68
7-295
16
15-472
68
6799
17
18-189
69
6-976
17
I5-389
69
6-521
18
18-072
70
6-650
18
15-306
7o
6-235
1 9
17-952
7i
6-311
19
I5-22O
7i
5-937
20
17-828
72
5-991
20
15-130
72
5-652
21
17-697
73
5-699
21
15-037
73
5-392
22
17-563
74
5'439
22
i4-939
74
5-159
23
17-423
75
5-224
23
14-838
75
4-965
24
17-277
76
5*012
24
14732
76
4-773
25
I7-I27
77
4-816
25
14-623
77
4-594
26
16-973
78
4-6I5
26
I4-5IO
78
4-411
27
16-814
79
4-390
27
I4-394
79
4-206
28
16-654
80
4-182
28
14-277
80
4-015
29
16-501
81
3-956
29
14-164
81
3-805
30
I6-358
82
3751
30
14-058
82
3-616
31
I6-2I2
83
3-542
31
13-951
83
3-421
32
16-062
84
3-339
32
I3-839
84
3-23!
33
15-903
85
3-I28
33
I372I
85
3-033
34
15737
86
2-944
34
13-597
86
2-860
35
15-565
87
2793
35
13-468
87
2718
36
I5-386
88
2701
36
I3-334
88
2-630
37
I5-203
89
2-596
37
13-197
89
2-530
38
15-016
90
2-438
38
13-056
90
2-380
39
I4-825
91
2-421
39
12-911
9i
2-364
40
I4-634
92
2-5I2
40
12766
92
2-451
4i
14-449
93
2-6I6
41
12-625
93
2-550
42
14-265
94
2-663
42
12-484
94
2-594
43
14-081
95
2-683
43
12-343
95
2-613
44
13-889
96
2-633
44
12-195
96
2-565
45
13-691
97
2-495
45
12-042
97
2-434
46
I3'483
98
2-333
46
11-881
98
2-279
47
I3-265
99
2-086
47
11711
99
2-044
48
I3-033
100
1-655
48
11-530
100
1-628
49
I278I
101
1-213
49
11-332
101
1-199
50
I2-5I3
102
765
50
11*121
102
759
51
12-228
103
323
51
10-896
103
322
CCXV1
THE ENGINEER'S VALUING ASSISTANT.
Single Life Annuities (Carlisle). Available Interest on Capital at the following
rates, Redemption being at 3 per cent.
Age
6 Per Cent.
Age
6 Per Cent.
Age
8 Per Cent.
Age
. 8 Per Cent.
O
11-398
52
9-638
O
9-282
52
8-080
I
I2'533
53
9-445
I
10-021
53
7-945
2
13-070
54
9-248
2
10-362
54
7-804
3
13-498
55
9'43
3
IO-629
55
7-658
4
13709
56
8-831
4
10759
56
7-506
5
13*849
57
8-613
5
10-845
57
7348
6
13-901
58
8-393
6
10-877
58
7-187
7
13-908
59
8-181
7
IO-88I
59
7-030
8
13-886
60
7-980
8
10-868
60
6'882
9
13-844
61
7799
9
10-842
61
6-746
10
13787
62
7-618
10
10-807
62
6-611
ii
13723
63
7-433
ii
10768
63
6-471
12
13-659
64
7-238
12
10-728
64
6-323
13
I3-594
65
7-035
13
10-688
65
6-167
14
13-528
66
6-823
H
10-647
66
6-003
15
13-462
67
6-599
15
10-606
67
5-830
16
I3399
68
6-366
16
10-567
68
5-647
17
I3'337
69
6-122
17
10-529
69
5-454
18
13-274
70
5'86 9
18
10-490
70
5-252
19
13-209
7i
5-604
19
10-449
7i
5-039
20
13-142
72
5'350
20
10-407
72
4-833
21
13-072
73
5'Il6
21
10-363
73
4-641
22
12-998
74
4-906
22
10-316
74
4-467
23
12-921
75
4-730
23
10-267
75
4-321
24
12-840
76
4-556
24
10-217
76
4-175
25
12757
77
4-392
25
10-164
77
4-038
26
12-672
78
4-225
26
10-110
78
3-896
27
12-583
79
4-036
27
10-053
79
3734
28
12-493
80
3-859
28
9-995
80
3-583
29
12-407
81
3-666
29
9-940
81
3-4I5
30
12-325
82
3-490
3O
9-888
82
3-262
31
12-243
83
3-308
31
9-835
83
3-102
32
12-157
8 4
3-130
32
9779
84
2-945
33
12-066
85
2-944
33
9-720
85
2-780
34
1 1 -970
86
2-780
34
9-658
86
2-634
35
11-870
87
2-645
35
9-593
87
2-512
36
11765
88
2-563
36
9-524
88
2-438
37
11-658
89
2-468
37
9-454
89
2-352
38
11-548
90
2-324
38
9-381
90
2-221
39
n-434
9i
2-309
39
9-306
91
2-207
40
11-321
92
2-392
40
9-231
92
2-283
4i
II-2IO
93
2-486
41
9-157
93
2-368
42
11-099
94
2-528
42
9-083
94
2-407
43
10-987
95
2-546
43
9-007
95
2-423
44
IO-870
96
2-501
44
8-929
96
2-382
45
10-748
97
2-376
45
8-846
97
2-268
46
IO-6I9
98
2-229
46
8-759
98
2-134
47
10-484
99
2-003
47
8-666
99
1-926
48
10-338
100
1-602
48
8-567
100
1-552
49
10-179
101
1-185-
49
8-457
IOI
I-I57
50
IO'OO8
1 02
754
50
8-339
102
742
51
9-825
1O3
321
51
8-212
1O3
318
TABLE XVII.
CCXVll
Single Life Annuities (Carlisle). Available Interest on Capital at the following
rates, Redemption being at 3 per cent.
Age
10 per cent.
Age
10 per cent.
Age
10 per cent.
ARC
10 per cent.
7-829
26
8-409
52
6-956
78
3-6I4
I
8-348
27
8-370
53
6-855
79
3-475
2
8-583
28
8-330
54
6751
80
3343
3
4
7
8
8-765
8-854
8-912
8-933
8-937
8-927
8./-k T s\
29
30
31
32
33
34
8-292 '
8-255
8-218
8-179
8-138
8-094
11
57
58
59
60
6-641
6-526
6-406
6-284
6-164
6-049
81
82
83
84
85
86
3-I97
3-062
2-921
2782
2634
2-502
9
m g\
910
8.QQ{.
35
8-048
61
5'944
87
2-392
10
OOO
36
8-000
62
5-839
88
2324
II
8-860
37
7-951
63
5-730
89
2-246
12
8-833
38
7-899
64
5-613
90
2-127
13
4
:t.
17
18
19
20
8-806
8778
8750
8723
8-697
8-67I
8-643
8-6I4
39
41
42
43
44
45
46
7-846
7792
7739
7-686
7-632
7-576
7-517
7'453
65
66
67
68
69
70
71
' 72
5-490
5-360
5-221
5-074
4-918
4-753
4-578
4-407
91
92
93
94
95
96
97
98
2-II4
2-183
2-26l
2-296
2-3II
2-274
2-I70
2-046
21
8-584
47
7-386
73
4-247
99
1-854
22
8-552
48
7-3I4
74
4'IQI
100
1-505
23
24
25
8-SI8
8-483
8-447
49
50
51
7-234
7-147
7'053
75
76
77
3-977
3-853
3-736
101
102
103
I-I3I
732
3 l6
e e
TABLE XVIII.
Decimal Equivalents for every Farthing in the Pound.
Calculated to 8 places of decimals.
By removing the decimal point two places to the right,
the rate per cent, corresponding to the s. d. columns will be
obtained : Thus lofd. = 0-44/9167, and by observing the
>V
rule referred to above, the number will be converted into
04^4791 67, which is the rate per cent.
TABLE XVIII.
Decimal Equivalents for every Farthing in the Pound.
ccxxi
. d.
Decimal
s. d.
Decimal
s. d.
Decimal
*. d.
Decimal
i
00104167
oi
05104167
2 Ol
10104167
3 i
15104167
00208333
05208333
2 0|
10208333
3oi
2
15208333
1
003125
of
053125
2 0}
103125
3 of
153125
00416667
I
05416667
2 I
10416667
3 i
15416667
!l
00520833
ii
05520833
2 J i
10520833
3 ii
15520833
l
00625
N
05625
2 l
10025
3 ii
15625
1 4
00729167
if
05729167
2 If
10729167
3 J 4
15729167
2
00833333
2
05833333
2 2
10833333
3 2
15833333
2 i
009375
2i
059375
2 2l
109375
3 21
159375
01041667
06041667
2 2l
11041667
16041667
2 4
01145883
2 4
06145883
2 2|
11145883
3 2 |
16145883
3
0125
3
0625
2 3
1125
3 3
1625
3i
01354167
3i
06354167
2 3i
II354I67
3 3i
16354167
01458333
if
06458333
II458333
3 3|
16458333
34
015625
3
065625
2 3f
115625
165625
4
01666667
4
06666667
2 4
II666667
3 4
16666667
4i
01770833
4i
06770833
2 4i
11770833
3 4i
16770833
01875
4f
06875
2 4^
II875
16875
44
01979167
41
06979167
2 4|
II979I67
3 4f
16979167
5
02083333
5
07083333
2 5
12083333
3 5
17083333
5i
021875
5i
071875
2 5i
I2I875
3 5i
171875
02291667
Si
07291667
12291667
3 5i
17291667
54
02395833
5f
07395833
2 5f
12395833
3 5f
17395833
6
025
6
075
2 6
125
3 6
175
6i
02604167
6i
07604167
2 6^
12604167
3 6i
17604167
n
02708333
028125
a
6}
07708333
078125
2 6
2 6}
12708333
128125
2 6j
3 6f
17708333
178125
7
02916667
7
07916667
2 7
12916667
3 7
17916667
7i
03020833
7i
08020833
2 7i
13020833
3 7i
18020833
03125
7|
08125
2 7
I3I25
18125
7t
03229167
08229167
2 7|
13229167
3 7f
18229167
8
03333333
8 4
08333333
2 8
13333333
3 8
18333333
8i
034375
8i
084375
2 1*
134375
3 8i
184375
8*
03541667
08541667
13541667
3 8
18541667
8?
