PRINCIPLES
PRACTICE
THE LIBRARY
OF
THE UNIVERSITY
OF CALIFORNIA
LOS ANGELES
SCHOOL OF LAW
GIFT OF
Walter ?. r . Atkinson
Dell L. Falls
C. Douglas Fikle
Of class of
A TREATISE
PRINCIPLES AND PRACTICE
LIFE INSURANCE:
BEING AN ARITHMETICAL EXPLANATION OF THE COMPUTATIONS
INVOLVED IN THE SCIENCE OF LlFE CONTINGENCIES,
TO WHICH ARE ADDED
VALUABLE TABLES FOR REFERENCE.
BY NATHAN WILLEY, ACTUARY.
NEW YORK:
Offices O/THE SPECTATOR,
J. H. AND C. M. GOODSELL, PUBLISHERS.
1872.
'Entered according to Act of Congress, in the year 1873, by
J. H. AND C. M. GOODSELL,
In the Office of the Librarian of Congress, at Washington.
THE SPECTATOR PRESS,
J. H. AND C. M. GOODSELL, Proprietors,
Nos. 93-95 Liberty St., New fork.
k
PREFACE.
The design of this work is to furnish the public with a
means of clearly understanding the fundamental principles of
Life Insurance, and to enable agents to present them in a concise
and forcible manner. To accomplish this result, the author has
attempted to explain the mathematical laws which the study and
experience of the past two centuries have shown to lie at the
foundation of the science. In this undertaking he has endeav-
ored to confine himself strictly to those topics which the experi-
ence of American companies, during the last few years, has shown
to be absolutely necessary to an intelligent and successful prose-
cution of the business, and to illustrate them in such a manner
that they may be comprehended by any one who is willing to
give the subject a careful investigation. Those who still remain
prejudiced against Life Insurance are confirmed in their opinions
more by a want of correct information than by any solid argu-
ment which they can produce against it, and the sooner it is
stripped of forbidden technical nomenclature and formulas,
and adapted to the comprehension of the average intellect of
business men, the greater will be the popular appreciation of its.
merits. Both officers and agents of companies should be able to-
meet any objections raised against Life Insurance, and to explain
its principles so clearly that the public may see that it is a plain
financial transaction, giving support to the families of thousands
of claimants every year, and throwing its mantle of protec-
tion around nearly a million of its living patrons.
CONTENTS.
PAGE.
Preface 3
Definitions 1 1
Interest and Discount 16
Compound Interest 16
Annuities certain at Compound Interest 19
Present Values and Discount 21
Deferred Annuities 23
Monetary Tables, 4 per cent 24
4X " 25
5 "
6 "
.7 "
8 "
" 9 "
10 "
Life Contingencies
Tables of Mortality 33
American Experience Table 33
Combined Experience ; or, Actuaries Table 34
Rate of Interest 34
Probability of Life 35
Commutation Columns 36
Explanation of Life Insurance 37
Life Annuities 43
Valuation of Policies . 45
Amount at Risk 47
Cost of Insurance 48
Distribution of Surplus 49
Tontines and Tontine Dividends 53
Expectation of Life . . 55
Tables of Expectation of Life 56, 57
Equation of Life 57
Table of Equation of Life 58
6 CONTENTS.
FAGX
Joint-Life Policies 59
Return-Premium Plan 60
Table illustrating Return Premiums, 61
Forfeiture of Policies and Paid-up Insurance 62
Surrender Values 64
Average Duration of Policies 66
American Experience, Mortality Table 68
Combined Experience, " 69
Commutation Columns, American Experience, 4^ per cent 70
" Combined Experience, 4 per cent 72
" American Experience, 6 per cent 74
Net Premiums, American Experience, 4^ P er cent 76
" Combined Experience, 4 per cent 77
" Term Insurance, American Experience, ^ l /z per
cent 78
" Term Insurance, Combined Experience, 4 per
cent 78
Explanation of Valuation Tables 80
Table of Comparative Values and Ratios of Values 81
Net values, Ordinary Life Policies, American Experience, 4^ per
cent ' 82
Net values, Ten-Payment Life Policies, American Experience, 4^
per cent 84
Net values, Ten-Year Endowment Policies, American Experience,
4% per cent 86
Net values, Fifteen-Year Endowment Policies, American Expe-
rience, 4X per cent 88
Net values, Twenty-Year Endowment Policies, American Expe-
rience, 4% per cent 90
Net values, Twenty-five Year Endowment Policies, American Ex-
perience, 4% per cent 92
Net values, Thirty-Year Endowment Policies, American Experience
4^ per cent 94
Net values, Thirty-five-Year Endowment Policies, American Expe-
rience, AfYz per cent 96
Combined Experience Table of Mortality 98
Net values, Ordinary Life Policies, Combined Experience, 4 per
cent 100
Net values, Ten-Payment Life Policies, Combined Experience, 4 per
cent 102
Net values, Ten-Year Endowment Policies, Combined Experience,
4 per cent 104
Net values, Fifteen-Year Endowment Policies, Combined Expe-
rience, 4 per cent 106
CONTENTS. 7
PAGK
Net values, Twenty-Year Endowment Policies, Combined Expe-
rience, 4 per cent 108
Net values, Twenty-five- Year Endowment Policies, Combined Ex-
perience, 4 per cent no
Net values, Thirty-Year Endowment Policies, Combined Expe-
rience, 4 per cent 112
Net premiums, Joint Life Policies, Combined Experience, 4 per
cent , . . 114
Net values, Ordinary Joint Life Policy, Equal ages, 4 per cent 115
" " " Difference in ages 5 years. . 116
" " " " 10 years.. 117
" " " " i 5 years.. 118
Explanation of Cost of Insurance Tables 1 20
Cost of Insufance, Ordinary Life, Single Premium Policy, Ameri-
can Experience, 4% per cent 121
Cost of Insurance, Ordinary Life, Single Premium Policy, Com-
bined Experience, 4 per cent 121
Cost of Insurance, Ordinary Life Policy, American Experience, 4^
per cent 122
Cost of Insurance, Ten-Payment Life Policy, American Experience,
4J^ per cent 123
Cost of Insurance, Ten-Year Endowment Policy, American Expe-
rience, 4^ per cent 1 24
Cost of Insurance, Fifteen- Year Endowment Policy, American Ex-
perince, 4^ per cent 125
Cost of Insurance, Twenty-Year Endowment Policy, American
Experience, 4^ per cent 1 26
Cost of Insurance, Twenty-five-Year Endowment Policy, Ameri-
can Experience, 4^ per cent 127
Cost of Insurance, Thirty-Year Endowment Policy, American Ex-
perience, 4j^ per cent 128
Cost of Insurance, Ordinary Life Policy, Combined Experience,
4 per cent 1 29
Cost of Insurance, Ten-Payment Life Policy, Combined Experience,
4 per cent 1 30
Cost of Insurance, Ten-Year Endowment Policy, Combined Ex-
perience, 4 per cent 131
Cost of Insurance, Fifteen-Year Endowment Policy, Combined Ex-
perience, 4 per cent 132
Cost of Insurance, Twenty-Year Endowment Policy, Combined
Experience, 4 per cent 133
Cost of Insurance, Twenty-five-Year Endowment Policy, Combined
Experience, 4 per cent 134
8 CONTENTS.
PAGE
Cost of Insurance, Thirty-Year Endowment Policy, Combined Ex-
perience, 4 per cent 135
Net Single Premiums applied to the Massachusetts Non-forfeiture
Law, Combined Experience, 4 per cent 136
Insurance due on Whole Life Policies, according to the Massachu-
setts Non-forfeiture Law 1 38
Decimal part of a year from date to January 1st following 140
Life Insurance Formulae -142
Formula for Annuities 143
" Whole Life Insurance 144
" Term Insurance 144
" Endowment - . 144
" Endowment Insurance . 145
" Single Premium, Life 146
" Annual Premium, Life 146
" Endowment Insurance 146
" Joint Life 146
" Return Premium Plan 147
Valuation of Policies 148
Prof. Wright's Accumulation Formula. 1 50
Fackler's Formula 1 50
McClintock's Formula 1 50
Romans' Contribution Formula 151
Formula for Verifying Commutation Columns 151
" Equation of Life 151
" Expectation of Life 151
Prof. Wright's Formula for Insurance Values 151
Prof. Bartlett's Formula for Surrender Values 152
Surrender Values, Table of 155
Valuation of Joint Life Policies. By Seth C. Chandler, Jr 1 56
Table of. 1 57
Valuation of Policies, McClintock's Method 158
Table of 160
Valuation Tables, American Experience, 4^ per cent 168
" " 6 per cent 173
" Combined Experience, 4 per cent 172
Index 174
DEFINITIONS IN LIFE INSURANCE.
Accumulation The annual premiums and interest during the
first years of a policy are largely in excess of the annual cost of
carrying the risk ; which is necessary in order to establish a fund
to pay the amount insured when it becomes a claim. Hence,
to provide for the payment of future claims, this excess
increases by compound interest and additions from the annual
premium, and is called accumulation. The accumulation for-
mula expresses, in algebraic language, the law by which this
increase takes place.
Actuary One who is proficient in that branch of life insur-
ance, which is strictly of a scientific and mathematical nature, as
the preparation of tables and formulae, calculation of policy lia-
bility, distribution of surplus, etc.
Annuity A sum of money payable at regular intervals. An
annuity contingent is dependent for its termination upon an event
which may or will occur, as the death of the annuitant or person
who receives it.
An annuity certain is a sum payable during a definite term of
years, and which does not cease in the meantime in the event of
any contingency. The interest on a six per cent bond of one
thousand dollars is an annuity certain of sixty dollars per annum
during the time which the bond has to run.
A perpetual annuity is a sum of money payable at regular
intervals during an unlimited seizes of years.
A deferred annuity is one in which the regular payments are
to commence at some future period.
A joint annuity is one which depends upon the joint existence
of two or more lives from year to year.
A survivorship annuity is one which continues during the life-
time of the survivor of two or more lives.
Assets All the funds and available property of any kind
belonging to a company.
12 PRINCIPLES AND PRACTICE
Bonus A dividend paid to policyholders from the surplus
of a company over and above the liabilities. " Bonus addition" to
a policy is another term for reversionary insurance.
Brokerage A commission on the first premiums paid to
solicitors of life insurance companies in lieu of all future com-
missions on the renewal premiums.
Commission A percentage given to a solicitor or agent on
premiums collected by him.
Commutation Columns Columns formed from a given table of
mortality and rate of interest, and used in the computation of
premium rates and other life insurance calculations.
Company, Insurance A number of persons associated to-
gether for the purpose of effecting insurance against risks of any
kind. A stock company has for its basis a capital stock, and in-
sures at lower premium rates than those of mixed or mutual
companies, so that whatever surplus may then accrue belongs
exclusively to the stockholders. In a mutual company the sur-
plus is returned to the insured. Mixed companies partake of
the nature of stock and mutual companies ; a certain portion of
the profits are paid to the stockholders, and the remainder is
distributed among the insured.
Contribution A term used to denote the method of distribu-
ting the surplus of a company, according to the amount each
policyholder has contributed to produce it.
Discount The difference between a sum of money payable
at any future time and the present value if paid immediately,
computed according to a given rate of interest.
Dividend The surplus or profit distributed to each stock or
policyholder after the liabilities of the company are reserved.
Dividends to policyholders are practically a misnomer. They
are mainly a restitution of the over-payments which have been
made in the premises. Reversionary dividends, the allotment
of the surplus converted into single premiums to purchase addi-
tional insurance payable according to the terms of the policy.
Deferred dividends, those which are payable after a certain
number of years. Tontine dividends, those which are payable
on the tontine method.
Endowment A sum of money assured and payable when
the policyholder arrives at a certain age. This is usually called
"Simple Endowment."
For " Endowment Insurance " see "Policy."
OF LIFE INSURANCE. 13
\
Expectation of Life A term applied to the mean or average
duration of the life of individuals, after any specified age and
according to a given table of mortality.
Experience The data upon which different life insurance
tables are made.
