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 * . 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 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 >>-. ..-: . - . 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 LOXD03T : PEIXTED BY 6POTTISTTOODE AND CO., KEW-STREET SQUARE AXD PARLIAMENT STREET 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the fast date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. 9Apr'64BG SENtONILL . -j, ^ r~v ~2> JUN 2 8 1996 .. ^ u _. -In ** vt * W iw*/w Mil C BE^KFLPY MAY23'^ 4 V* Wi **^ iixuiu.c; f ift'Siii'.? '** M/|y o / Q^ 1 f?-;:t M Q LD 21A-40m-ll,'63 (E1602slO)476B General Library University of California Berkeley