03645833
8}
08645833
2 8}
13645833
3 8f
1864583^
9
0375
9
0875
2 9
1375
3 9
1875
9i
03854167
9i
08854167
2 9i
13854167
3 .9i
18854167
9 t
9*
03958333
040625
91
9l
08958333
090625
2 9
2 9f
13958333
140625
III
18958333
190625
10
04166667
10
09166667
2 10
14166667
3 10
19166663
ioi
04270833
ioi
09270833
2 IQl
14270833
3 ioi
1927083;;
'oi
04375
IO^
09375
2 IO^
14375
3 ii
19375
io|
04479167
10}
09479167
2 10}
14479167
3 io|
1947916;
II
04583333
II
09583333
2 II
14583333
3 ii
Hi
046875
III
096875
2 Hi
146875
3 ni
196875
04791667
1 1 \
09791667
2 Ilf
14791667
3 n
19791665
Il
04895833
Ilf
09895833
2 Il|
14895833
3 nf
1989583:
I
5
2.
'I
*^ o
^5
4- O
20
ccxxii THE ENGINEER'S VALUING ASSISTANT.
Decimal Equivalents for every Farthing in the Pound.
s. d.
Decimal
s. d.
Decimal
s. d.
Decimal
s. d.
Decimal
4 oi
20104167
5 oi
25104167
6 o4-
30104167
7 oi
,35104167
4 o
20208333
5 o
25208333
6 o
30208333
7 o
35208333
4 of
203125
5 of
253125
6 of
303125
7 of
353125
4 i
20416667
5 i
25416667
6 i
30416667
7 i
35416667
4 ii
20520833
5 H
25520833
6 ii
30520833
7 ii
35520833
4 ii
20625
5 i*
25625
6 ^
30625
7 ii
35625
4 if
20729167
5 if
25729167
6 if
30729167
7 if
35729167
4 2
20833333
5 2
25833333
6 2
30833333
7 2
35833333
4 21
209375
5 21
259375
6 21
309375
7 21
'359375
4 2i
21041667
5 2i
26041667
6 2$
31045967
7 2i
36041667
4 2f
21145883
5 2f
26145883
6 2f
3II45883
7 2f
36145883
4 3
2125
5 3
2625
6 3
3125
7 3
3625
4 3i
21354167
5 3i
26354167
6 3i
3I354I6
7 3i
36354167
4 3i
21458333
5 3*
26458333
6 3*
3H58333
7 3i
36458333
4 3*
215625
5 31
265625
6 3f
315625
7 3f
365625
4 4
21666667
5 4
26666667
6 4
31666667
7 4
36666667
4 4i
21770833
5 4i
26770833
6 4i
31770833
7 4i
36770833
4 4i
21875
5 4i
26875
6 4*
31875
7 4i
36875
4 4t
21979167
5 41
26979167
6 4|
3I979I67
7 4|
36979167
4 5
22083333
5 5
27083333
6 5
32083333
7 5
37083333
4 Si
221875
5 Si
271875
6 Si
321875
7 Si
371875
4 5
22291667
5 5i
27291667
6 5*
32291667
7 5*
37291667
4 5t
22395833
5 51
27395833
6 51
32395833
7 5f
37395833
4 6
225
5 6
275
6 6
325
7 6
'375
4 6i
22604167
5 6i
27604167
6 6i
32604167
7 6i
37604167
4 6
22708333
5 6i
27708333
6 6
37708333
7 6
37708333
4 6}
228125
5 6f
278125
6 6f
328125
7 6f
378125
4 7
22916667
5 7
27916667
6 7
32916667
7 7
37916667
4 7i
23020833
5 7i
28020833
6 7i
33020833
7 7i
38020833
4 7*
23125
5 7i
28125
6 7
33125
7 7i
38125
4 7l
23229167
5 7f
28229167
6 7f
33229167
7 7f
38229167
4 8
23333333
5 8
28333333
6 8
'33333333
7 8
38333333
4 8i
234375
5 8i
284375
6 8i
'334375
7 8i
384375
4 8i
23541667
5 8i
28541667
6 8*
33541667
7 8i
38541667
4 8f
23645833
5 8f
28645833
6 8f
33645833
7 8f
38645833
4 9
2375
5 9
3875
6 9
'3375
7 9
3875
4 9i
23854167
5 9i
28854167
6 9i
33854167
7 9i
38854167
4 9i
23958333
5 9i
28958333
6 9*
33958333
7 9i
38958333
4 9l
240625
5 9f
290625
6 9f
340625
7 9t
390625
4 10
24166667
5 10
29166667
6 10
34166667
7 10
39166667
4 ioi
24270833
5 ioi
29270833
6 ioi
34270833
7 ioi
39270833
4 io
24375
5 ioi
29375
6 loj
'34375
7 ii
'39375
4 iof
24479167
5 iof
29479167
6 iof
34479167
7 iof
39479167
4 ii
24583333
5 ii
29583333
6 ii
34583333
7 ii
39583333
4 ni
246875
5 ni
296875
6 ni
346875
7 ni
396875
4 ii*
24791667
5 n
29791667
6 ni
34791667
7 ni
39791667
4 nf
24895833
5 nf
29895833
6 iif
34895833 '
7 ii*
39895 8 33
5 o
25
6 o
3
7 o ; -35
8 o ' -40
TABLE XVIII.
Decimal Equivalents for every Farthing in the Pound.
CCXXlll
*. d.
Decimal
*. d.
Decimal
s. d.
Decimal
s. d.
Decimal
8 o
40104167
9 oi
45104167
10 oi
50104167
ii o
55104167
I t
40208333
9 o
45208333
10
50208333
II
55208333
8 of
403125
9 of
453125
10 of
503125
II Of
553125
8 i
40416667
9 i
45416667
10 I
50416667
II I
55416667
8 ii
40520833
9 ^
45520833
10 ii
50520833
II Ii
55520833
8 i*
40625
9 i
45925
10 l
50625
II I*
55625
8 if
40729167
9 if
45729167
10 if
50729167
II if
55729167
8 2
40833333
9 2
-45833333
10 2
50833333
II 2
55833333
8 2i
409375
9 2i
"459375
IO 2i
509375
II 2i
'559375
8 2*
41041667
9 2
46041667
10 2
51041667
II 2
56041667
8 2f
41145883
9 2|
46145883
10 2f
5II45883
II 2f
56145883
8 3
4125
9 3
4625
10 3
5125
II 3
5625
8 3i
41354167
9 3*
46354167
10 3i
5I354I67
ii 3i
56354167
8 3*
4H58333
9 3*
46458333
10 3
5H58333
ii 3k
56458333
8 3l
415625
9 3f
465625
10 3f
515625
ii 3t
565625
8 4
41666667
9 4
46666667
10 4
51666667
ii 4
56666667
8 4i
8 4*
41770833
41875
9 4i
9 4i
46770833
46875
10 4i
10 4|
51770833
51875
ii 4i
ii 4i
56770833
56875
8 4*
41979167
9 4f
46979167
10 4f
51979167
ii 4|
56979167
8 5
42083333
9 5
47083333
10 5
52083333
ii 5
57083333
8 Si
421875
9 5i
471875
10 5i
521875
ii Si
571875
8 5*
42291667
9 5i
47291667
10 5
52291667
ii Si
57291667
8 5t
42395833
9 5t
47395833
10 5f
52395833
ii 51
57395833
8 6
425
9 6
475
10 6
525
ii 6
575
8 6i
42604167
9 6i
47604167
10 6
52604167
ii 6i
57604167
8 8
42708333
9 6*
47708333
10 6i
52708333
ii 6
57708333
8 6f
428125
9 6}
478125
10 6}
528125
ii 6f
578125
8 7
42916667
9 7
47916667
10 7
52916667
ii 7
57916667
8 7i
43020833
9 7i
48020833
10 ;i
53020833
H 7i
58020833
8 7
43125
9 7i
48125
10 7i
53125
ii 7i
58125
8 7^
43229167
9 7*
48229167
10 7f
53229167
ii 7f
58229167
8 8
'43333333
9 8
48333333
10 8
'53333333
ii 8
58333333
8 8i
434375
9 8i
484375
10 8i
"534375
ti 8
584375
8 8
43541667
9 8J
48541667
10 8^
53541667
ii 8|
58541667
8 8f
43645833
9 8|
48645833
10 8f
53645833
ii 8f
58645833
8 9
4375
9 9
4875
10 9
5375
ii 9
5875
8 9i
43854167
9 9i
48854167
10 9i
53854167
H 9i
58854167
8 9*
8 93
43958333
440625
9 9i
9 9f
48958333
490625
10 9^
10 9|
53958333
540625
ii 9^
H 9l
58958333
590625
8 10
44166667
9 10
49166667
10 IO
54166667
II IO
59166667
8 ioi
44270833
9 ioi
49270833
10 io|
54270833
ii ioi
59270833
8 io
'44375
9 io
49375
10 10^
'54375
II I0
'59375
8 lof
44479167
9 iof
49479167
10 io|
54479167
II lOf
59479167
8 ii
44583333
9 ii
49583333
II II
54583333
II II
59583333
8 ni
446875
9 ni
496875
10 \\\
546875
ii ii
596875
8 ii -44791667
9 n
49791667
10 11^
54791667
ii n|
59791667
8 nf
44o95 8 33
9 "S
49895833
10 Iif
54895833
ii nf
59895833
9 o
45
10
50
II
'55
12
60
CCXX1V
THE ENGINEER'S VALUING ASSISTANT.