Forfeiture The violation of some of the conditions of a
policy which enables the company to cancel the contract made
with the policyholder.
Ins^lrance, Life An agreement by a life insurance com-
pany, in consideration of a stipulated premium, to pay a certain
sum of money on the death of a policyholder or upon his attain-
ing a certain age. Cost of Insurance The annual tabular
expense which the company incurs upon a policy in force, or the
amount at risk multiplied by the probability of dying that year.
Insurance Value The present value of the future cost of insur-
ance assured by the company when it gives a policy upon the
life of another. Self Insurance The amount of reserve which
is in the hands of the company, or the amount upon which the
company does not assume any risk of being obliged to pay from
the premiums of other policyholders. *
Interest A stipulated amount per annum paid for the use
of money.
Lapse The expiration of the contract of insurance occa-
sioned by the non-payment of premiums.
Liabilities Actual losses unpaid, expenses and contingent
debts of a company, for the payment of which its assets are held
liable. The whole amount insured is a contingent debt, but it is
regarded as a liability only to the extent of the " reserve " on
the policy.
* Assurance and Insurance. "I do not accept the distinction laid
down by some writers as to the use of the words assurance and insurance,
by which the former is restricted to life and the latter to fire risks. The
more correct distinction I believe to be that a man insures the life of him-
self or of some other person, or his house, or his ships, or the fidelity of
his servants, and that the office assures to him in each of these cases a
sum of money payable in certain contingencies. Hence the office is the
assurer or assurers and the man the assured; while we may speak of the
life assured or the life insured or the sum assured or the sum insured,
according as we take the point of view of the office or the individual. So
also we may speak either of ' Life Insurance' or ' Life Assurance,' as,
for instance, we may say that a man believes in the duty and advantage
of life insurance, in that a certain company finds the business of life
assurance very profitable." Thomas Bond Sprague, Vice-President Insti-
tute of Actuaries, London.
! 4 PRINCIPLES AND PRACTICE
Loading A percentage added to the net premium in order
to defray expenses and provide for an excess of mortality.
Loss The payment of a claim upon the death of a policy-
holder. Matured endowments, strictly speaking, are not losses.
Margin The same as " loading."
Mortality Having a given number of persons of the same
age living at the beginning of a year, the mortality is the num-
ber dying during that year. The rate of mortality is the ratio of
the dying to the number of living. A table of mortality is a
tabulated exhibit of the number of survivors and the number of
dying each year, among a number of persons taken at a given
age.
Policy The contract effected between the insurer and the
insured, or the instrument containing the terms and conditions.
on which a company undertakes to indemnify a person in whose
favor a policy is issued against the loss of the life of the policy-
holder, or upon his attaining a certain age. Life Policy When
the sum insured is payable on the death of the policyholdeiv
Term Policy One taken for a limited number of years, the sum
insured payable only in case of the death of the policy holder dur-
ing this period. Endowment Insurance Policy One payable
when the policyholder attains a certain age or at death if it
should take place before that time. Limited Payment Policy
One in which the number of payments is not to exceed a certain
limit. Joint Life Policy One payable on the death of the
first of two or more persons insured. Survivorship Policy One
payable on the death of the survivor of two or more persons.
Premium The sum required to keep a policy in force accord-
ing to its conditions. Net Premium The lowest rate, according
to a given table of mortality and interest at which an insur-
ance can be effected. Gross, or Office, Premium The pre-
mium increased by the loading or margin. Single Premium
A sum of money paid for insurance and in consideration of
which all future premiums are forborne. The Net Single Pre-
mium is the present value of all future net annual premiums,
diminished by the probability of dying each year.
Premium Notes and Loans Notes given by policyholders
in lieu of a part of the cash payment of the premium ; Loans
are granted by the company for the same purpose. These notes
or loans are never intended to be paid in cash, but to be can-
OF LIFE INSURANCE. 15
celled by dividends, or deducted from the amount insured in case
of death.
Present Values The present value of a given sum payable
at a certain future time is the amount which, placed at interest,
will equal this sum in the time specified. The present value of
an annnity is the sum of money which will purchase, at a given
rate of discount, all the future payments. The present value of
a perpetual annuity, is that sum which, invested at a given rate
of interest, will always produce the amount required. The pre-
sent value of a deferred annuity is that sum which, invested at a
given rate of interest, will, at the end of the period during which
the annuity is deferred, amount to the sum which will then pur-
chase all the future payments.
Reserve That part of the premiums of a policy, with the
interest thereon, which is reserved or set aside as a fund for the
payment of the policy when it becomes due.
Reversion A sum payable on the occurrence of some event,
as the death of a policyholder. It is usually applied to annuities
and surplus on policies, when payable in this manner.
Risk, Amount at The difference between the sum insured
and the reserve, or the amount of hazard which the company
assumes.
Scrip A certificate entitling the policyholder to certain
profits or surplus, when payable.
Solvency, Test of- A rule to determine the ability of a com-
pany to pay all the losses, which, according to a given table of
mortality and rate of interest, may occur.
Surplus The sum left, after providing for the liabilities,
claims and expenses of a company.
Tontine A fund purchased jointly by a number of persons,
the profits divided among the oldest survivors. Tontine Divi-
dend A distribution of surplus among the diminished number
who are entitled to it after a certain period.
Valuation A method of finding the necessary reserve on a
policy.
Value of a Policy The Reserve. The net value of a policy is
the difference between the net single premium for the sum insured
at the age of the policyholder when the policy is valued, and
the present value of all future net premiums calculated to be
i6 PRINCIPLES AND PRACTICE
received on the life of the party insured. The gross value of a
policy is the difference between the net single premium, as given
above, and the present value of all future gross premiums to be
received on the policy.
INTEREST AND DISCOUNT.
In many life insurance calculations, a great amount of time
and labor is often saved by a familiarity with the use of interest
and discount tables, there being many operations which can be
done in a much more accurate and expeditious manner by them
than by the seriatim method, and therefore a clear understand-
ing of them is of great importance.
COMPOUND INTEREST.
1 . In compound interest the interest of a given sum is added to
the principal, increasing it at the end of each year or period
when it becomes payable, instead of being paid as often as it
becomes due. Thus, at 6 per cent, the amount of $i for one
year is $i. 06; the amount at compound interest for two years
is $i.o6x$i.o6=$i.i236 ; for three years it is $i. 06 x $1.1236=
$1.1910.
2. Tables of compound interest are made by multiplying
$i by the amount of $i for one year at the given rate per cent,
and this product by the amount of $i for one year which gives
the amount of $i for two years, and so on for the number of
years required. The last product gives the amount for the
given number of years. The compound interest is found by
subtracting $i from it. Thus the compound interest of $i for
3 years, at 6 per cent, is $1.1910 $1^.1910.
3. To find the amount of any sum at compound interest for any
number of years at a given rate per cent, by the use of the tables,
we have only to look in the tables, under the given rate
per cent, and opposite to the required number of years for the
amount of $i and multiply this amount by the given sum.
OF LIFE INSURANCE. 17
Thus, the amount of $i for 20 years, at 4 per cent, is $2.1911,
and at 7 per cent for the same period is $3.8697. The amount
of $200 at 4 per cent would be $200 x $2. 1911 =$438.22,
and at 7 per cent, $2OOx$3-S697=$773.94. The compound
interest, is found by substracting the principal from the amount
of the principal and interest ; thus, $438.22 $2oo=$238.22=
the compound interest in the first case given above.
4. The above rule gives the compound interest for a whole
number of years. To find the compound interest for a number
of years and a fractional part of a year, we first find the amount
by the tables for the entire years, and then the interest for the
part of the following year, by subtracting the amount for the
entire years required from the amount of the ndxt year in the
tables, and this result gives the interest for the entire year of
which the fractional part is required. The next step is to find
this fractional part, and add it to the amount of the entire year's
principal and interest.
Thus to find the amount at compound interest, 4 per cent, or
$i for 20 years and 6 months, we have :
Amount of $i for 20 years, ------- $2.19112
" $i for 21 years, ---_,_ 2.27876
Compound interest, 2ist year, ------ .08764
" " for 6 months, ----- .04382
Amount of $i for 20 years and 6 months, $2.i9ii2+$o43S2=$2.23494
Compound interest=$2. 23495 $1= ----- $1.23494
To find the compound interest of $i for 20 years and 73
days, at4 per cent, we have : $2. i9ii2 + .oS764x- ; , T b %=$2. 191124.
.01753 the amount of $i for the given time=$2. 20865, and
the compound interest is $2.20865 $i =$1.20865
5. To find the time in which a given sum will increase to a
given amount at a given rate per cent, divide the given amount
by the given sum, and the result is the amount of $i in the time
required. By comparing this result with the amounts of $i dur-
ing a series of years and at the given rate per cent, the time
required can easily be obtained.
Example. The number of years required for $200 to
double itself at compound interest, 4 per cent, is found as
follows: 4OO-=-2OO=2. The amount of $i for 17 years, at
4 per cent, according to Table No. I, is $1.9479, and for 18
years is $2.0258 ; consequently the exact time required is be-
18 PRINCIPLES AND PRACTICE.
tween these two periods, or $2.0258 $i.9479=.o779, which is
the compound interest on $i during the eighteenth year. The dif-
ference between 1.9479 and 2 is .0521, and we have this propor-
tion. If it requires 365 days for $i during the eighteenth year
at compound interest to earn .0779, how long is required for it
to earn .0521 ? By the rule of three .0779 : .0521 : : 365 : 244
days. Hence, the time required is 17 years and 244 days.
6. The rate per cent is very nearly determined by a similar
method.
Example. If $i increases to $2 in nine years, what is the
rate per cent? By inspecting Table No. VI, we find, by running
the eye along the columns opposite to 9 years, that $i, at 8 per
cent per annum, will amount to $1.999, which shows that 8 per
cent is the neai'est rate required.
7. To find the principal which will amount to a certain sum at
compound interest, the time and rate per cent being given,
divide the given amount by the amount of $r increased at com-
pound interest, according to the required conditions of the
principal.
Example. To find the principal, which will amount to $2.000
in 10 years, at 6 per cent compound interest, we find, by
Table No. IV, that the amount of $i during this term, at 6 per
cent, is $1.7908, and consequently we have the proportions
1.7908 : i.oo : : 2,000 : 1,1 i6-79=the principal required.
8. It sometimes happens, in making calculations of consider-
able accuracy, that the amount of compound interest of a certain
sum is required when the interest is added to the principal
semi-annually or oftener.
When the interest is added semi-annually, the following rule
is a very expeditious one to use, provided the proper tables are
at hand :
In the column giving the amounts of $i at one-half the
annual rate of interest given, take double the number of years,
and proceed as when the interest is payable annually.
Example. To find the amount at compound interest of $i
for 10 years, at 10 per cent interest, added semi-annually, find
the amount at compound interest of $i for 20 years at 5
per cent, which is $2.6533, the answer required. To find the
amount at compound interest of $l for 20 years at 8 per cent,
interest added semi-annually, find the amount at compound in-
OF ZIFE INSURANCE.
terest of $i for 40 years, at 4 per cent, which is $4.8010, the
answer required.
9. If the interest is added tri-annually, select the column giving
the amounts of $i at one-third the rate of interest, and take
three times the number of years ; if added quarterly, select the
column giving the amounts of $i at one-fourth the rate of interest
given, and take four times the number of years.
10. In the last example the amount at compound interest of
$i for 20 years, at 8 per cent interest, added annually, is
$4.660957; semi-annually, $4.801021 ; quarterly, $4.875439.
To find the amount at compound interest, added semi-annually
or quarterly, in cases where the ordinary interest tables do not
apply, multiply the principal by the proper amounts of $i as
given in the following table, for the required number of years :
THE AMOUNTS OF $i IN ONE YEAR, WITH -NTEREST ADDED ANNUALLY,
HALF YEARLY AND QUARTERLY.
Rale of
Interest.
How Payable.
Am 't of $'i
in one year.
Rale of
Interest.
How Payable.
Ain't cf$i
in one year.
4 per
cent.
Annually.