Decimal Equivalents for every Farthing in the Pound.
s. d.
Decimal
s. d.
Decimal
*. d.
Decimal
s. d.
Decimal
12 Ql
60104167
13 oi
65104167
14 oi
70104167
15 oi
75104167
12 oj
60208333
13 oi
65208333
M oi
70208333
15 oi
75208333
12 Of
603125
13 of
653125
14 Of
703125
15 of
753125
12 I
60416667
13 I
65416667
H I
70416667
15 I
75416667
12 II
60520833
13 ii
65520833
H I?
70520833
15 Ii
75520833
12 ii
60625
13 ii
H ii
70625
15 ii
75625
12 if
60729167
13 if
65729167
H if
70729167
15 if
75729167
12 2
'60833333
13 2
65833333
14 2
70833333
15 2
75833333
12 21
60559375
13 21
65559375
14 2l
70559375
15 21
75559375
12 2j
61041667
13 2i
66041667
H 2 i
71041667
15 2l
76041667
12 2f
61145883
I 3 2f
66145883
14 2f
71145883
15 2f
76145883
12 3
6125
13 3
6625
H 3
7125
15 3
7625
12 3i
6I354I67
13 3i
66354167
14 3?
71354167
15 3i
76354167
12 3i
61458333
13 3i
66458333
71458333
15 3i
76458333
12 3f
615625
13 3f
665625
H 3i
715625
15 3f
765625
12 4
61666667
13 4
66666667
14 4
71666667
15 4
76666667
12 4!
61770833
13 4i
66770833
14 4i
71770833
15 4i
76770833
12 4i
6l875
13 4i
66875
14 4i
71875
15 4i
76875
12 4f
61979167
13 41
66979167
14 4f
71979167
15 4f
76979167
12 5
62083333
13 5
'67083333
14 5
72083333
15 5
77083333
12 si
621875
13 Si
671875
H 5i
721875
15 54
771875
12 5i
62291667
13 5i
67291667
14 5i
72291667
15 5i
77291667
12 5f
62395833
13 5f
67395833
72395833
15 5f
77395833
12 6
625
13 6
675
14 6
725
15 6
775
12 61
62604167
13 6i
67604167
14 6i
72604167
15 6i
77604167
12 6i
62708333
J 3 6 i
67708333
14 6i
72708333
15 61
77708333
12 6f
628125
13 6f
678125
H 6f
728125
15 6f
778125
12 7
62916667
13 7
67916667
14 7
72916667
15 7
77916667
12 7i
63020833
13 7i
68020833
H 7i
73020833
15 7i
78020833
12 7i
63125
13 7i
68125
14 7i
73125
78125
12 7f
63229167
13 7f
68229167
73229167
15 1\
78229167
12 8
63333333
13 8
68333333
14 8 4
73333333
i S 8
78333333
12 81
634375
13 8i
684375
14 8i
734375
15 8i
784375
12 8|
63541667
I "^ Oo"
68541667
14 8i
73541667
15 8i
78541667
12 8f
63645833
13 8f
68645833
14 8f
73645833
15 8f
78645833
12 9
6375
13 9
6875
14 9
7375
15 9
7875
12 9!
63854167
13 9?
68854167
H 9i
73854167
15 9i
78854167
12 91
63958333
13 9i
68958333
73958333
15 9i
78958333
12 9f
640625
13 9f
690625
H 9f
740625
15 93
790625
12 IO
64166667
13 10
69166667
14 10
74166667
15 10
79166667
12 IO
64270833
13 ioi
69270833
14 ioi
74270833
15 ioi
79270833
12 loj
64375
13 ioi
69375
14 ioi
74375
15 ii
79375
12 lOf
64478167
13 lof
69479167
14 lof
74479167
15 I0 f
79479167
12 II
64583333
13 ii
69583333
14 II
74583333
15 H
79583333
12 Il
646875
13 ni
696875
14 II?
746875
15 ni
796875
12 Il|
64791667
13 ni
69791667
14 Hi
74791667
15 ni
79791667
12 Ilf
64895833
13 m
69895833
H H}
74895833
15 nf
79895833
13 o
65
14 o
70
15 o
75
16 o
80
TABLE XVIII.
Decimal Equivalents for every Farthing in the Pound.
ccxxv
1. d.
Decimal
*. d .
Decimal
s. d.
Decimal
! s. d.
Decimal
16 oi
80104167
17 oi
85104167
18 oi
90104167
19 oi
95104167
16 o
80208333
17 o
85208333
18 ol
90208333
19 o^
95208333
16 of
803125
17 of
853125
18 of
903125
19 of
953125
16 i
80416667
17 I
85416667
18 i
90416667
19 I
95416667
16 ii
80520833
17 ii
85520833
18 ii
90520833
19 ii
95520833
16 i|
80625
17 i
85625
18 i|
90625
19 ii
95625
16 if
80729167
17 if
85729167
18 if
90729167
19 if
95^9167
16 2
'80833333
17 2
85833333
18 2
90833333
19 2
95833333
16 2i
80559375
17 2i
85559375
18 2i
90559375
19 2i
'95559375
16 2$
81041667
17 2$
86041667
18 2i-
91041667
19 2
96041667
16 2 f
81145883
17 2f
86145883
18 2f
9IM58S3
19 2f
96145883
16 3
8125
17 3
8625
18 3
9125
19 3
9625
16 3i
81354167
17 3*
86354167
18 3i
91354167
'9 3?
96354167
16 3*
81458333
17 3*'
86458333
18 3*
9H58333
19 3^
96458333
16 3 ; f
815625
17 3*
865625
18 3f
915625
19 3?
965625
16 4
81666667
17 4
86666667
18 4
91666667
19 4
96666667
16 4i
81770833
17 4i
86770833
18 4i
91770833
19 4i
96770833
16 4
81875
17 4^
86875
18 4$
91875
19 4i
96875
16 4f
81979167
17 4?
86^79167
18 4 f
91979167
19 4l
96979167
16 5
82083333
17 5
87083333
18 5
92083333
19 5
97083331
16 si
821875
17 Si
871875
18 Si
921875
J 9 5i
971875
16 5
82291667
17 5i
87291667
18 5i
92291667
97291667
16 sf
82395833
17 5*-
87395833
1 8 5f
92395833
19 5?
97395833
16 6
825
17 6
875
18 6
925
19 6
'975
16 6i
82604167
17 6i
87604167
18 6i
92604167
19 6i
97604167
16 6
82708333
17 6|
87708333
18 6|
92708333
19 6^
97708333
16 6f
828125
17 6?
878125
18 6f
928125
19 6f
978125
16 7
82916667
17 7
87916667
18 7
92916667
19 7
97916667
16 7i
83020833
17 7*
88020833
18 7i
93020833
19 7?
98020833
1 6 7$
83125
17 72
88125
18 7!
93125
19 7^
98125
16 7*
83229167
17 74"
88229167
18 7f
93229167
19 7f
98229167
16 8
83333333
17 8
88333333
18 8
93333333
19 8
98333333
16 8i
834375
17 8i
884375
18 8i
'934375
19 8i
984375
16 8^
83541667
17 8i
88541667
18 8
93541667
19 8^
98541667
16 85
83645833
17 8f
88645833
18 8%
93645833
19 8f
98645833
16 9
8375
17 9
8875
18 9
'9375
19 9
9875
16 9i
83854167
17 9i
88854167
1 8 9i
93854167
19 gi
98854167
1 6 9^
83958333
17 9^
88958333
18 9!
93958333
19 92
98958333
16 9?
840625
17 94
890625
1 8 9*
940625
19 9f
990625
16 10
84166667
17 10
89166667
18 10'
94166667
19 10
99166667
1 6 ioi
84270833
17 ioi
89270833
1 8 ioi
94270833
19 ioi
99270833
16 io
84375
17 io
89375
18 io|
'94375
19 io
'99375
16 iof
84479167
17 iof
89479167
18 iof
94479167
19 iof
99479167
16 ii
84583333
17 ii
89583333 ,
18 ii
04583333
19 II
99583333
16 ni
846875
17 ni
896875
18 ni
946875
19 ni
996875
16 n
84791667 j
17 n
89791667 i 18 n
94791667
19 Il|
99791667
16 ill
84895833 !
17 iif
89895833; 1 8 n2
94895833
19 nf
99895833
17 o
85
18 o -90 19 o -95
20
*
INDEX.
PAGE
A PROBLEMATICAL CASE . r,i <; ftf j j ,^, ,',.' > 9-
f* A rule cannot be laid down expressing risk in mining adventure . 19
Acts of Parliament, recent, relating to mining . . / '' >'?. . 5
Acquaintance with mineral district necessary -ri f r ! .- - . . 9
Advantage of receiving interest quarterly . .-.* . . . -25
formula, with example . . 26
Advantage of adequate arrangements ..156
Adventure, tern; of lease should be sufficiently long to justify . .114
Adjoining property, characteristics of, a good guide . . '" , . 1 1
Ample percentage should be allowed on mining property to cover risk . 1 3
time should be allowed for development where several seams
exist . .-'.; /.->'.: f. '>. '!'''; ' -J ,. : *". : " -', -'* ' . 114
machinery and surface arrangements should be provided . .156
Amount of i per annum in n years formula . . . '. . 27
rule for finding . . . .27
,, with interest realised m times in
a year . ._; ., - ^ , ..^ . 27
,, ,, formula and example *. ., . . 27
capital invested in mining . . . . - # 5
Amounts, an additional test of the accuracy of the table of . . .42
American railways . . . . . . . . . 1 50
America, purchase of mineral tracts in, for future development . .152
Annuity once determined, must be purchased at a certain agreed per-
centage ....... . . . . .20
from unopened mines deferred during period of development . 20
every sum of money annually accruing may be treated as an 23
not payable until after a fixed number of
years, is a deferred . . . 23
anticipated, formula for finding value of . . . . .- . 25
found by adding redemption fund to interest . . .30, 32
deferred, value of, may be derived from value immediate 35, 36
with two rates of interest which i will purchase . 36
immediate . 37
and redemption fund, detailed example showing accuracy of
the mode .....>. 40
[2] INDEX.
PAGB
Annuity, deferred, Thoman's definition of ... . ^ . 55
n only embraces one rate of interest 5 5
value compared with true value, showing
discrepancy . . . . 56
surplus, should not be invested in same mines as annuity is
derived from . . . *. . . . -59
value of, derived from a given output . . . . .80
of lessor is dependent upon success of lessee . . . .115
value of, by tables of multiples 1 24
deferred ' 7 .~ J 26
which i will purchase 131
constant, how to obtain from new colliery . . . .156
Annuities, transferable 23
deferred, have been considered very complicated . . 37
present value of i per annum wrong in all writers on . 43
Mr. Peter Hardy's Papers on, in 1850 46
,, deferred, with two rates of interest, not dealt with before . 55
previous rules only give approximations . . . 55
general principle applied to . . . -55
terminable ; original purchase-money should be redeemed
within the term of . . . . . . . .62
Rouse's Investigation of the errors of all writers on . . 60
amount of, at compound interest . . . . . .69
present value of, at compound interest . . ' . . 74
cases and examples by the tables and by logs 4' . . 70
perpetual, treatment of -.','*:>; * -. . 75
,, present value of . . . . v . 75
deferred, or reversions . . . . . . . .76
cases and examples by the tables and by logs 76, 77
Appendix to Inwood's Tables, cumbrous rule introduced into . . 43
Area of coal leased, when too large, injurious to interest of lessor . . 1 1 5
small, lessee . .115
matters which require attention when assigning area 1 1 5
Argentine Republic, silver and lead mines of the 153
drawbacks connected with mining in the . .153
Arithmetic, Byrne's Dual ...... ! ,'.'.-. 72
Arrangements, defective, occasion great loss . . -. . , , . . 9
Assurance Magazine, letters to, by Peter Gray, F.R.A.S. . . 47
important note by Editor of . '.- < .49
Australia, mining in . . , - . . . . . .153
As the rate for redemption is increased, the redemption fund decreases . 148
detailed example illustrating above . .148
BANKS, Joint Stock, Limited , . , , , . . .151
Barren and denuded tracts of ground should le allowed for in
making estimate . i .12
Benwell, -Mr., his pamphlet . - . . . . . .43
INDEX. [3]
PJLGE
Biden, Mr. Downing, small table by 50
his opinion of the old tables . . . .61
' Binomial theorem ' . . . . < . , . . 26
Boards of Directors, interference by, absurd 10
Bond fide undertakings, every facility should be offered for . . .115
Bonds, loans, and stocks ; foreign . .- *'.-.,, . .151
Boring in search of coal and other minerals . . . _, . .*,,'.. 8
Brazils, mining in the . . *. . . . - *V" * *.'' 153
Buddie, Mr., examined before Committee of House of Lords . . 14
Dunn's reference to, in his work on the coal trade . .15
Byrne's Dual Arithmetic -* * * ..." ^ , . . .72
/CAPITAL, amount of, invested in mining . . V . 5
\J and machinery, deep mining a question of . .6
percentage should be allowed purchaser for redemption of 14
redemption of, what it means . .... t . * . . 58
a question of great importance . . .61
unless provided for, capital is lost . . 62
if provided for, capital can be re-invested . 62
three per cent, normal rate of interest for . 79
,, practical example 83
and labour . . 157
,, results of starting with insufficient . . .,-. - ,, . 158
Capitalists often misled by opinions of unqualified persons . .,. . 6
discouraged when high royalties are demanded . / v . 115
home mining should receive attention of ... . : .154
Care and judgment required in selecting investments . -i -V . 151
Case, a problematical . . . . . . . f ~ > .. -, . 9
Cero-de-Pasco, silver mines of the . -, . . , . ; ; ..*_ .. * 153
Characteristics of adjoining property a good guide : . * * . . 1 1
Clause, short leases of mineral property should contain an extension . 114
Coal and other minerals, boring in search of ' . . . . 8
quantity per acre may be determined by specific gravity . .11
proportion of large and small 12
area of leased, when too large, injurious to interest of lessor . 1 1 5
small, lessee -115
matters which require consideration when assigning 115
Coal-fields ; Somersetshire, Leicestershire, and Staffordshire ... 8
extension of Staffordshire, due to Mr. Johnson ... 8
trade, Dunn's reference to Mr. Buddie in his work on the . .15
years' purchase ; . . . - ' . .16
Colonial Government investments . . . . . . .150
Colliery, Sand well Park 8
undeveloped freehold with overlying estate, valuation of . .91
ditto, with half-yearly and quarterly payments . . 93
difference in values 96
how to lay out a new < 1 SS) 1 S^
[4] INDEX.
PAGE
Commercial centres, firms of engineers needed in . 7
Cominittea of House of Lords, in 1829 . . H;. . ,, . 14
Mr. Buddie examined before ;crt*5ss' . 14
,, Oomnions on rating of mines . -". " t 15, 51
misled by evidence .".ic?r; ; ; -4 'v " : . 52
Commercial excitement taken advantage of to float worthless schemes . 155
Companies, insurance . " - * . . . ; /i^" ' Jj-:. . .150
dock and shipping . , - * * v:-^ -.*' - . . 151
telegraph . ''''' -' ; .''^^''nv>-r**7':- ! . ; -.''..:'. . 151
English, in Spain ^ '<''' &$ '- ->-.' 3tftNNf$ -i*i;;% . .154
Complicated, subject of deferred annuities has been considered very . 37
Compound interest, examples and cases by logs and tables . . .67
amount of annuities at . . . . . .69
- V present value of sums at o. r : ,lo J:.i.- r.%"; T*,'*/'/ . 72
,, present value of annuities at . u^V"i-'< *"" . . 74
Computation of minerals complicated where faults exist *VVS .11
comparatively simple when property is opened
up :;-0 ii<5': II
Conditions considered in calculating the tables for this work . -33
and circumstances which affect value of royalty . . .91
Constant annuity, how to obtain from new colliery . . . .156
Construction and use of valuation tables :/ - "<'-. . - . . * . 21
- of tables very tedious . . ';x v '^ ... . .33
Cost of winning affects value of mineral property . ' * ''>. ^f>~;-'' . .'. 1 2
production depends on the labour market . ^V-i^- : *'> J '',..>".- . 13
winning is the same whatever the term of leaee iii';&fJO;.; . 1 14
Cotterell, Mr. J. IT., his opinion respecting years' purchase . . . 15
Crown, rights of the, as lord of the manor . ' f - ^ ' r ."T. * 'i : -. 'V. '* ' . 116
Cumbrous rule in Inwood's appendix . . . . fc^-liynsCrf^-t; '- . 43
' Customary interest ' . . . . <>U/ ^ :p:ii>j2;;37i-4 s : -y '+".- ,. 86
Comparison of values at different rates of interest -:ojkc 'Cf?'/' ^ .. .147
Causes which affect the price of stock . -' + r ;-" J, : I fy&)Q&&tjfa . 149
DAVIES, Mr. G., first to compute tables with two rates of interest . 43
Dean Forest, Mr. Marcus Scott's report on some portions of . . 1 8
Decimals, Tables (I), (II), and (III) in this work originally calculated
to 15 places of . . V' " J 3 r "~/; . 43
Deep mining a question of capital and machinery . .-:"., , ',.:' . 6
Deferred annuity, definition of >>-. ..-:</.! !, V .V- - .1 v> . - . 23
formula for finding value of I^.K'.^V^; ..u'- .;. ..' :;, 25
value may be derived from value immediate . 35, 36
which 1 will purchase with two rates of interest . 36
Thoman's definition of .. - . :-"--* -.-* -^.i ", '-' , 55
j, only embraces one rate of interest 55
value compared with true value, showing
discrepancy. . . ' * f 56
. value of tables by multiples .... . 126, 127
INDEX. [5]
PAGH
Deferred annuities with two rates of interest, relation between imme-
diate and 34
have been considered very complicated . . . 37
with two rates of interest never dealt with before . 55
previous rules only give approximations . . 55
general principle applied to . . . . -55
or reversions * . . " '.* V- i . 76
cases and examples by the tables and by logs . 76, 77
values may be obtained directly from Tables (IV) and (VII) . 128
at high rates of interest ; examples . . . . 1 59
and Immediate Values at high rates of interest ; Tables
(A, B, 0, andD) ...... 159-164
Deducing values from tables of multiples . . . '.''. .121
Defect, excess in size of machinery better than . . .- . . 10
Defective arrangements cause great loss . . .-.- . 9
Definition of ' Value ' . . . . . . . . . 3
Denuded and barren tracts of ground should be allowed for in making
estimate . '" ....-... . 12
Depths, term of lease should be longer when minerals exist at great . 114
Detailed examples of valuation of mineral property . .- . . 80
Development, ample time should be allowed for, where several seams exist 114
Difference of opinion as to amount of percentage to be allowed . .14
Difficulties of deep mining not insuperable . . ..*".. . 6
Difficulty of discovering faults . . . . ". - . n
Directors, interference by Boards of, absurd . . ' ' J '* / . . 10
Discoveries of minerals yet to be made - " - '.'. ; . . 5
Distinctive features which affect value, every property has . ; . . . 1 1
skill and judgment of engineer must determine the 1 1
Dobson, Mr., his opinion respecting years' purchase ' .* ''". '<' ' , " . 15
Dock and shipping companies . . .-/". . .. . . 151
Dormant, owners receive no benefit from minerals lying , " fi f .115
Downing Biden, Mr., small table by .;'-'. . . . 5
his opinion of the old tables ' . .' . . 61
Drawbacks connected with virgin properties *' ' t-j". * ... . 6
mining in the Argentine Kepublic . .153
Dual Arithmetic, Byrne's "',';:.-'. . 72
Dunn's reference to Mr. Buddie in his work on the coal trade ... . 15
years' purchase . . . > ' , " " . ; r .. .. 16
compared with true value . . ' ' .* .. .51
EAELY exhaustion of minerals erroneous . . . . - t . . 5
Editor of Assurance Magazine, important note by ... 49
Engineer, all advice on mining comes within his province ... 7
should personally ascertain every fact for or against a property 10
determine distinctive features of property . . .n
Engineers, firms of, needed in commercial centres ..... 7
should be financiers ........ 7
[6] INDEX.