Half Yearly.
Quarterly.
1.040000
1.040400
1.040604
7 Per-
cent.
Annually.
HalfYearly.
Quarterly.
1.070000
1.071225
1.071859
4iper
cent.
Annually.
Half Yearly.
Quarterly.
1.045000
1.045506
I-045765
8 per
cent.
Annually.
HalfYearly.
Quarterly.
i.oSoooo
I. 081600 .
1.082432
5 Pet-
cent.
Annually.
Half Yearly.
Quarterly.
1.050000
1.050625
1.050946
9 per
cent.
Annually.
HalfYearly.
Quarterly.
1.090000
1.092025
1.093083
6 per
cent.
Annually.
HalfYearly.
Quarterly.
1.060000
1.060900
1.061364
10 per
cent.
Annually.
HalfYearly.
Quarterly.
I.IOOOOO
1.102500
1.103813
ANNUITIES CERTAIN AT COMPOUND INTEREST.
i. In the Tables we have the amount of $i per annum, paid in
advance, and improved at different rates of interest, for any
number of years not exceeding 50. At the end of the first year
the amount of $i at 4 per cent interest is $1.04. At the be-
ginning of the second year $i is added to this amount, making
$2.04 ; and the interest on this sum at the end of the second year
increases it to $2.1216. This increased by $i at the beginning
20 PRINCIPLES AND PRACTICE
of the third year is $3.1216, and at the end of the year it amounts
to $3.2465. By continuing this process the columns of annuities
certain are formed.
2. These columns may also be formed from the compound in-
terest columns, as illustrated by the following examples :
The amount of $i for 4 years at 4 per cent compound in-
terest is $1.1698585. Subtracting the amount of $i for t year, we
have $1.1698585 1.04=. 1298585, and, dividing by .04, the rate
of interest, we have .1 298585 -=-.04= $3. 24646, the amount of $i
per annum for 3 years. The explanation of this operation is in
the fact that .1298585 is the annuity of .04 for 3 years, improved
at 4 per cent interest. And hence we have the proportion,
..04 : i.oo : : .1298585 : 3.24646.
3. To find the amount of $i per annum for 49 years, take the
amount of $i at 4 per cent compound interest for 5 years,
which is $7.1066833, then (7.1066833 i. 04)^.04= 15 1.66708.
Hence, to find the annuity certain of $i per annum for any
number of years, we have the following rule : From the amount
of $i in the compound interest columns at the given rate per cent,
and taken at the given number of years plus one, subtract the
amount of $i for one year at the given rate, and divide the re-
mainder by the rate per cent.
4. When the annuity is payable at the end of the year, as in the
old English tables, instead of at the beginning, the rule is as
follows :
From the amount at compound interest in the tables, at the
given rate per cent, and taken at the given number of years, sub-
tract $i, and divide the remainder by the rate per cent, and
the quotient is the amount of an annuity of $i for that term.
Thus, in the last example, the amount of $i for 50 years is
7.1068833 ; subtracting $i, we have 6.io6S833-^-.o4=$i52.667o8,
the amount of $i per annum for 50 years, instead of 49 years, as
in the previous rule.
In this example, deducting $i from the amount, we have the
annuity certain of .04 for 50 years at compound interest; there-
fore, .04: $i : : $6.1066833 : $152.66708.
5. In life insurance it is often necessary to make such calcula-
tions as the following, in order to estimate the probable advan-
tages of accepting a risk :
If an annual net premium on a life policy of $1,000 is $23.68,
OF LIFE INSURANCE. 21
how long will it be necessary for the insured to l\ve, in order that
the company may realize the amount insured?
Dividing $1,000 by $23.68, we have $43.2297; therefore, it
would require the same time which it takes $i per annum at
7 per cent compound interest to amount to this sum. By Table V,
we find that $i per annum, for 19 years, at 7 per cent, amounts
to $39-9955) and for 20 years the amount is $43.8652. It is evi-
dent, then, that the time required is between 19 and 20 years.
The exact date is thus found. At the beginning of the twentieth
year, as the premiums are payable in advance, the amount of
$i per annum would be $39-9955+$ i =$40.9955. The difference
between this and $42.2297 is $1.2342, which is the amount of in-
terest required to be earned after the beginning of the twentieth
year. The total amount of interest earned during the twentieth
year is $43.8652 $4O.9955=$2.8697- Therefore, we have the
proportion, if it requires i year for $40.9955 to earn $2.8697 m "
terest, how long does it require to earn $1.2342, or $2.8697:
$1.2342 : : 365 1157 days. That is, it would require 19 years and
157 days, or twenty premiums and the interest thereon for 157
days after the twentieth premium is paid.
PRESENT VALUES AND DISCOUNT.
A familiarity with the present values of sums payable, is quite
as important as that of interest.
1. The present value of $i for one year at 6 per cent discount,
is the sum which, placed at 6 per cent interest for i year, will
amount to $i. This quantity is found by the following propor-
tion : if $i will amount to $1.06 in i year, what sum is required
to amount to $i ? or $1.06 : $i : : $i : .943396, or |- -^ =.943396.
vp I .OO
~n i c ef c $I.OO $I.OO
The present value of $i for 2 years is 5 z=J- ,=
/ $i.o6x$i.o6 $1.236
00 / i r $I.OO $I.OO /-
.889996 ; and for -* years * , ; , ... 2=^ ,=.8-59610.
J $i.o6x$i.o6x$i.o6 $1.191016 oy y
In this manner the columns of present values are found.
2. To find the number of years which the payment of a sum
of money must be deferred in order that it may have a certain
present value, divide the given present value by the amount and
the result is the present value of $i for the time required. By
comparing this result with the present values of $i during a series
22 PRINCIPLES AND PRACTICE
of years and at the given rate per cent, as given in the tables,
the time required can be obtained.
Let it be required to find the number of years which the pay-
ment of $i must be deferred to have a present value of .50
at 6 per cent discount. By referring to Table IV, we find in the
6 per cent column that the present value of $i for n years is
.526788, and at 12 years it is .496969; the difference between
these two quantities is .029819. The difference between .526788
and .50 is .026788. To find the number of days required in ad-
dition to the 1 1 years, we have the following proportion : if it
requires one year for the present value of $i at the end of n
years to diminish .029819, how long will it require to diminish
.026788 ? and the ratios are stated as follows : .029819 : .026788 : :
365:328 days. Hence the time required, n years and 328
days.
3. To find the rate per cent of discount required for a given
sum to have a certain present value in a given number of years,
we find the present value of $i according to the terms given, and
compare this result with the present values of $i in the tables
at the required number of years.
Thus to find the rate per cent required for $i, payable 14
years hence, to have a present value of .50, we divide .50 by
$i, and we have the result .50, then, by inspecting the columns
of present values along the lines representing the values of $i,
payable 14 years hence, we find, under the 5 per cent column,
that the present value of $i is .505068, which indicates that 5 per
cent is very nearly the rate required.
4. The present value of $i per annum, at the end of each year
for any number of years, is the present value of $i for one year,
plus the present value of $i for two years, plus the present value
of $i for three years, and so on. By referring to Table II, we
find the present value of $i, at 4^ per cent for one year, is
.956938, and for two years, is .915730. Adding these together,
we have 1.872668= the present value of $i per annum for two
years. The present value of $i, per annum, for three years, is
5. The present value of $i, per annum, for any number of
years, at any given rate per cent, may be easily found by the
following rule: Subtract the present value of $i, as found
in the tables, for the given time and rate, from unity, or $i,
OF LIFE INSURANCE.
2 3
and divide this difference by the given rate for $i, the result
will be the required present value of $i, per annum. Thus, in
the last example we have $i .876297=. 123703 -4-.O45=$2. 74896.
The quantity .123703 becomes the present value of 4 1-2 cents,
payable annually for three years, and hence .123 703-5- .045=
2.74896, or .045 : 123703 : : i.oo : 2.74896.
6. The present value of a perpetual annuity is the sum which,
paid now and invested at a given rate per cent, will produce the
annuity. To find the present value of the perpetual annuity of
$i at 5 per cent interest, we have the following proportion :
.05 : .1 : : i : 20, or $i divided by the given rate per cent, will
give the present value of the perpetual annuity of $i, and
from this the present value of any other sum may be found.
7- In making calculations by means of these tables, care should
be taken to examine whether the annuity is payable at the
beginning or at the end of the year. In the above example the
present value of $i payable at the beginning of the first year
is $i ; for the second year $1.9569; for the third year
$2.8727 ; for the fourth year $3.7490, and so on. This caution
becomes the more necessary as all life insurance premiums are
regarded as being paid at the beginning of each year, while an-
nuities are usually payable at the end.
8. The present value of the premium $23.68 for twenty years,
at seven per cent discount, the first premium being paid in ad-
vance, is computed thus : ($10.335595 + 1)
DEFERRED ANNUITIES.
1. The present value of a deferred annuity certain of $i, pay-
able at the end of the year, deferred for four ) r ears, and then to
continue six years, at 6 per cent discount, is found by taking the
difference between the present value of $i for the whole annuity
term and the present value of $i for the deferred term ; thus, by
Table IV, 7.360087-3.465 1 06= $3. 894981.
2. To find the present value of an annuity certain to continue
a given number of years, after a given term, multiply the differ-
ence of the present value of $i per annum for the whole term,
and of $i per annum for the deferred term by the given an-
nuity ; the result will be the required value.
PRINCIPLES AND PRACTICE
TABLE No. I.
MONETARY TABLES, 4 PER CENT.
N
Tears.
Amount of$i
in N years.
Present
Value of $i
due N years
hence.
Amount of
$ i per annum
in N years.
Present
Value of $i
per annum for
N years.
Sinking
fund Unit will
amount to i
in N years.
I
1.0400
.961538
1.0400
.9615
9 6l 54
2
.0816
.924556
2.1216
I.8S6I
47 '34
3
.1249
.888996
3-2465
2-7751
.30802
4
.1699
.854804
4-4I63
3.6299
.22643
5
.2167
.821927
5-6330
' 4-45I8
17753
6
2653
TQOS 1 .?
6-8983
5.2421
.14496
7
3!59
.759918
8.2142
6.OO2I
.12174
8
. 3 6S6
.730690
9.5828
6.7327
10435
9
4233
.702587
11.0061
7-4353
.09086
10
.4802
675564
12.4864
8.1109
.08009
ii
5395
.649581
14.0258
8.7605
.07130
12
.6010
.624597
15.6268
9-3851
.06399
J 3
.6651
.600574
17.2919
9.9856
05783
*4
73^7
577475
190236
10.5631
05257
15
.8009
555265
20.8245
11.1184
.04802
16
.8730
5339S
22.6975
11.6523
.04406
17
9479
513373
24.6454
12.1657
.04058
18
2.02 S8
.493628
26.6712
12.6593
03/50
J 9
2.1068
.474642
28.7781
I3-I339
03475
20
2.1911
456387 .
30.9692
i3-59 3
.03229
21
2.2788
438834
33-248o
14.0292
.03008
22
2.3699
421955
35-6i79
H-45U
.02808
23
2.4647
405726
38.0826
14.8568
.02626
24
2.5633
.390121
40.6459
15.2470
.02460
25
2.6658
375"7
43-3II7
15.6221
.02309
26
2.7725
.360689
46.0842
15.9828
.02 i 70
27
2.8*34
.346817
48.9676
16.3296
.02042
23
2.9987
333477
51.9663
16.6631
.01924
29
3.1187
.320651
55-oS49
16.9837
.01816
3
3-2434
.308319
58-3283
17.2920
.01714
3 1
3-3731
.296460
61.7015
17-5885
.01621
3 3
3- 5"Si
.285058
65.2095
17.8736
01534
33
3.6484
.274094
68.0579
18.1476
.01452
34,
3-7943
263552
72-6522
18.4112
.01376
35
3-946i
253415
76.5983
18.6646
.01306
36
4.1039
.243669
80.7022
18.9083
.01239
37
4.2681
234297
84.9703
19.1426
.01177
33
4.4388
.225285
89.4091
19.3679
.01119
39
4.6164
.216621
94-0255
I9-5845
.01064
40
4.8010
.208289
98.8265
19.7928
.OIOI2
4i
49931
.200278
103.8196
19.9931
.00963
42
5.1928
i9 2 575
109.0124
20.1856
.00917
43
5-4005
.185168
114.4129
20.3708
.00874
44
5-6165
.178046
120.0294
20.5488
.00833
45
5.8412
.171198
125.8706
20.7200
.00794
46
6.0748
.164614
131-9454
20.8847
.00758
47
6.3178
.158283
138.2632
21.0429
.00723
48
6,5705
152195
I44-8337
21.1951
.00691
49
6-8333
.146341
151.6671
21-3415
.00659
50
7.1067
.140713
158.7738
21.4822
.00630
OF LIFE INSURANCE
TABLE No. II.