PAGH
Engineers should be geologists . . . --; ! ; < ' -t^ " . 8
English companies in Spain . . . . , . .. . . - .. . 154
Government funds . . . 149
Errors of writers on Annuities, Rouse's investigation of , . .60
Error of investing indiscriminately in foreign mines ; ... . . .152
Erroneous, present value of 1 per annum by the old rule is . .31
Every sum of money annually accruing may be treated as an annuity . 23
Evidence, Committee of House of Commons misled by . . . 52
Evil effects of heavy royalties ' ...-.; ." .-. .116
Example in validation, where a certain sum has to be spent in additional
works to continue the annuity over the whole term . . .86
Examples demonstrating accuracy of formulae in this work . . 37-41
of deferred values at high rates of interest . . . . 159
Examination of outcroppings necessary before operating . . .10
,, to compute quantity of water . 10
Excess in size of machinery better than defect 10
Expenditure of large sums of money should be entrusted to men of judg-
ment . . . . . . 10
Experience and judgment should determine amount of royalty . . 91
Extension of Staffordshire coal-field due to Mr. Johnson ... 8
clause, short lease of mineral property should contain . .114
Extra risk incurred in purchasing foreign mines . . . . .158
TjlACILITIES should be offered to encourage londjuh undertakings .115
J- Ear West, silver and gold mines of the, unsafe . , , . . . 152
Faults, difficulty of discovering 1 1
render computation of quantity of minerals very complicated . 1 1
Tee simple' in mines, lost, unless capital is redeemed . . . .62
Features which affect value, every property has distinctive . . .11
,, skill and judgment of engineer must deter-
mine ii
Financiers, engineers should be 7
Firms of engineers needed in commercial centres 7
Foreign stocks, loans, and bonds 151
mines, error of investing indiscriminately in . . . .152
isolated position of many precludes success . . .152
extra risk incurred in purchasing 158
higher rates of interest should be allowed on . .158
Tables (A, B, C, and D) for valuing . . . 159-164
Forest of Dean, Mr. Marcus Scott's report on some portions of the . 1 8
' free miners' of the . . -., ,.;--.- . . 116
Formation and HFC of tables of multiples ..', - . - . * r .121
Formulae, recapitulation of . . . ...... 165-167
Formulae and rules. Increase of principal at compound interest . . 23
Present value of a perpetuity of i receivable
once in every wth year . . .-'*-. ..'-:. . 24
Present value of a perpetuity of i deferred n years 2 5
[7]
Formulae and rules. Advantage of receiving interest quarterly . . 26
,, Amount of i per annum in n years . . 26, 27
Amount of i per annum in n years, with interest
convertible in times in a year . . .27
, ,, Present value of i due n years hence . .28
,,. Present value of i due n years hence, with in-
terest convertible m times in a year . .28
Redemption fund to amount to i in n years . 29
Redemption fund to amount to i in n years
with interest convertible m times in a year . 29
Immediate annuity which i will purchase, with
two rates of interest 30
,, , Present value of i per annum for n years by
the old rule 31
Present value of i per annum for n years, with
one rate of interest on capital and another for
redemption . . . . . . 31
Ditto, with interest convertible m times in a
year .... . . .31
,, Redemption fund and interest on capital are equal
, to annuity ; demonstration . . 32, 33
,, Relation between immediate and deferred annui-
ties with two rates of interest ;.:. . . 34
Examples demonstrating accuracy of formulae 37-41
in this work are given in their simplest form . 41
Fortunes to be made in Spain 154
Freehold undeveloped colliery with overlying estate, valuation of. . 91
half-yearly and quarterly payments . 93
t difference in values. . . . ,96
Funds, English Government .149
C\ feNERAL accounts, income from mines ascertained from , .14
principle applied to deferred annuities . . . -55
Gentlemen embarking in mining should understand what they are
undertaking 7
Geologists, engineers should be 8
Gold and silver mines of the Far West, unsafe . . - ' . . .152
Tables for use in purchasing , . . 159-164
Government investments, Colonial 150
Funds, English 149
Gravity, specific, quantity of coal per acre may be determined by . . 1 1
Gray, Peter, F.R.A.S., letters to Assurance Magazine by . . 47
Great attention should be given to nature of strata passed through in
sinking . . . . . . . . . . . .12
Griffith Davies, Mr., first to compute tables with two rates of interest . 43
Gross values ; reduction to nett values detailed examples . 88, 1 06, 112
Guide, characteristics of adjoining property a good . . . .11
[8] INDEX,
PAGE
HALF-YEARLY and quarterly payments, valuation of undeveloped
freehold colliery with -'>...*:. -93
Half-yearly and quarterly payments, greatly in favour of purchaser. . 96
Half-yearly and quarterly payments, difference in values . . .96
Hardy's papers on annuities in 1850 . . ^ - . . . .46
table introduced into ImuoocTs Tabks in 1853 . . . .49
WillicKs 1871 . . . .49
Heavy royalties, evil effects of *. --V * x --*-. . . .116
Haematite iron mines, yield of .' * >-> ^?.-^v . . . .12
Home mining, importance of ?'-Y" n -^-- : -V . . . . -4
should receive attention of capitalists . . . .154
House of Lords, Committee of, in 1829 14
Mr. Buddie examined before 14
House of Commons, Committee of, on Rating of Mines . . . 15, 51
misled by evidence . . . . 52
How to lay out a new colliery ; ,' '. 156
obtain constant annuity from new colliery . . . .156
Hurst's Architectural Handbook, tables in . . . .50
High rates of interest for redemption, against interest of purchaser . 148
should be allowed on foreign mines . . .158
Tables (A, B, C, and D) for . . .159-164
TGNORANOE of nature of mineral tract sometimes occasions great
J- loss 9
Immediate and deferred annuities with two rates of interest, relation
between. " "*: %"--v-'f -...;* ' ,. t -v. ,-,- , t .34
and deferred values at high rates of interest ; Tables (A, B,
0, and D) 159-164
value, deferred value may be derived from . , . 35, 36
,, annuity which 1 will purchase with two rates of interest . 37
n )) >, by tables of multiples . 124,125
Importance of home mining . . . . " ; ; . " * . 4
Important note by Editor of Assurance Magazine . -"' ' v. . . . 49
Inaccurate tables, valuations made by, must be incorrect . . . 54
Income from mines ascertained from general accounts . . . . 14
Increase of principal illustrated . . , . .... 23
rule for calculating r - . V' .-" : " -.'"' . 24
India, mining in . , '-' v' -'V- *'V - . c V . . . . 154
Industry, mining a leading branch of . ' T -. i ;r '"'v ; '- " . 5
Inspection of tables, years' purchase obtained by . / -;,- ;; v ' . . 41
Insurance Companies . . .''-; r; f '- if> . '"--,... r ; .150
Insufficient capital, results of starting with . / ':. '. . . 158
Interest, advantage of receiving quarterly . < . ! ' . '';'.'. 26
realised m times in a year, amount of i with ^. * ^ . 27
added to redemption fund gives annuity . .< ' . ' . 30, 32
deferred annuity which i will purchase, with two rates of
interest . . . . . . . y . 36
INDEX. [9]
PAGE
Interest allowed on mines, 10 to 25 per cent. . . . . 50
deferred annuities with two rates of, never dealt with before . 55
Thoman's definition of a deferred annuity only embraces one
rate of S& Y . 55
simple, cases and examples 65
., compound, examples arid cases by logs and by the Tables . 67
amount of annuities at . . . , * u-- - ' . 69
present value of annuities at . .-';; , ^ . 74
. cases and examples by
the Tables and by logs 74, 75
present value of sums at . .> '*' s . . 72
cases and examples by
the Tables and by logs . 73
^monetary transactions should be governed by average rate of . 79
normal rate for redemption of capital 3 per cent. . . . 79
'customary' ... y ; '<-, . *.X-..-^i ;- , ' . .86
source and rate of fixed, values may be obtained from the
Tables 147
comparison of values at different rates of :<. ^ . . 147
Interference by Boards of Directors absurd . . . . . r . 10
Investments, Colonial Government . . . .' , . r . . 150
great care and judgment required in selecting . . ,,.151
1 Investigation of the errors of all writers on annuities} Rouse's . . 60
ImcoocTs Tables) cumbrous rule introduced into appendix of . . . 43
useless when two rates of interest are involved . . 58
years' purchase "'... . 50
compared with true value . . . -54
serious discrepancy \ . . . -54
table of value of i per annum identical with
Smart's and other Tables . - . . . 50
Iron mines, yield of hfematite . . * . .-...12
Isolated position of many foreign mines precludes success . . .152
Importance of selecting proper investments . . . - -, ; . 147
JOHNSON, Mr., extension of Staffordshire coal-field due to . .8
*J Joint Stock Limited Banks . .151
Judgment, expenditure of large sums of money should be entrusted to
men of . 4 ^ -*-*' .10
of engineer must determine distinctive features of property . 1 1
and experience should determine amount of royalties . .91
LABOUR, mainspring of wealth . . . . . . .3
market, cost of production depends on . . . .13
and capital . . . ...'. . .157
Large and small coal, proportion of . . , . .12
[10] INDEX.