MONETARY TABLES, 4^ PER CENT.
N
Tears.
Amount of $i
'/; N years.
Present
Value of $i
due N years
hence.
Amount of
$ i per annum
in N years.
Present
Value of $i
per annum for
N years.
Sinking
fund Hint tvill
amount to $i
in N years.
I
1.0450
956938
1.0450
0.9569
95695
2
1.0920
9!5730
2.1370
1.8727
46795
3
I.I4I2
.876297
3.2782
2.7490
30505
4
1.1925
.838561
4.4707
3-5875
.22368
5
1.2462
.802451
5-7I69
4.3900
.17494
6
1.3023
.767896
7.0192
5-^579
14247
7
1.3609
.734828
8.3800
5-8927
"933
8
1.4221
703185
9.8021
6-5959
.10202
9
1.4861
.672904
II.2SS2
7.2688
.088^9
10
1-5530
.643928
12.8412
7.9127
.07788
ii
1.6229
.616199
14.4640
8.5289
.06914
12
1.6959'
. .589664
16.1599
9.1186
.06188
13
1.7722
.564272
17.9321
9.6829
05577
H
1.8519
539973
19.7841
10.2228
05055
15
1-9353
' .516720
21.7193
10-7395
.04604
16
2.0224
494469
23-74I7
11.2340
.04212
17
2.1134
473 ! /6
25-855I
11.7072
.03868
18
2.2085
.452800
28.0636
12.1600
03563
J 9
2.3079
433302
30-37H
12.5933
03^93
20
2-4117
.414643
32-7S3I
13.0079
.030^0
21
2.5202
.396787
35-3034
13-4047
02833
22
2-6337
.379701
37.9370
13-7844
.02636
23
2.7522
363350
40.6892
14.1478
,02458
24
2-8760
347703
43-5652
14-4955
02295
25
3-0054
332731
46.5706
14.8282
02147
26
3-M07
.318402
49-7 "3
15.1466
.02012
=7
3.2820
.304691
52-9933
15-4513
.01887
28
3-4297
.291571
56.4230
15-7429
.01772
29
3-5840
.279015
60.0071
16.0219
.01667
3
3-7453
.267000
63-7524
16.2889
.01569
3 1
39'39
255502
67.6662
16.5444
.01478
3 2
4-0900
24450
71.7562
16.7889
.01394
33
4-2740
233971
76.0303
17.0229
.01316
34
4.4664
.223896
80.4966
17.2468
.01242
35
4.6673
214254
85.1640
17.4610
.01174
36
4.8774
.205028
900413
17.6660
.OI MI
37
5.0969
.196199
95.1382
17 8622
.01051
38
5-3-6-2
.187750
100.4644
18.0500
.00996
39
5-56?9
.179665
106.0303
18.2297
.00043
40
5.8164
.171929
111.8467
18.4016
.00894
4i
6.0781
.164525
117.9248
185661
.00848
42
6-35 J6
157440
124.2764
18.7235
.00804
43
6-6374
.150661
130.9138
18.8742
.00764
44
6.9361
H4I73
137.8500
19.0184
.00725
45
7.2482
.137964
145.0982
19- '563
.00689
46
7-5744
.132023
152.6726
19.2884
.00055
47
7-9 '53
.126338
1 60. =1879
19.4147
.00f>23
48
8.2715
.120898
168.8594
I9-5356
.00592
49
8-6437
.115692
177-5030
19.6513
.00563
50
9.0326
.110710
186.5357
19.7620
.00536
26
PRINCIPLES AND PRACTICE
TABLE No. III.
MONETARY TABLES, 5 PER CENT.
N
Amount q/"$i
Present
Value of $i
Amount of
Present
Value of $i
Sinking
fund that ivill
hence.
in N years.
Jor N years.
N years.
I
1.0500
.952381
1.0500
9524
95238
2
I.IO25
.907029
2-I525
1.8594
.46458
3
1.1576
.863838
3-3JOI
2.7232
.30211
4
.822702
4.15256
3-5460
.22097
5
1.2763
783526
5.8019
.17236
6
I.340I
.746215
7.1420
5-0757
.14002
7
1.4071
.710681
8.5491
5.7864
.11697
8
1-4775
.676839
10.0266
6.4632
9973
9
I-55I.3
.644609
"5779
7.1078
.08637
10
1.6289
.613913
13.2068
7.7217
0757 2
ii
1.7103
.584679
14.9171
8.3064
.06704
12
1-7959
.556837
16.7130
8.8633
05983
13
1.8856
.530321
18.5986
9-3936
5377
'4
1.9799
.505068
20. 15786
. 9.8986
.04859
15
2.0789
.481017
22.6575
IO -3797
.04414
16
2.1829
.458112
24.8404
10.8378
.04026
17
2.2920
436297
27.1324
11.2741
.03686
18
2.4066
4I552I
29-5390
11.6896
03385
19
2.5270
395734
32.0660
12.0853
.03119
20
2-6533
.376889
34-7193
12.4622
.02880
21
2.7860
358942
37-5052
12.8212
.02666
22
2-9253
.341850
40.4305
13.1630
02473
23
3-0715
325571
43.5020
13.4886
.02299
2 4
3-2251
.310068
46.7271
13.7986
.02140
25
3.3864
295303
5- "35
14.0939
.01996
26
3-5557
.281241
53.6691
'4-3752
.01863
27
3-7335 '
.267848
57.4026
14.6430
.01742
28
3.9201
255094
61.3227
14.8981
.01631
29
4.1161
.242946
65.4388
15.1411
.01528
30
4.3219
231377
69.7608
I5-3725
.01434
31
4-538o
.220359
74.2988
.01346
32
4.7649
.209866
79.0638
15.8027
.01265
33
5-0032
.199873
84.0670
16.0025
.01190
34
5-2533
.190355
893203
16.1929
.OII20
35
.181290
94-8363
16.3742
01055
36'
5-7918
.172657
100.6281
16.5469
.00994
37
6.0814
.164436
106.7095
16.7113
.00937
38
6-3855
.156605
113.0950
16.8679
.00884
39
6.7048
.149148
119.7998
17.0170
.00835
40
7.0400
.142046
126.8398
17.1591
.00788
41
7.3920
.135282
134.2318
17.2944
.00745
42
7.7616
.128840
I4I-9933
17.4232
.00704
43
8.1497
.122704
150.1430
17-5459
.OO666
44
8-5572
.116861
1158.7002
17.6628
.00630
45
8.9850
.111297
167.6852
17.7741
.00597
46
9-4343
.105997
177.1194
17.8801
.00565
47
9.9060
.100949
187.0254
17.9801
00535
48
10.4013
.096142
197.4267
18 0772
.00506
49
10.9213
.091564
208.3480
18.1687
.00480
50
11.4674
.087204
219.8154
18.2559
00455
OF LIFE INSURANCE,
TABLE No. IV.
MONETARY TABLES, 6 PER CENT.
N
Tears.
!
Amount of '$i
i N years.
Present
value of $i
due N years
hence.
Amount of
$i per annum
in N years.
Present
Value o/"$i,
per annum for
N years.
Sinking
\ fund ihnt will
amount to $i in
N years.
I
1. 0600
943396
I. 0600
0-9434
.Q4340
2
1.1236
.889996
2.1836
1-8334
45796
3
1.1910
.839619
3-3746
2.6730
29633
4
1.2625
.792094
4-6371
3-465I
21565
5
I-3382
747258
5-9753
4.2124
16735
6
1.4185
.704961
7-3938
4-9173
13525
7
I-5 36
.665057
8.8975
5-5824
.11239
8
I-593S
.627412
10.4913
6.2098
09532
9
1.6895
.591898
12.1808
6.8017
.0821O
10
1.7908
558395
13.9716
7.3601
07157
ii
1.8983
.526788
15.8699
7.8869
.06301
12
2.0122
.496969
17.8821
8.3838
05592
13
2.1329
468839
20.0151
8.8527
.04996
14
2.2609
.442301
22.2760
9.2950
.04489
15
2.3966
417265
24.6725
9.7122
04053
16
2.5404
393646
27.2129
10. 1059
03675
17
2.6928
371364
29.9057
10-4773
03344
18
2-S543
350344
32.7600
10.8276
03053
19
3-0256
330513
35-7856
11.15^1
.02794
20
3.2071
.311805
38.9927
11.4699
02565
21
3-3996
294155
42-3923
11.7641
02359
22
3-6035
277505
45-9958
12.0416
.02174
23
3-8i97
.261797
49.8156
12.3034
.O?OO7
2 4
4.0489
246979
53-8645
12.5504
.01857
2 5
4.2919
.232999
58.1564
12.7834
.01720
26
4-5494
.ZigSlO
62.70^8
13.0032
01595
27
4.8223
.207368
67-5281
13.2105
.01481
28
5-ni7
.195630
72.6398
13.4062
01377
2 9
5-4184
184557
78.0582
I3-5907
.01281
30
5-7435
.I74IIO
83.8017
13.7648
.01193
31
6.0881
.164255
89.8898
139291
.OIII2
32
6-4534
154957
96-3432
14.0840
.01038
33
6.8406
.146186
103.1838
14.2302
.00969
34
7.2510
.137912
110.4348
14.3681
.00905
35
7.6861
.130105
118.1209
14.4982
.00847
36
8-H73
.122741
126.2681
14.6210
.00792
37
8.6361
"5793
134.9042
14.7368
.00741
38
9- J 543
109239
144.0^85
14.8460
.00694
39
9-7035
.103056
153.7620
14.9491
.00651
40
10.2857
.097222
164.0477
15.0463
.00610
4i
10.9029
.091719
1 74- 9505
15.1380
.00572
42
"5570
.086527
186.5076
15-2245
.00536
43
12.2505
.081630
198.7580
15.3062
.C0503
44
12.9855
.077009
2H-7435
15-3832
.C0472
45
13.7646
.072650
225.5081
15-4558
.00443
46
I4-5905
.068^38
240.0986
I5-5244
.00417
47
15-4659
.064658
255-5645
15.5890
.00392
48
16.3939
.060998
271.9584
15.6500
.00368
49
17-3775
057546
289.3359
15.7076
.00346
50 18.4202
.054288
37-7.s6i
15.7619
00325
28
PRINCIPLES AND PRACTICE
TABLE No. V.
MONETARY TABLES, 7 PER CENT.
N
Years.
Amount of $i
tit N years.
Present
Value of $i
due N years
hence.
Amount of
$i per annum
in N years.
Present
Value of $i
per annum for
N years.
Shikiiiff
fund that iv ill
amount to $1
in N years.
I
1.0700
934579
I.O7OO
9346
93458
2
1.1449
873439
2.2149
I. 8080
45H9
3
1.2250
.816298
3-4399
2-6243
.29071
4
1.3108
.762895
4-7507
3-3S72
.21050
5
1.4026
.712986
6.1533
4.1002
.16251
6
1.5007
.666342
7.6540
4.7665
.13065
7
1.6058
.622750
9.2598
5-3S93
.10799
8
1.7182
.582009
10.9780
5.9713
.09109
9
1-8385
543934
12.8164
6-5152
.07803
10
1.9672
508349
14.7836
7.0236
.06764
ii
2.1049
475093
I6.S8S5
7.4987
.05921
12
2.2522
.444012
19.1406
7-9427
.05224
13
2.4098
.414964
21-5505
8-3577
.04640
H
2-5785
.387817
24.1290
8-7455
.04144
15
2.7590
.362446
26.8881
9.1079
03719
16
2-9S22
338735
29.8402
9.4466
03351
17
3-I5S8
316574
32.9990
9.7632
.03030
18
3-3799
29.5864
36.3790
10.0591
.02749
19
3-6165
.276508
39-9955
10.3356
.02500
20
3.8697
.258419
43.8652
10.5940
.02280
21
4.1406
.241513
48.0057
10.8355
.02083
22
4.4304
.225713
52.4361
n. 0612
.01907
23
4-7405
.210947
57.1767
11.2722
.01749
24
5.0724
.197147
62.2490
11.4693
.Ol6o6
25
5-4274
.184249
67.6765
11.6536
.01478
26
.5.8074
.172195
73-4838
11.8258
.01361
27
6.2139
.160930
79.6977
11.9867
01255
28
6.6488
.150402
86.3465
12.1371
.01158
29
7-IH3
140563
93.4608
12.2777
.OIO7O
30
7.6123
131367
101.0730
12.4090
.00989
31
8.1451
.122773
109.2182
12.5318
.00915
32
8.7153
.114741
"7-9334
12.6466
.00848
33
9-3253
J07235
127.2588
12.7538
.00786
34
9.9781
.100219
137-2369
12.8540
.00729
35
10.6766
.093663
H7-9 I 35
12.9477
.00676
36
11.4239
087535
159-3374
13.0352
.00628
37
12.2236
.081809
171.5610
13.1170
.00583
33
i3- 793
.076457
184.6403
i3-!935
.00542
39
13.9948
.07H55
198.6351
13.2649
.00503
40
14-9745
.066780
213.6006
I3-33I7
.00468
4i
16.0227
.062412
229.6322
i3.394r
00435
42
I7-M43
.058329
246.7765
I3-4524
.00405
43
18.3444
054513
265.1209
I3-5070
00377
44
19.6285
.050946
284.7493
I3.5579
.00351
45
21.0025
.047613
305-75i8
13-6055
.00327
46
22.4726
044499
328.2244
13.6500
.00305
47
24.0457
.041587
352.2701
13.6916
.00284
48
25.7289
.038867
377,9990
13-7305
.00265
49
27.5299
.036324
405.5289
13.7668
.00247
50
29.4570
033948
434.9860
13.8007
.00230
OF LIFE INSURANCE.
TABLE No. VI.
MONETARY TABLES, 8 PER CENT.
N
Tears.
Amount of$t
in ti years.
Present
Value of $i
due N years
hence.
Amount of
$\fer annum
in N years.
Present
Value of $i
per annum for
N years.
Sinking'
fund that mill
amount to $i
in nysars.
I
I. 0800
.925926
1. 0800
9 2 59
92593
2
1.1664
857339
2.2464
L7833
.44516
3
1-2597
793832
3.5061
2-5771
.28522
4
I-3605
735030
4.8666
3-3I2I
.20548
5
1.4693
.680583
6-3359
3-99 2 7
15783
6
1.5869
.630170
7.9228
4.6229
.12622
7
I. 7 I38
58349
9.6366
5.2064
10377
8
1.8509
.540269
11.4876
5.7466
.08705
9
1.9990
.500249
13.4866
6.2469
. -074H
10
2.1589
463193
I5-6455
6.7101
.06392
ii
2.3316
.428883
17.9771
7-I390
05563
12
2.5182
397"4
20.4953
7-536I
.04879
13
2.7196
.367698
23.2149
7-9038
.04308
14
2.9372
.340461
26.1521
8.2442
.03824
IS
3.1722
.315242
29-3243
8-5595
.03410
16-
3-4259
.291890
32.7502
8.8514
03053
17
3.7000
.270269
36.4502
9.1216
.02744
18
3.9960
.250249
40.4463
93719
.02472
*9
4-3I57
.231712
44.7620
9.6036
.02234
20
4.6610
.214548
49.4229
0.8181
.02023
21
5-0338
.198656
54-4568
10.0168
.01836
22
5-4365
.183941
59-S933
10.2007
.01670
23
5-8715
I703I5
65.7648
10.3711
.01521
24
6.3412
.157699
72.1059
10.5288
.01387
25
6.8485
.146018
78-9544
10.6748
.01267
26
7-3964
.135202
86.3508
10.8100
.01158
27
7.9881
.125187
94-3388
10.9352
.01060
28
8.6271
.115914
102.9659
11.0511
.00971
29
9-3I73
.107328
112.2832
11.1584
.00891
30
10.0627
099377
122.3459
11.2578
.00817
31
10.8677
.092016
I33-2I35
11.3498
.00751
32
"-737I
.085200
144.9506
"4350
.00690
33
12.6760
.078889
157.6267
".5139
.00634
34
13.6901
073045
171.3168
11.5869
.00584
35
I4-7853
.067635
186.1021
11.6546
00537
36
15.9682
.062625
202.0703
11.7172
.00495
37
17.2456
.057986
2I9-3I59
11.7752
.00456
33
18.6253
.053690
237.9412
11.8289
.00421
39
20.1153
.049713
258.0565
11.8786
.00387
40
21.7245
.046031
279.7810
11.9246
00357
4i
23.4625
.042621
303-2435
11.9672
.00330
42
25-3395
039464
328.5830
12.0067
.00304
43
27.3666
.036541
355 '9496
12.0432
.00281
44
29.5560
033834
385.5056
12.0771
.00259
45
31.9204
.031328
417.4261
12.1084
.00240
4 6
34-4741
.029007
451.9002
12.1374
.00221
47
37.2320
.026859
489.1322
12.1643
.O0204
48
40.2106
.024869
529-3427
12.1891
.OOlSg
49
43-4274
.023027
572.7702
12.2122
-00175
50
46.9016
.021321
619.6718
".2335
.00161
PRINCIPLES AND PRACTICE
TABLE No. VII.
MONETARY TABLES, 9 PER CENT.
N
Years.
Amount of $i
' N years.
Present
Value of $1
due N years
hence.
Amount of
$i per annum
in N years.
Present
Value of $ i
per annum for
N years.
Sinking
fund that -will
amount to$i
in N years.
I
I.OgOO
9 I 743 I
I. ogOO
0.9174
9!743
2
1.1881
.841680
2.2781
I-759I
.43896
3
1.2950
.772184
3-5731
2.53I3
.27987
4
1.4116
.708425
4.9847
3-2397
.20061
5
1-5386
.649931
6.5233
3.8897
15330
6
1.6771
.596267
8.2004
4.4859
.12195
7
1.8280
547034
10.0285
5-0330
.09972
8
1.9926
.501866
I2.O2IO
5-5348
.08319
9
2.1719
.460428
14.1929
5-9952
.07046
10
2.3674
.422410
16.5603
6.4177
.06039
ii
2.5804
387533
19.1407
6.8052
.05225
12
2.8127
355535
21-9534
7.1607
04555
13
3.0658
.326179
25.0192
7.4869
03997
14
3-34I7
.299247
28.3609
7.7861
.03526
15
3-6425
274532
32-0034
8.0607
'03125
16
3-9703
.251870
35-9737
8.3125
.02780
17
4.3276
.231073
40.3013
8.5436
.02481
18
4.7171
.211993
45.0185
8-7556
.02221
19
5-I4I7
.194489
50.1601
8.9501
.01994
20
5.6044
.178431
55-7645
9.1285
01793
21
6.1088
.163697
61-8733
9.2922
.Ol6l6
22
6.6586
.150182
68.5319
9.4424
.01459
23
7-2579
-I3778I
75.7898
9.5802
.01319
24
7. 9 III
.126405
83.7009
9.7066
.01195
25
8.6231
.115967
92.3240
9.8226
.01083
26
9.3992
.106392
101.7231
9.9290
.00983
27
10.2451
.097608
111.9682
IO.O266
.00893
28
11.1671
.089548
123.1354
10.1161
.008l2
29
12.1722
.082155
I35-3075
10.1983
.00739
3
13.2677
075371
148-5752
10.2736
00673
3 1
14.4618
.069148
161-0370
10.3428
.00613
3 2
I5-7633
.063438
178.8003
10.4062
00559
33
17.1820
.058200
195.9823
10.4644
.00510
34
18.7284
053395
214.7108
10.5178
.00466
35
20.4140
.048986
235-1247
10.5668
00425
36
22.2512
.044941
257-3759
10.6117
.00389
37
24-2538
.041230
281.6298
10.6530
90355
38
26.4367
.037826
308.0665
10.6908
00325
39
28.8160
034703
336.8824
IO-7255
.00297
40
31.4094
.031838
368.2919
10-7573
00272
4i
342363
.029209
402. 15281
10.7866
.00248
42
37-3I7?
.026797
4.39-8457
10.8134
.00227
43
40.6761
.024584
480.5218
10.8379
.00208
44
44-3370
.022554
524.8587
10.8605
00191
45
48-3273
.020692
573 1860
10.8812
.00174
46
52.6767
.018983
62^.8628
10.9002
.00160
47
57-4I76
.017416
683.2804
10.9176
.00146
48
62.5852
.015978
745.8656
10.9336
.00134
49
68.2179
.014659
814.0836
10.9482
.00123
50 .
74-3575
.013448
888.4411
10.9617
.00113
OF LIFE INSURANCE.
TABLE No. VIII.
MONETARY TABLES, 10 PER CENT.
N
Tears.
Amount of$i
in N years.
Present
Value of $i
due N years
hence.
Amount of
\per annum
in N years.
Present
Value o/"$i
per annum for
N years.
Sinking
fund that -will
amount to $i
in N years.
I
.IOOO
.909091
I. IOOO
0.9091
.90909
2
.2IOO
.826446
2.3100
1-7355
.43290
3
3310
75I3I5
3.6410
2.6849
27465
4
.4641
683013
5-I05I
3.1699
.19588
5
.610^
.620921
6.7156
3.7908
.14891
6
.7716
564474
8.4872
4-3543
.11783
7
1.9487
5I3I58
10-4359
4.8684
.09582
8
2.1436
.466508
12-5795
5-3349
07949
9
2-3579
.424098
H-9374
5-7590
.06695
10
2-5937
385544
I7-53I2
6.1446
05691
ii
2.8531
35 494
20.3843
6.4951
.04906
12
3-1384
.318631
23.5227
6.8137
.04251
13
3-4523
.289664
26.9750
7-1034
.03707
14
3-7975
263331
30-7725
7-3677
.03250
15
4.1772
23939 2
34-Q497
7.6061
.02861
16
4-5950
.217629
39-5447
7-8237
.02529
17
5-0545
.197845
44-5992
8.0216
.02242
18
5-5599
.179859
5- I 59 l
8.2014
.01994
*9
6.1159
.163508
56.2750
8.3649
.01777
20
6.7275
.148644
63.0025
8-5136
.01587
21
7.4002
I35I30
70.4027
8.6487
.01420
22
8.1403
.122846
78.5430
8-77I5
.01273
23
8-9543
.111678
87-4973
8.8832
.01143
24
9.8497
.101526
97-3471
8.9847
.01027
25
10.8347
.092296
108.1818
9.0770
.00924
26
11.9182
.083905
120.0999
9.1609
.00833
27
13.1100
.076278
133.2099
9.2372
00751
28
14.4210
069343
147.6309
9.3066
.00677
29
15-8631
.063039
163-4940
9.3696
.00612
30
17.4494
057309
180.9434
9.4269
00553
3 1
19.1943
.052099
200.1378
9.4790
.00500
3 2
21.1138
.047362
221-2515
9-5264
00452
33
23.2252
043057
244-4767
9.5694
.00409
34
25-5477
039H3
270.0244
9-6086
-00370
35
28.1024
035584
298.1268
9.6442
00335
36
30.9127
032349
329-0395
9.6765
.00304
37
34-0039
.029408
363-0434
9-7059
00275
38
37.4043
026735
400.4478
9-7327
.00250
39
41.1448
.024360
441.5926
9-7570
.00226
40
45-2593
.022095
486.8518
9.7791
.00205
4i
49.7852
.020086
536-6370
9.7991
.00186
42
54.7637
.018260
591.4007
9.8174
.00169
43
60.2401
.016600
651.6408
9.8340
00153
44
66.2641
.015091
717.9048
9.8491
00139
45
72.8905
.013719
790-7953
9.8628
.OOI26
46
80.1795
.012472
870.9749
9-8753
.00115
47
88.1975
.011338
959-I723
9.8866
.00104
48
97.0172
.010307
1056.1896
9.8969
.00095
49
106.7190
.009370
1162.9085
9.9063
.00086
5
117.3909
.008519
1280.2994
9.9148
.00078
LIFE CONTINGENCIES.