PASB
Large fortunes to be made in Spain 'V V-> ^' " * '- 154
annual output necessary . . . " . , -:.'. 155
Lease, term of, should be sufficiently long to justify adventure . .114
longer when minerals exist at great depths . 114
short term of decreases value of mineral property . . .114
of mineral property 21 years too short a term for developing . 114
Leases, short, do not benefit lessor or lessee . *- - . . .114
,, short, should contain extension clause . . . .114
Legislation, mining .......... 5
Legitimate home mining should receive attention of capitalists . .154
Leicestershire, Somersetshire, and Staffordshire coal-fields ... 8
Lessee, too small an area of coal leased, injurious to interest of . .115
Lessor, too large . . 115
Lessors annuity depends upon success of lessee . . . . .115
Letters to Assurance Magazine by Peter Gray, F.K.A.S. . . -47
Limited Joint Stock Banks 151
Loans, stocks, and bonds foreign . . . . . . . 1 5 1
Logarithms. Base of the Napierian ..... . . .26
Amount of sums at compound interest by . . 67, 68
annuities . . 69-71
Present value of sums at . 72, 73
annuities ... 75
reversions or deferred annuities at com-
pound interest by . . 77, 78
Logarithmic calculations, remarks on 140
,, properties of logarithms . . . 140,141
,, Mr. Peter Gray's work on logarithms . . 141
1 2-figure tables . . .141
,, amount of i in n years, by logs . . .141
. difference between 7 and 1 2-figure logs . . 142
present value of i per annum in n years,
with two rates of interest, by logs . . 142
difference-" between 1 2-figure logs and Table
(VII) 142
, present value deferred, by logs . . 142, 143
difference between 7 and 1 2-figure logs and
Table X . 143
,, ,, redemption fund, by logs . . . .143
difference between Table V, and 7 and 1 2-figure
logs 143
present value of i due n years her.ce, by
t logs H3
difference between Table IV, and 1 2-figure
logs 143
tLo annuity which 1 will purchase, by
logs' 143, 144
deferred annuity which 1 will purchase, by
logs . /"',:./ V v, . . 144
INDEX. [11]
PAGE
Lord of the manor, rights of the Crown as 116
Lords, Committee of House of, in 1 829 14
Mr. Buddie examined before . .14
Loss, defective arrangements occasion great ..**.. 9
MACHINERY, excess in size of, better than defect ,. ; ,. .> , . V . 10
and plant, valuation of . . *, >. . . * . 82
Magazine, Assurance, letters to, by Peter Gray, F.R.A.S. . . 47
important note by Editor of . *.. v - ... . 49
Managing salaries . ' . . . . . . .158
Management, unscientific proprietors interfering with . . . .158
Manor, rights of the. Crown as lord of the . . '/ .116
Mineral district, acquaintance with, necessary 9
property, short leases of, should contain extension clause . 114
cost of winning affects value of . . . .12
the same, whatever the term of lease 114
detailed examples of valuation of (see V) . f . . 63
short term of lease diminishes value of . , ..114
21 years too short a lease for . . , , .114
short leases of, do not benefit lessor or lessee . .114
value of, affected by its position , f v-jteT! X J 3
the Author's practice in valuing undeveloped . 19
previous tables useless for valuing . . ... . 50
when to purchase . . . .,. > , , . 155
Mineral tracts, ignorance of nature of, sometimes occasions great loss . 9
in America, purchase of, for future development . .152
Minerals, boring in search of coal and other . . . ~ . 8
computation of quantity very complicated where faults exist . 1 1
comparatively simple when property
is opened up . . . . 1 1
discoveries of, yet to be made 5
early exhaustion of, erroneous ...... 5
lying dormant, owners receive no benefit from . . .115
in the United Kingdom, vast stores of, not yet explored . . 155
Mines, income from, ascertained from general accounts . . . -14
Committee of House of Commons on rating of . . . 15,51
,, misled by evidence . .52
unopened, annuity expected from, deferred during period of
development .......... 20
interest allowed on, 10 to 25 per cent. ..... 50
,, valuation of, examples . .80
foreign, error of investing indiscriminately in . . . .152
extra risk incurred in purchasing 158
higher rates of interest should be allowed on . .158
Tables (A, B, C, and D) for use in valuing . . 159-164
Mining, importance of home 4
not always entrusted to proper pei sons ..... 4
[12] INDEX.
PACK
Mining, operations widespread, "*. 'U; 4
great skill and judgment requisite for success in .*".-;,...; > 4
a lucrative undertaking . . . , .. . . 4
worthless schemes .... -;..;.:-: . 4
recent Acts of Parliament relating to ..... 5
all advice on, comes within province of engineer ... 7
amount of capital invested in . *- 5
a leading branch of industry . *v >- : *^ .... 5
success in other trades greatly depends on .,*;>. . . 5
deep, a question of capital and machinery .... 6
virgin tracts, a question of sufficient capital to develop . . 8
reports, writers of, should be men of status .' '' T ./ v .- . 7
much depends on ' * fl*v-.-; : H-J, vt .... 7
sometimes concocted for a purpose .... 6
gentlemen embarking in, should understand what they are un-
dertaking . . ^^7/.;::v^?.-. : ^-:.;, 7
property, ample per centage should be allowed on, to cover risk 1 3
adventure, rule cannot be laid down expressing risk in . .19
in the Argentine Republic, drawbacks connected with . .153
Brazils. . -.. ^ V*; >; -;V - -''.. . . .153
in Australia . . : -.- ; '-' ; /- ! .- '; ' : - /'; .... 153
in India . . ::v ^. 154
in New Zealand . 1 54
in Spain . . - V* '-' i . A - ; '"'v '--. . . ! 54
- n persons with very limited capital should not engage in . .158
Money, expenditure of large sums of, should be entrusted iff men of
judgment ' , ? ';' ' J^ '' 4 : \ f> '',.,. ' . 'i- : . . .10
every sum of, annually accruing may be treated as an annuity . 23
market much influenced by the Press . - ,* >;i ir H9
Monetary transactions should be governed by average rate of interest . 79
Morgan's rule for value of i in n years, with two rates of interest . 45
Mules, transit of ore by . . ''*#' -* ,- : ^-jT f .'- . . .153
Multiples, tables of : formation and use . . * ".". . .121
rule for finding values from . : . . . .124
value of immediate annuities by . - v . 124,125
deferred ' ; : .-. . .126
,*, redemption fund, by . . '; '".-. . 133,134
various methods of arranging . . . 135-140
,, specimen Tables and examples showing their ( 123-127
utility (128-140
NETT VALUES, reduction from gross to & ; "V V --, 88, 1 06, 1 12
New colliery, how to lay out . - -.* ' . '. . . 155, 156
New Zealand, mining in ; ! .' -:^-- '-V.'" ' t -'- -,' : ' t . .154
Normal rate of interest for redemption of capital, 3 per cent. . . 79
Notation, system of . , . . . . . 165-167
Note, important, by Editor of Assurance Magazine . . , .49
INDEX. [13]
PAGE
OLD TABLES, Mr. Downing Bideu's opinion of the . . . .61
Operations on virgin tracts a question of capital .... 8
Opinions of unqualified persons, capitalists misled by . . .6
Opinion, valuation has hitherto been considered a mere matter of . . . 14
difference of, as to amount of interest to be allowed . . .14
of Mr. Buddie ... 14
of Mr. S. Dobson respecting- years' purchase . . . .15
of Mr. J. H. Ootterell respecting years' purchase . . . 1 5
of Mr. J. Pease .... 15
of Mr. T.J.Taylor .... 15
of Mr. II. W. Schneider, M.P. . 16
Mr. Buddie's ; Dunn's reference to 15
Ordinary tables of value of i per annum all wrong . . . 43
demonstration of error . . 43
Ore, transit of, by mules 153
Outcroppings, examination of, necessary before commencing operations . 10
to compute quantity of water . 10
Output, value of annuity derived from a given .... . . .80
large annual, necessary . . . . - . . . . 155
Owners receive no benefit from minerals lying dormant . . . J 1 5
annuity is dependent upon success of lessee . . . .115
PAMPHLET, Mr. Benwell's 43
-L Papers on annuities in 1850, Mr. Hardy's . . . . .46
Parliament, recent Acts of, relating to mining . . . . . 5
Payments, advantage of receiving quarterly . . . . . 25,96
Pease, J., his opinion respecting years' purchase . . . . 1 5
Percentage, ample, should be allowed on mining property to cover risk . 1 3
should be allowed purchaser for redemption of capital . 14
to be allowed on mineral property, difference of opinion as to 14
annuity, when determined, must be purchased at a certain
agreed 20
Perpetuities, treatment of 75
present value of 75
cases and examples 75
Perpetuity of i payable every nth year, present value of formula . 24
deferred n years, . 25
anticipated n years, . 25
Peter Hardy's Papers on annuities 46
Points for consideration in making a valuation . . . . .13
Previous tables useless for valuing mineral property . . . .50
Purchase^money should be redeemed within period of terminable annuity 60
of mineral tracts in America for future development , .152
Purchaser, half-yearly and quarterly payments in favour of . . .96
Purchasing foreign mines j extra risk incurred 158
higher rate of interest should be allowed . 158
n )) Tables (A, B, C, and D) for use in . 159-164
[14] INDEX.