The first fundamental basis of all life insurance calculations is
the law of mortality, or inversely the duration of human life.
The age which any individual will attain is always a matter of
great uncertainty, as death in a thousand different ways is liable
to take away human life ; and yet there is a certain uniform death
rate when applied to a large number of people of any given age
which would be truly astonishing, were it not one of the recog-
nized laws which govern human affairs. The uniformity of these
occurrences, which many regard as entirely fortuitous, is one of
the most interesting discoveries of modern science. The statis-
tics of our fire insurance companies show that the ratios of losses
to premium receipts occur from year to year with surprising
uniformity ; the aggregate number of suicides and murders annu-
ally occurring from year to year in a civilized country vary but
very little ; the prevailing direction of the winds and the fall of
rain during the corresponding seasons of each year display
almost uniform results in their yearly aggregates. It is on the
same principle, by collecting the statistics of the deaths of a large
number of persons, that the different tables of mortality have been
formed.
According to the American table of mortality, which is adopted
by the state of New York, and several other states, as the official
standard for making the valuations of the Insurance Department,
out of a class of 100,000 persons living at the age of 10 years,
92,637 will be living at 20, 85,441 at 30, 78,106 at 40 years of
age, and so on ; or the percentage of mortality in a class of 100,000
at the age 20 is 780 ; at 30, 843 ; at 40, 979.
This rate of mortality does not have a uniform increment ; but if
we represent the probability of dying from 10 to 95 years of age by
a line, it will describe a curve very nearly the same as a cycloid.
The various tables of mortality, constructed in different coun-
tries and periods, show a great degree of uniformity in the prob-
OF LIFE INSURANCE. 33
ability of life at the same age ; and yet it is an interesting and
encouraging fact, that each successive century is slowly length-
ening the average duration of human life. Improvements in
civilization, more abundant supply of food, new discoveries in
medicine, and a more general knowledge of the laws of physiology
and hygiene, are having a favorable influence in lessening the rate
of mortality.
TABLES OF MORTALITY.
The value of life insurance calculations depends in a great
degree upon accurate and reliable tables of mortality, since it
is this and the assumed rate of interest which determines the net
premiums, the proper reserves, and, to some extent, the margin
for expenses, and distribution of surplus to policyholders. With-
out a reliable and well adjusted table of mortality, conforming
very closely to actual experience, it would be impossible for
these terms to be correctly computed, or the policyholders to be
equitably treated. It was not till tolerably correct tables were
made that life insurance rose to the dignity of a science. Pre-
vious to this it was all conjecture. In its early history statistics
of mortality were almost entirely neglected. In a few parishes
of England there were registers of the living and the dying, but
they were so imperfectly kept as to be almost wholly unreliable.
And the best informed public men could not tell whether the
population of the country was increasing or decreasing. The
great truth, reserved for discovery in later times, that there are
certain laws to which the average duration of human life con-
forms, was never thought of. It was for this reason that when
life insurance companies were first organized in England the
rates were the same for all ages, as the fees and dues for co-
operative associations, burial clubs, workingmen's unions and
friendly societies are at the present day. But a short period of
observation revealed the fact, which is now regarded as self-
evident, that the aged are much more likely to die than the young,
and the necessity for a different guide to determine the probable
length of human life became evident.
THE AMERICAN EXPERIENCE TABLE.
This table, first adopted by the state of New York, in the year
1868, as a basis for the valuation of policies, was constructed by
34
PRINCIPLES AND PRACTICE
Mr. Sheppard Homans, from the experience of the Mutual Life
Insurance Company, of New York, who also availed himself of
other statistics, to ascertain the laws of mortality as applicable
to healthy insured lives in this country. All the standard Euro-
pean tables were used in adjusting it. This table of mortality,
with 41-2 per cent rate of interest, is now made the legal standard
of valuation in several of the states.
In the illustrations and explanations given in this part of the
work, the American Table of Mortality and 4 1-2 per cent in-
terest will be used as a basis, unless some other table and rate
are expressly named.
THE COMBINED EXPERIENCE, OR ACTUARIES'
TABLE.
This table was prepared by a committee of eminent actuaries,
on the data afforded by the combined experience of seventeen of
the principal life insurance offices in England. It was deduced
from 62,537 assurances, first published by Mr. Jenkin Jones, in
1843, and furnishes a very accurate graduation of assured lives.
Some of the objections advanced against it are that certain lives,
having been more than once, assured, have appeared twice or
oftener as elements of the calculation, and that the data for the
older ages were insufficient. The mortality amongst assured
females, taking all ages together, is greater than amongst assured
males. A more careful comparison of the different classes in-
sured reveals the fact that the average duration of male lives
under 36 years of age is greater than that of females, and from
36 to 6 1 years of age the average duration of the lives of females
is greater than that of males ; but after the age of 61 the male
lives have a greater expectation than female lives. The average
duration of all the policies was a little less than 8 1-2 years.
RATE OF INTEREST.
The second principal element of all the calculations in life as-
surance is the rate of interest assumed by the companies to be
realized on their assets. A contract of insurance made between
the company and the policyholder is designed to exist as long as
the policy can be continued in force, either during a term of
years or the lifetime of the policyholder. In contracts extending
OF LIFE INSURANCE.
35
over a long series of years, the continued and ultimate solvency
of the company is of the highest importance, and the adoption of
any erroneous principles of calculation, and increased from year
to year at each renewal of the premiums, and moreover multi-
plied by thousands of policies in force, cannot fail to work out a
disastrous result in time. Hence it is of the highest importance
that the primary elements of mortality and of interest should be
such as are perfectly safe to the insured. The company assumes
that the adopted rate of mortality will be experienced in the
future, and m each annual premium there is a certain part set
aside or reserved to pay the claim of the policyholder when it
becomes due ; and this reserve, according to the laws and as-
sumptions of life insurance, accumulates at compound interest as
long as the policy remains in force. The question now arises,
what rate of interest must be assumed as the one which these re-
serves will earn during the years that intervene between the pay-
ment of the first premium and the final settlement of the claim ?
The opinions of Hon. Elizur Wright on this subject are worth
quoting here :
"A very large part of the immense sums promised to be paid in the
distant future is to be produced by the accumulation of interest, and the
premium, being fixed at the outset and unalterable, it will make a life
or death difference with the company whether six per cent interest is al-
ways to be received on investments, or the rate is to fall occasionally or
permanently to four or three per cent. If the interest is to be more, the
premium may be less, and if it is to be less, the premium must be more.
The only safety is to assume a rate of interest so low that the profits on
investments may always exceed it, and to divide at short intervals the
surplus that may result from the excess."
"It is historically certain that all experiments of life insurance that
have been tried long enough to test results, without reserving premium
on an assumption of interest lower than the current interest on invest-
ments, have proved failures." Mass. Report, 1865,^. 305.
The standard rate of interest adopted by the state of New
York and several other states, is 4 1-2 per cent ; in Massachusetts,
Illinois and some other states it is 4 per cent.
PROBABILITY OF LIFE.
The probability of life is the likelihood which a person has,
according to the table of mortality, of living a certain number of
years. The probability of death is the likelihood a person has of
36 PRINCIPLES AND PRACTICE
dying within a given period. As it is absolutely certain that a per-
son will always be dead or alive, the probability of death is found
bv subtracting the probability of life from unity, and vice versa.
Example. Required, the probability that a person aged thirty
will live to be fifty years old, American table.
The number living at the age 50 is 69,804.
The number living at the age 30 is 85,441.
Therefore p^=.8i6gS the probability.
85>44i
As there are 85,441 chances in all of the persons aged 30 at-
taining to fifty years, and as the probability is that only 69,804
will live, the contingency that each individual will live, is, .81698,
and hence the contingency of his dying is, i .8 1698=. 18302, or
I 5 6 37 and
J44 1
These operations are sometimes useful in making estimates
upon endowment policies, as to whether a person will live to
complete his payments, and on term policies, whether the party
will die during the period of insurance.
COMMUTATION COLUMNS.
The commutation columns are now universally used in the
computation of premium rates, annuities and many other cal-
culations. The four principal columns are denoted by the capital
letters D, N, C, M. In increasing insurance S and R are used.
The column D, usually written D#, denotes the number of living
at any age #, discounted by such a power of 1.045, or whatever
rate of interest is assumed, as corresponds to the age x. For the
sake of convenience and uniformity we use that power of -
which corresponds to the age of the insured. It would make
no difference in the result if we took the first power of -
1.045
to discount the living at the age 10, and the second power for the
age ii, &c., since the ratio between the different numbers in the
column is not changed by taking a different exponent of discount.
The first number in the column D against the age 10 is found by
multiplying 100,000, the tabular number living at that age, by
( V 9 or .64392768, which gives 010 = 64392.768. The
second number, or Dn, is found by multiplying 99,251 by
OF LIFE INSURANCE.
37
V 1 or .6162087, which gives 61158.341. In this manner
all the remaining terms in column D are found. C denotes the
number of dying at the age x, discounted by the x+i power of
, for the reason that the deaths are computed as .taking place
at the end of the year, while the premiums are paid at the begin-
ning. Thus, at the age 10, 0=749 x fj-^-) n =749 x . 6162087=
461.5329, and at the age n, 0=746 x ( r ^) 12 =746 x .58966385=
439.8892, and so on with the remainder of the column. The N
column is found by taking the sums of the numbers in the D
column beginning with the oldest age, as follows : D at the age
95=3x( ) 95 = .045822, and is the same as N at the same
age, or N95=.O45822. N94=D95+D94=.o45822+.335iSS=
.381010. N93=D95 +094+093=^4+093=381010+1.317687
=1.698697. Continuing this process through all the ages in the
mortality table, we have the N column complete. The M column
is found by adding together the terms of the C column in the same
manner as the N column. The S and R columns are found by
adding together the numbers in the N and M column respectively,
in the same manner as N and M were obtained from D and C.
EXPLANATION OF LIFE INSURANCE.
The table of mortality enables us to determine the ratio there
is between the number living at a given age at the beginning of
a year and the number dying during that year. At the age 30
there are 85.441 living, and during that year there are 720 deaths,
and, therefore, the probability that a person aged 30 will die dur-
ing that year is ^ =.0084269. If 1 ,000 persons aged 30 insure
for $i each for one year, the net premium required of each, with-
out reckoning interest, will be one thousandth part of the total
losses at the end of the year. As the total losses are 8.4269, the
net premium required of each policyholder will be .0084269.
But as the premiums paid at the beginning of the year are in-
creased by 4 1-2 per cent interest, and the losses are reckoned to
take place at the end of the year, this amount of premiums re-
quired must be discounted at 4 1-2 per cent, which reduces the
38 PRINCIPLES AND PRACTICE
total amount of premiums required to $8.0640, anil the amount
required to insure $i for one year at the age above given is
.0080640. At the age 31 the net premium for orfe year is
.0081438, and at 32 it is .0082365.
The foregoing explanation relates entirely to temporary insur-
ance from year to year, and, if carried on through life, the pre-
mium would have to be changed each successive year. In order
to find the uniform annual premium required on a policy payable
at death, and to simplify the explanation we will take an example
in which the element of interest is omitted.
At the age 95, according to the American Experience Table
of Mortality, there are three persons living, all of whom die
during the year. Consequently, if each of these were insured to
the amount of $i, there would be three claims of $i each to pay
during the year. At the age of 94 we have 21 persons living,
18 of whom die during the first year and 3 during the next,
hence there are 21+3 premiums paid, and only 21 claims to be
met; and, therefore, the amount of each premium would be
=.875. At the age of 93 there are 79 living, and the first year
24
there are 79 premiums paid, the second 21, and the third 3, mak-
ing 103 premiums to 79 losses, and the annual premium to insure
$i is -^-=.76699.
103 ' **
From the above example it will be seen that the fundamental
principle for finding the premium to insure $i through life for
any given age (without regarding interest) is as follows : Divide
the number of living, or future deaths, at any given age, by the
total number of premiums to be paid till the death of the last
survivor.
It is clear from the above example that in life insurance some
persons insured pay much more than the company returns, and
others less. At the age 93 there are 79 living, of whom 58 pay
.76699 each, and the company returns $i for each loss. At the
age 94 there are 18 claims of $i each, for which 18 persons have
paid $1.53398 each in two annual premiums. At the age 95
there are 3 losses of $i each, on which 3 persons insured have
each paid premiums amounting to $2.30097.
In computing the net annual premium at 4 1-2 per cent interest,
the same general principles given above are applicable. In the
OF LIFE INSURANCE.
39
foregoing example we have 3 persons living at the age 95. Ac-
cording to the mortality table there would be 3 premiums to be
paid at the beginning of the year, and 3 claims of $i each at the
end of the year ; and, therefore, the premium required to insure
$i for one year would be the present value of $i for one year, or
- =.9^694.
1.045 *> "
At the age 94 there are 21 living, and the annual premium to
be paid is found as follows :
Premiums at the beginning of the first year, - - - - 21
Premiums at the beginning of the second year discounted=
3 x .95694= 2.87082
Total premiums discounted, - ....-. 23.87082
The next step is to find the present value of the future losses.
Losses of the first year, present value, i8x .95694
Losses second year, present value, 3 x .91573=
Total losses, present value, - .
Annual premium, age 94=19.97211 -f-
17.22492
2.74719
$19.97211
"79
. 20.09574
. 2.74719
- 101.84293
55-5 O2 S 2
. 1648314
- 2.62890
. $74.61456
At the age 93 there are 79 living.
Premiums at the beginning of the first year, - -
Premiums second year, 21 x .95694= ...
Premiums third year, 3 x .91573= ....
Total number discounted premiums, . -
Losses first year, present value, 58 x .95694= -
Losses second year, present value, iSx .91573= .
Losses third year, present value, 3 x .87630= - -
Total losses, present value, ...
Annual premium=$74.6i456-f-ioi.84293=.732643.
In each of the above examples the number of premiums to be
paid and the number of losses to be met are discounted by a
different power of -- . It is easy to see that in computing pre-
miums for the younger ages this would be an exceedingly difficult
anc| tedious operation, were not some more expeditious method
discovered. The commutation columns enable us to perform
these operations with much greater facility.
Under the head of " Commutation Columns," page 36, we
found that N is the sum of the numbers in the D column, or the
4 PRINCIPLES AND PRACTICE
discounted numbers of the living, and M is the sum of the C's or
discounted numbers of the dying. In the last example we have
the quantity 101.84293 equals the total number of discounted
premiums, or number of living at the beginning of each year, and
therefore it corresponds to N93, discounted by a different power of
. The quantity 74.61456 is the discounted number of the
losses or dying each year, and corresponds to M93. Therefore,
the annual premium 74.61456-*- ioi.84293=-r=.73264. And
generally the annual premium for one dollar on a whole life
policy is found by dividing the discounted number of future losses
by the discounted number of future premiums to be paid. Hence
the formula for finding the annual premium on a whole life policy
M*
18 ^r-
N*
By referring again to the commutation columns, we find that
-rJ^= ^=.77264. In the same manner the net annual pre-
N93 1.698696 /0
mium for the age 30 is-^ T 3 = ''- 7 ^=.Qi<^6 ; that is, at the age
390642.05 JJO
30 the discounted number of future death claims, according to
the table is 5990.8434, and the discounted number of future pre-
miums is 390642.05, making the average value of each premium
.015336 on an insurance of $i. Hence the rule for finding the
net annual premiums by means of the commutation columns is :
Divide the discounted sum of the dying at the given age in the
M column by the discounted sum of the future premiums to be
paid as found in the N column at that age, and multiply the quo-
tient by the sum insured.
In the commutation columns N93 is the sum of the D's dis-
counted by the ninety-third, fourth and fifth power of -- -, and
die M column is the sum of the C's multiplied into one higher
power of . The reason why these figures give the same re-
sult, as when we take the living and dying in the mortality table
and discount them by the first, second and third powers of - , is
that it makes no difference in the result what power of we
1.045
use to discount by, provided we take a power higher by one at
OF LIFE INSURANCE. 4!
each successive age. In the first case we have I 093 x - + C 9 4 x
In
i.o45/, Vi.045/ 1-045 Vi.045
thelatterwe have [C 93 x (^) 94 +C 94 x ( I ^) M + C 95 x ( r ^)' ']
045 / 1-045 / 1-045 / - 1-045
( - ) .
Vi.045/ J
Since both numerator and denominator are
.045
/ j S g ;
multiplied by the same quantity f - J ' the result is not
changed.
The net single premium is the sum which, paid in advance,
will insure a person during life. Were it not for the discount
the net single premium would be equal to the sum insured at all
ages. To find the net single premium we give the following
illustration : At the age 9 3 we have 7 9 lives to insure in the sum
of $i each. The present value of all the future annual premiums
which they would pay is (page 40) 74.61456, consequently the
single premium which would be required of each is ' =
.94449. Here the numerator represents MX, and we have seen
that the denominator represents D#; therefore the formula is
M# -r, ,, .. Mg3 1.24415367
-VT . BV the commutation columns we have -r^=
Dx J 093 1.317686
. , . ,
.94449. At the age
The general rule given on page 40, for finding the net annual
premium on a whole life policy, will also apply to find the annual
premium on a policy with a limited number of annual payments.
A person insures in the sum of $i at the age 30 on the ten pay-
ment plan. The discounted number of future claims at this age is
5990.8434, and the discounted number of future premiums during
ten years from the age 30 is N3<D N4o=39o642.O2 208640.18=
182001.87 ; therefore, if it requires 182001.84 premiums to meet
5990.8434 claims of $i each, what will be the amount of each
premium? It is evident that 599O.S434-f-iS2Ooi.84=.O329i6 the
annual premium. Here, as before, we divide the discounted
number of future claims by the discounted number of future pre-
miums to be received during the years in which these premiums
42 PRINCIPLES AND PRACTICE
are to be paid. The formula for limited premium life policies is
N _ N , in which n= the number of years during which the
annual payments are made.
In term or temporary insurance the premiums are payable
during a limited number of years, and the amount insured is paid
only in case the policyholder dies during this period. The pre-
mium is the ratio which the discounted number of premiums in
the column N, during the period of insurance, bears to the dis-
counted number of claims in the column M for the same time,
and multiplied by the sum insured ; and is found by dividing the
difference between the number of deaths in the M column, at the
time when the insurance commences, and the number when the
policy ceases to be in force, by the difference between the corres-
ponding N numbers at the same ages. The term insurance for
a policy of $i , issued at the age 30, for ten years, is (M3O M4o) -*.
(N30-N40) = (5990.8434-4444. 1 583) -(390642. 05 -208640. 1 8)
=1546. 6851 182001. S7=.ooS4982 ; that is, we assume that there
will be 1546.6851 deaths to 182001.87 premiums paid, and there-
fore each premium required would be .0084982.
Simple endowment is a form of insurance in which the sum
insured is payable only in case the policyholder is alive at the
time when the policy expires by limitation. The annual pre-
mium is the ratio between the number of payments made by the
living during this term and the number living at the end of the
term. Thus the simple endowment on a person aged 30, payable
at 40, if living, is the ratio between the tabular number of pay-
ments for ten years, commencing at 30, and the number of living
at the age 40, or D4O-j-(N3o N4o)= 13428. 663 (390642. 02
2o864o.iS)=i3428.663 -4-182001 .S4=.o737S3. In this example,
according to the commutation columns, the discounted number
of premiums to be paid during ten years is 182001.84, anc ^ tne
discounted number of claims is 13428.663.
Simple endowments are very seldom issued, for the reason that
the policyholder assumes all the risk, and the company is merely
a depository of the premiums paid. The death of the policy-
holder allows the company to retain all the premiums, and, as a
general rule, the same amount of money can be realized from the
premiums by the ordinary methods of investment. " Children's
endowments" usually come under this form of so-called insurance.
OF LIFE INSURANCE. 43
Endowment insurance consists of two parts, the simple endow-
ment and term insurance. We have seen how these are found
separately ; it remains only to unite them in one expression. It
will be noticed that in the last two examples the denominators
are the same, N3O N4O, and that the numerators are 040 and
MSO M4O ; that is, the denominator comprises the discounted
number of premiums to be paid during the ten years the policy
is in force, and the numerator is D^o, the discounted number of
survivors at the age 40, and M/3O IVfyo, the discounted number
of losses during the period the policy is in force. Hence the
whole number of claims divided by the whole number of pre-
miums gives the annual premium for $i of insurance. Carried out
by figures, the operation is (13428.66 + 5990.84344444.1583)-*-
(390642.05 208640. 1 8=14975.345 -4-182001. S3=.o822Si.
For an endowment insurance policy with a less number of
premiums than the policy has years to run, we apply the same
principle as before, dividing the discounted number of claims by
the discounted number of premiums. In a ten year endowment
policy, issued on a life aged 30, premiums payable in five years,
we have the same numerator as before, 040+ M3OM4O ; and for
a denominator, N3O N35, or (13428.66+5990.84344444.1583)
-*- (39 6 4 2 -5 - 287677.63) =.14544.
The single premium in these endowments is found by dividing
the numerator, as given above, by the discounted number of living
in the D column at the age of insurance. Thus the net single pre-
mium on a ten annual endowment policy of $i, issued at the age
30, is (040 +M30 M4o) -=-030=14975.3451 -=-2281 2. 75=.656446.
Since all premiums are simply the ratio of the discounted
number of premiums payable during life or a given number of
years to the discounted number of claims during the time the
policy is in force, the general rule for finding the net premium
for any kind of a policy is simply this : Divide the number of
claims, as represented in the commutation columns during the
time when the risk is in force, by the number of premiums during
the period of their payment, and multiply the quotient by the sum
insured.
LIFE ANNUITIES.
The duration of any life annuity depends upon the existence
of the person called the nominee, and according to the American
44
PRINCIPLES AND PRACTICE
Experience Table of Mortality this must cease in eveiy case at or
before attaining the age of 95.
Let us take 847 persons at the age 90, according to the Ameri-
can Experience Table, and compute the present value of an
annuity of $i per annum, payable at the end of the year, on the
lives of each of them. At the end of the first year 385 will have
died ; hence the probability that each person will pay one dollar
at the end of the year is I ~ = | . The present value of $i
payable at the end of the year, at 4 1-2 per cent discount, is
.956938; hence |-^x.956938=.52i97, the present value of the
contingent payment of $i from each of the members living
at the end of the first year. The present value of $i to be
paid at the end of the second year by each of the 847 mem-
Third year, -|2- x
Fourth year, x
Fifth year, g^-x. 802451 =.00284.
Placing these in a series, we have for the present value of
$i per annum, payable at the end of the year through life,
on a person aged 90 years, (||x .956938) +(g|x .91573) + (|| x
.876297 ) + ( ^ x .838561 ) + ( g^ x .802451 ) =.52197+ .23353 +
.081 73 + .02079 + -oo284=.86o86.