PAGE
Plant and machinery, valuation of .... *-. i '"*- -I "T . 83
Practical examples in valuation .... '": ".. ; . " ',; x> . . 63
of mines . . ",';*: "i 1- . 80
of the redemption of capital . ' ~;> : . -* . .83
Present value of i due n years hence formula, rule, and example . 28
,, with interest m times in a year 28
< per annum by the old rule, formula for finding . 3 1
as deduced by the old rule erroneous . 3 1
: with two rates of interest . . .31
,, with interest m times in a year . -31
wrong in all writers on annuities . . 43
demonstration of error . 43
with two rates of interest, Mr. Morgan's
rule . . . . -45
,* with two rates of interest, Mr. Gray's
method ....*. 47
sums at compound interest . . . . . . 72
cases and examples by the
Tables and by logs 72, 73
annuities at compound interest . . . 74
cases and examples by the
Tables and by logs 74, 75
an iron mine depending on the life of a person, A, .117
detailed valuation . .117
a royalty depending on the life of a person, A, . .118
detailed valuation . . .118
annuities by tables of multiples .... 123-133
Principal, increase of, illustrated 23
rule for calculating ^ : ", - ..: '-,- ' f . . .24
Principles, tables in this work carefully calculated from first . .41
Problematical case , .' * . >_... . . . .9
Production, cost of, depends upon labour market .-..'. . . 13
Proper persons, mines not always entrusted to . -, . . . . 4
Property, engineer should ascertain every fact for or against . . .10
every, has distinctive features which affect value . . . i r
distinctive features must be determined by skill and judgment
of engineer ..-,.. i . . . . . . i r
when opened, much easier to determine value of . . .11
Proportion of large and small coal , - . . .. ' '. . ' * '' ' ' 12
Proprietors, unscientific, interfering with management . ' . 158
Provision for underground extension . '. - V - -.;< . L - " : ^' : - . 156
Proper investments, importance of selecting . " . . > '. 147
Press, money market much influenced by the V ; , . .149
QUANTITY, OF COAL per acre may be determined by specific
gravity . . . . . . . . i r
Quantity of minerals, computation of, very complicated where faults exist 1 1
INDEX. [15]
PAGE
Quantity of minerals, computation of, comparatively easy when property
is opened up . f - ' . . . . . , . . .11
Quarterly, advantage of receiving interest ...... 25
formula and example . . 26
and half-yearly payments, valuation of freehold undeveloped
colliery with ; ". . . * -93
difference in values / , . . 96
,j in favour of purchaser . . , . 96
Question of great importance, redemption of capital is a . .61
RATE of interest on mining property, 10 to 25 per cent. , . . 50
Rating of mines, Committee of House of Commons on . f . 15, 5 1
misled by evidence . 52
Reasonable output must be assumed in making valuation . . 19
Railways, English . . + , * "* . . . . 149
Indian ... ... . , . ,..,. . . ..... .150
Colonial . . *. ~ . - ...* . .150
,, American ...,.,.. ^ ._.. . . .150
Recapitulation of Formulae . ,, . , - , : V . ., . 165-167
Recent Acts of Parliament relating to mining ..'-.-.'. . . 5
Redemption of capital, what it means . . . . * - . . 58
a question of great importance . . . .61
percentage should be allowed a purchaser for . 14
unless provided for, capital is lost . . .62
if provided for, capital can be re-invested . . 62
by effecting an insurance on a life . . . 1 1 7
sources for the . . t ." . t . .,. . , . 145
3 per cent, normal rate of interest for . . 79
Redemption fund, formula for , . ^ #- . , A . * . . . 29
anmuty found by adding interest to . * . 30, 32
,, detailed example demonstrating accuracy of mode . 40
practical example . ,r ... if ^ . . 81
Reduction from gross to nett values . .'-. ' . . /: '
| loo, 1 12
Relation between immediate and deferred annuities with two rates of
interest . ...:*.. V * ....../ . -34
Relative worth . . .. , . . ...,,.- *.*... .-'. T 3
Remarks on detailed example of valuation . . * , . . . 108
Report on some portion of the Forest of Dean by Mr. Marcus Scott . 1 8
Reports, mining, writers of, should be men of status . . ^ . . 7
much depends on . . 4 . , # . . . 7
sometimes concocted for a purpose . . . .6
Republic, Argentine, drawbacks to mining in the ^ . . -153
silver mines of the . . . . . . 153
Results of starting with insufficient capital . . . . , .158
Reversions, or deferred annuities ........ 76
cases and examples by Tables and by logs 76, 77
99
[16] INDEX.
PAGE
Rights of the Crown as lord of the manor . . . . . .116
Risk, ample percentage should be allowed on mining property to cover . 13
on foreign mines greater than on home mines . . . .158
Royalty, valuation of . . . . . . . . , . 83
at different amounts in the same term, vamation of ^ . 87
,, remarks on . "... 90
depending on a life, valuation of . . ^T, ..... .118
Royalties, when very high, discourage capitalists . >. i ' . .115
evil effects of heavy . . . . , ... .116
conditions and circumstances which affect value of . -91
judgment and experience should determine amount of . .91
Rouse's Investigation of the errors of all writers on annuities . . , . 60
Rule for finding increase of principal at compound interest . . . 24
amount of I per annum in n years . . . .27
present value of I due n years hence . . .28
redemption fund that will amount to 1 inn years . 29
values by tables of multiples 1 24
Mr. Morgan's, for finding value of i inn years with two rates of
interest . . . J -.-... . . . -45
present value of I per annum wrong by the old . . . .31
cannot be laid down expressing risk in mining adventure . . ' 19
Redemption, high rates of interest for, are against interest of purchaser . 148
as the rate for, is increased the redemption fund decreases. 148
SALARIES, managing . . > . : * . . . .157
Sandwell Park Colliery - . - , 8
Schemes, worthless . . . . .^ < . ... . -. 4
commercial excitement taken advantage of to float . 155
Schneider, H. W., M.P., opinion respecting years' purchase . . .16
Scott, Mr. Marcus, report on some portions of the Forest of Dean . .18
years' purchase - s ,-.. . . . .18
reference to WiV.icKs Tables , . . . -19
Seams, where several exist, ample time should be allowed for develop-
ment . . . . . . -.-.'. . . .114
Serious discrepancy in InwoocFs years' purchase .*:;-.. . . 54
Shafts partially sunk, valuation of a colliery with two . . .. ,. .96
Shipping and Dock Companies . --. .... * , .-' . .151
Short term of lease diminishes value of mineral property . : . .114
does not benefit lessor or lessee , . .114
should contain extension clause . . ; . . .114
Silver and gold mines of the Far West ."..,- ... - . . 152
n Tables for use in valuing . -. , . 159-164
mines of the Argentine Republic V * . . . .153
mines of the Cero-de-Pasco . . > -. . . . .153
Simple interest, cases and examples . . . . . . .65
Simplest form, formulas and rules in this work given in their : > -41
Somersetshire, Leicestershire, and Staffordshire coal-fields . 8
INDEX. [17]
I'AGE
Success in mining requires great skill and judgment .... 4
isolated position of many foreign mines precludes . . .152
,, in other trades great' y depends on mining .... 5
Summary of values . /'. . . . . .. . . 107, 113
Surplus annuity should not be invested in same mines as annuity is
derived from . ,;'-.. ' . . .*;"<' 1 : : ,'. 59
Small and large coal, proportion of ..'.'.. , . ' , . r > - . 12
Smart's Tables, published in 1726 . ..... . , .- * . 42
(4) and (5) inaccurate . --"* -.- -. i .. *.- -. .-.. - . . 42
of the value of i per aiinuni, InwoocYs identical with . 50
Spain, mining in . '.' * : .. . 154
English companies in . .-.-. "-.--' . .,*-> .- . ' v .154
large fortunes to be made in . *- ; . ; . - . .. , . 154
Specific gravity, quantity of coal per acre may be determined by . .11
Staffordshire coal-fields, extension of, due to Mr. Johnson ... 8
Starting with insufficient capital, results of . "". . . . . .158
Stocks, loans, and bonds ; foreign. . . . . . . . .151
Strata passed through in sinking, great attention should be paid to .12
System of notation . . . ..;.-. . . . 165-167
Source and rate of interest fixed, the values may be obtained from the
tables . -, ; .* .*. ... .. . . . r .- . 147
Stocks, causes which affect value of . , . . . . . . .149
^ABLE, Mr. Downing Biderfs small . . . . . -5
Tables, construction and use of Valuation 21
of, very tedious . . . . . '33
years' purchase obtained by mere inspection of . . .41
WtilicWs, Mr. Scott's reference to . . .19
Ward's, published in 1710 . . . . . . .42
in this work calculated from first principles . . ' . 41
SmarCsj published in 1726 . . . . . .42
none of the old ones computed higher than 10 per cent. . 42
in this work believed to be free from error ... . 42
(I), (II), and (III), in this work, originally calculated to
15 places of decimals . , . . . .43
of Amounts, an additional test for the . . . .42
for this work, conditions considered in calculating . . 33
cumbrous rule introduced into appendix of Inwooffs . . 43
with two rates of interest, Mr. Griffiths Dames first to com-
pute . ." . . , . . '. % . ' . . ^ 43
Hardy's, introduced into InwoocFs in 1853 . . . -49
WUKcKs in 1 87 1 . . . 49
Inwood's, useless when two rates of interest are involved . 57
of the value ol i per annum identical with
Smart's and other tables . , , - - . . . 50
Smart's, (4) and (5) inaccurate . . . ,42
[18] INDEX.
PAGE
ITables, old, not sufficiently extensive for valuing mineral property . 50
,, ,, Mr. Downing Bidwi's opinion of the . * . ; . * .61
in Hurst" s ' Architectural Handbook ' "/* - * " . .' . 50
and rules in this work introduced for the first time . > , 55
inaccurate ; valuations made by, must be incorrect . . -54
(IV) and (VII), deferred values may be obtained directly
from . -. "- -. -'-* ; . . . . 127
,. example . .128
of multiples, deducing values from . < -.< . . .121
specimen table No. I, present value of an annuity
for a given term and rate per cent. . . .123
specimen table No. 2, present value of a de-
ferred annuity for a given term and rate per
cent. . , 127
specimen table No. 3, conversion of tables (IV)
and (VII) for deducing present value de-
ferred . . .128
specimen table No. 4. Present value immediate . 1 30
specimen table No. 5. Present value of l for
n years, after t years' deference . . .132
specimen table No. 6. Multiples of redemption
fund . . . . . . . 133
\ariousmethodsofarranging . . . 135-140
Taylor, Mr. T. J., his opinion respecting years' purchase . . .15
years' purchase compared with true value . . 5 1
Telegraph Companies . . . .151
Term of lease should be sufficiently long to justify adventure . . 1 14
when short diminishes value of mineral property . .114
should be longer where minerals exist at great depths . 114
2 1 years too short for mineral property . . . .114
Terminable annuities should be purchased so that capital may be re-
deemed ............ 62
' Theorem, Binomial '.......... 26
Thoman's definition of a deferred annuity . . . . . .55
^ o n ly embraces one rate of in-
terest . . . -55
value compared with true value, showing discrepancy . .56
The Author's practice in valuing unopened mines 19
Time, ample, should be allowed for development where several seams
exist ..'.-.. . . . . . . . .114
Transferable, annuities are 23
Transit of ores by mules . . . . . . .153
Treatment of perpetual annuities . 75
Two rates of interest, present value of I per annum with . . .31
Tables, source and rate of interest fixed, the values may be obtained
from the . . . . . . > * . . 147
(A, B, 0, and D) of Immediate and Deferred Values at high
rates of interest . , . i.- - . . . 159-164
INDEX. [19]
PAGE
T UNDERGROUND extension, pro vision for . . . . .156
U Undertakings, every facility should be offered for bondjide . . 115
Undeveloped freehold colliery and overlying estate, valuation of . .91
& ' ditto, with half-yearly and quarterly payments . 93
, difference in values ..*... 96
colliery with two shafts sunk . . . .96
United Kingdom, vast stores of minerals in the, not yet explored . .155
Unopened mineral property, the Author's practice in valuing . ; . 19
mines, annuity from, deferred during period of development . 20
Unqualified persons should not express opinions ..... 6
opinions of, mislead capitalists .... 6
Unscientific proprietors interfering with management . . . .158
< 17 ALUE,' definition of %, . . 3
' of mineral property, cost of winning affects . .. . 12
Value, every property has distinctive features which affect its . .11
of mineral property, affected by its position . ." ' . .13
diminished through defective arrangements. 9
by short term of lease .114
of anticipated annuity, formula for finding . . - . 25
deferred .... 25
may be derived from value immediate 35, 36
T/wman's, compared with true value
showing discrepancy . V . . 56
I per annum, ordinary tables all wrong . . . 43
demonstration of error . . 43
royalty, conditions and circumstances which affect . . . c, i
1 per annum: Inwootfs table identical with Smart's and
others . . . . . . -5
in n years at two rates of interest, Morgan's
rule , -* . . . V . . . . -45
a matter of vital importance . . . , . , 52
Imvood's years' purchase compared with true value . . -54
Dunn's . i . 51
Values deduced from tables of multiples . . . v . .121
deferred, may be obtained directly from Tables (IV) and (VII) . 127
,, example . . .128
gross, reduction to nett . . . . f . 88, 106, 112
Valuation has hitherto been considered a mere matter of opinion . .14
points for consideration in making a . . . . . 13
,, reasonable output must be assumed in making a . . 19
Valuation tables, construction and use of 21
construction of, very tedious ...... . . 33
made by inaccurate tables must be wrong . . -54
of mines, practical examples in , * ^ * . .80
annuity derived from a given output . 80
redemption fund to replace capital . . . . .81
[20] INDEX.
Valuation of machinery and plant . , ..... 83
royalty . ; . . . . . .83
where its amount varies in same term . - . ; . 86
,, of mines. Example where a certain sum has to be expended
in additional works, to continue annuity over the whole
term ......... . ." . 86
freehold undeveloped colliery with overlying estate . . .91
ditto with half-yearly and quarterly payments . . 93
difference in values .... , v ; . 96
mineral property, detailed example . i " ., ' 96
description of property . . . .' .96
conditions of purchase . '.., -.;,"' . 98
ist valuation; annuity derived from
output of coal . . . . .98
2nd valuation ; ditto . . . .99
,, 3rd valuation ; annuity de lived from iron
ore . ... . . '99
,, 4th valuation; annuity derived from
clay . . . . . . . 100
5th valuation, Part I ; annuity derived
from way-leaves . . . .100
5th valuation, Part 2 ; ditto . . . 101
3 ; ditto . . .101
6th valuation ; annuity derived from
freehold ground-rents . . .102
,, 7th valuation ; annuity derived from
royalty to lessor . . . .102
8th valuation ; ditto . ; . . . 103
9th valuation ; annuity derived from
royalty on iron ore and clay . .103
loth valuation, Part I ; annuity derived
from lessor's royalty to be sold . .104
,, loth valuation, Part 2 ; ditto . . .104
3 ; ditto . . .105
., ,, Summary of values .... 107
? , remarks on the foregoing case . .108
detailed valuation of same property under
shorter lease ..... 109
ditto, reduction from gross to nett values 1 1 2
ditto, summary of values . . . 1 1 3
Valuing unopened mineral property, the Author's practice in . .19
mineral property, previous tables useless for . . . .50
Various methods of arranging Tables of multiples . . . 135-140
Ventilation .-,. .-'.. V 6
Virgin properties, drawbacks connected with ..... 6
operations on, a question of capital .... 8
Values at different rates of interest, comparison of .. . . .147
deferred, at high rates of interest ; examples . . .159
INDEX. [21]
PAGE
V T alues deferred and immediate, at high rates of interest; Tables (A,
JB, 0, andD) 159-164
Tables j published in 1710 ' . 42
Water, examination of outeroppings necessary to compute quan-
tity of . -. . . . : . . . .10
Wealth, labour mainspring of . . . . . - . . . 3
When to purchase mineral properties . . . . ' . 155
Writers of mining reports should be men of status . . . . .7
on annuities, present value of 1 per annum wrong in all -43
Winning, cost of, affects value of mineral property . . . .12
; , the same, whatever the term of lease . .. . .114
WiLlicKs Tables, Mr. Scott's reference to . . .' . 19
Mr. Hardy's table introduced into, in 1 87 1 . , -49
Worth, relative . . . , . . ... . .3
Worthless schemes . . . . . . . .... 4
commercial excitement taken advantage of to float . 155
L.RS' purchase, Dunn's . . . . . v T . 16
compared with true value . . .51
ImvoocTs ........ 50
compared with true value . ~ . .54
serious discre-
pancy ;.;. . . . - . .54
Mr. T. J. Taylor's opinion respecting . , 1 5
)) ,, compared with true value . 5 1
,, ,, Mr. Cotterell's opinion respecting . - "". 15
Mr. S. Dobson's < * . . 1 5
Mr. J. Pease's . . . . 15
,, Mr. Marcus Scott's . . . . 18
H. W. Schneider, M.P. . .- . .16
,, obtained by mere inspection of the tables . .41
Yield of haematite iron mines . . . . . '..'.12
Years' purchase is augmented as rate for redemption is increased . .147
J7EALAND, New, mining in . . . . . . . . 1 54
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