If the first payment is to be made at the beginning of the first
year, it is evident that the present value of the life annuity is
1+86086=1.86086, and the terms would read thus: - +
047
x - + 5 x( - V etc. By inspecting these fractions we
847 1.045 847 Vi.045/ ' '
find that the numbers 847, 462, 216, etc., are the numbers of the
living at the beginning of each year, and, when discounted by
the proper powers of -- , their sum corresponds to the num-
ber opposite 90 in the N column, with this difference, that a
different rate of discount is used, and that the denominator 847 is
the same as 090 before it is discounted. Now, if, instead of
OF LIFE INSURANCE. 45
multiplying the numerators by the first, second, third, etc. pow-
ers of - , we multiply them by the ninety-first, ninety-second,
1.045
ninety-third, etc. powers of and the denominator 847 by
the ninetieth power, the relative value of these fractions will not
be altered, and we shall have for the denominator, 090 or
16.12194 and for the numerators 16.12194, 8.415104, etc., or
090 + 091+092, etc. The sum of these numerators is N9O,
which is placed over the denominator 090 thus, ^-=1.86086=
the present value of a premium of $i per annum on a person
aged 90 ; or, in other words, the present value of a life annuity of
$i on a life aged 90, the first payment made at the beginning of
the first year. If the first payment is made at the end of the first
year, leave out the 090 from the sum of the numerators and we
liave -jz^=i3.87S7i-5-i6.i2i94=.86oS6. If the first paymentis
deferred for two years, the present value of the deferred annuity is
=^-=5.463610-5-16. 1 2i94=.33889. The general expression for
Dyo
an annuity is =y- and for a deferred annuity is =: .
The difference between the present value of an annuity for
life and the single premium is this : The annuity is the present
value, of $i multiplied by the probability of living at the end of
each year, because the annuity is payable only in case the nomi-
nee is living. Since all deaths are supposed to take place at the
end of the year, the payment of each policy is regarded as taking
place then, and hence the single premium is equal to the present
value of $i payable at the end of each year, multiplied by the
probability of dying that year. It is evident that the greater the
probability of dying the greater will the premium be, while on
the other hand, the greater the probability of living the greater
the annuity.
VALUATION OF POLICIES.
We have seen (page 40) that the net annual premium to
insure a person aged 30 in the amount of $i during life is
^^-=.015336. If he should postpone insuring for one year he
would not save this amount, for at the age of 31 the net annual
46 PRINCIPLES AND PRACTICE
premium is .015787, and the difference between these two pre-
miums is .000451. By insuring at age 30 he pays .000451 less
premium every year of his life, and the present value of this
is found by multiplying it by the then present value of the life
annuity of $i, or .000451x16.9926=00766366. If he should
postpone insuring till he reaches the age of 32, his net annual
premium will be .016265 and the difference between this and
the premium at 30 is .016265 oi5336=.ooo929- Multiplying
this by the life annuity at age 32, we have .000929 x 16.85573=
.01565897. This is called the net value of the policy. If the
sum insured is $1.000, the net values are $7.66366 and $15.65897.
It is clear from this illustration that if he insures at the age of 30,
instead of deferring it one or two years, he does not lose all the
premiums he has paid. These net values are the same as so
much ready money at 4 1-2 per cent interest, to be used for
paying future premiums. As we proceed further, we shall find
that no part of the net premium is lost, strictly speaking.
The net value of a policy is also found by taking the differ-
ence between the net single premium at the age when the policy
is valued and the present value of the future net premiums to
be paid on it. At age 31, the net single premium for $i is
.268261, and the then present value of all the net premiums on a
life aged 30 is the net premium at 30 multiplied by the life
annuity at 31 or .015336 x 16.9926=. 260598, and the difference
.268261 260598=. 007663, the net value.
The premium on a policy of $i to insure it for one year
only at age 30 is .008064. This is the reserve at the beginning
of the year ; at the end of the year this premium is entirely
absorbed in carrying the annual risk. At the end of six months
this premium is half gone, and therefore the reserve is .008064-1-
In the gross valuation of a policy the present value of the future
gross premiums receivable is considered as an asset, and the pre-
sent value of the future net premiums taken at the age of valua-
tion as a liability. If the latter is greater than the former the
difference is the gross value of the policy, otherwise there is a
surplus in the hands of the company. If the net single premium
for $i at age 31 is .268261, and the gross annual premium at
age 30 is .0227, then the present value of the future gross pre-
miums receivable will be .0227 multiplied by the present value
OF LIFE INSURANCE.
47
of the annuity of $i , or .0227 x i6.9926=.385732. The difference
between .385732 and .268261 is .1 17471 the surplus. That is, the
present value of the future receipts is .117471 greater than the
present value of the future liabilities.
At age 40, multiplying the gross premium by the present
value of the annuity, we have .0227 x 15.5369 .352688. But the
single premium at age 40 is .330946, and there is still a sur-
plus of .021742. At age 50 we have the present value of the
future premiums = .0227 x I3.235S=.3OO453, and the net single
premium at that age is .430037, leaving a gross value of
.129584.
The defect in this method of valuation is that no provision is
made for future expenses.
A modified form of this method of valuation is sometimes prac-
tised by taking off a percentage of the gross premiums for ex-
penses, and proceeding as before.
AMOUNT AT RISK.
When a person takes out a policy of insurance, the risk which
the company assumes as liable to lose is not the whole amount
insured, but the amount of the policy less the reserve. For the
sake of uniformity, the reserve at the end of the year is taken.
Hence the sum insured may be divided into two parts, the insur-
ance which the company carries and that assumed by the policy-
holder. In this last example of a policy of $i issued at age
30, it is clear that the policyholder has a deposit in the hands
of the company of .007663, thus insuring himself for this amount,
while the company insures the balance or .992337. This is what
the company would lose if he should die at the end of the first
year. At the end of the second year the risk which the
company assumes is .984341, and that of the policyholder
.015659.
The reserve on a policy when compared with the amount at
risk is called by Hon. Elizur Wright " self insurance," since it is
the unearned and unexpended part of the premiums which the
policyholder has on deposit in the company to provide for the
future payment of his claim. For this reason Hon. Gustavus W.
Smith, Insurance Commissioner of Kentucky, calls it the "trust
fund deposit."
The amount at risk varies greatly in different kinds of policies,
48 PRINCIPLES AND PRACTICE
and it is owing to the want of a proper understanding of this
subject that many people find themselves greatly mistaken in
their opinions of the benefits of short term endowments. Thus ,
a person paying a premium on a whole life policy of $1,000 is
insured at the end of each of the first ten years for $992.34,
$9 8 4-34> $97 6 - 01 ' $9 6 7-34> $95 8 -3 r i $94 8 - 8 9' $939- IQ $928.91,
$9 l8 -33> $97-33 5 average amount, $952.09.
On a ten annual payment endowment for the same age and same
amount he is insured at the end of each year as follows : $921.78,
$839.42, $752.69, $661.34, $565-11, $463-7^ $356-83, $244.16,
$i 25.34, $0.00 ; average insurance, $493.04. That is in a ten year
endowment a man insures himself on an average for more than
one-half of the amount of the policy. The annual net premium on
a ten annual endowment for this age and amount is $82.29, and
on the whole life policy given above $15.34. O n tne endow-
ment plan as above described, during the ten years the policy-
holder pays between five and six times as much net annual pre-
mium and gets only about half the insurance as on the whole life
plan. But there is a partial offset to this, as the premiums in
the former case cease in ten years when the amount insured is
paid, and in the latter they may continue till the policyholder is
95 years old, according to the assumptions of the American mor-
tality table.
COST OF INSURANCE.
We have seen that the amount at risk is the sum insured less
the reserve at the end of the year. On an ordinary life policy
of $i, issued at age 30, the amount insured at the end of the
first year is .99234. The expense of insuring $i for one year
at age 30 is 7 20 =.0084269, and therefore the cost of insuring
05.441
.99234 for one year is .99234 X .oo84269=..oo83623. This is the
net cost of insurance, and is found by multiplying the amount at
risk by the probability that the insured will die that year.
The cost of insurance at age 31 is found in the same manner.
Amount of policy, --------- $i.
Reserve at end of second year, ...--- 0.01566
Amount at risk, --------- -98434
Number of dying, age 31, ------- 721
Number of living, " -------- 84.721
Probability of dying, 721-7-84721= .0085103
Cost of insurance, .98434 x .0085103 ------ .008377
OF LIFE INSURANCE. 49
The cost of insurance on an ordinary life policy at age 95 and on
an endowment insurance in the last year of its duration is nothing,
because in these cases the reserve equals the amount insured.
Having the net premiums and reserves, the cost of insurance
can be found very easily by adding 41-2 per cent interest to the
net premium and subtracting the reserve, and the remainder is
the cost of insurance for the first year. For the second and sub-
sequent years, the cost of insurance is obtained by adding the
net premium to the reserve of the previous year, increasing this
amount by the interest and subtracting the reserve for that year.
In the example above given
First year Net premium, -....-- .015336
Interest 4^ per cent, ....... .0x30690
Amount, --........ .016026
Reserve first year, -..-..-- .007664
Cost of insurance, ........ .008362
Second year Reserve first year, ------ .007664
Net premium, ---..-..- .015336
Amount, -....._.. .023000
Interest 4^ per cent, -------- .001035
Amount, ---._...- .024035
Reserve second year, ....... .015657
Cost of insurance, --.-...- .008378
From this view of the subject we see that there is an actual
expense incurred in cariying a risk in life insurance in case the
policyholder survives, since in the example above given the 720
losses which occur at the age 30 must be met by the 85,441
premiums, and in this respect life insurance adopts the same
law which runs through all other kinds of insurance. At any
age the greater the reserve the less the cost of insurance, and
conversely. In the case of a whole-life policy issued at age
30, the 'cost of insurance during the first year of issue is greater
than the reserve, and therefore a company would not be justified
in paying a surrender value of even one-half the net premium,
while in a ten-payment endowment it could return nearly the
whole.
DISTRIBUTION OF SURPLUS.
Having explained the method of finding the reserve and the
50 PRINCIPLES AND PRACTICE
cost of insurance, we are now prepared to examine the methods
of distributing the surplus.
The method of distribution now almost universal in this
country is called the " Contribution Plan,'l because it returns to
each policyholder the amount of surplus contributed by him.
There are three sources of surplus, and each of these will have
to be considered separately. There is a surplus from loading,
when this is greater than the expenses, or the expenses and
mortality, over the tabular rate. If the loading on ordinary life
policies is 40 per cent and the average expense is but 15, we
have a surplus of 25 per cent on the net premium to return to the
policyholder. The second source is from excess of interest. If
the tabular rate of interest on reserves is 4 1-2 per cent, and the
actual rate of interest on assets is 6 1-2, then here is a gain of 2
per cent on the reserves, and a further gain of 6 1-2 per cent on
that part of the loading not taken for expenses. The third source
is from diminished mortality. If the actual mortality during the
year does not equal the tabular mortality, the difference is so much
gained and goes to swell the surplus ; but if, on the other hand, it
is greater, then its deficiency must be made up from the loading.
The arithmetical explanation of this plan will be best under-
stood by taking the example of a whole-life policy for $1,000,
issued at age 30 ; gross premium, $22.70. We will assume that
the experience of the company at the end of each year shows
that the expenses are 15 per cent of the gross premiums, that the
average rate of interest realized is 6 i2 per cent, and that the
mortality is only three-quarters of the tabular rate. The three
sources of surplus will be as follows :
First Source From loading,
Gross premium, -----....
Net premium, ----..---
Loading, ----------- $7.36
Expenses $22.70 x 15= -.-.--- 3.41
Difference, ..------.. $3.95
Interest at 6.^ per cent, ------- .j-
Surplus from loading, ------._ $4.20
Second Source Interest on reserves.
Reserve at end of first year, ----.. $7.66
Difference between the actual and assumed rate of interest 2
per cent x $7.66= - - - - - - - - .15
OF LIFE INSURANCE, 51
Third Source Cost of insurance, ------ $8.39
Gain of one-fourth, -------- 2.09
Total surplus $4.20 + .15 + $2.09= ... 6.44
SECOND YEAR.
First Source Surplus from loading same as before, - - - $4.20
Second Source Interest on reserves, $15.66 x. 02= - - .31
O -Q
Third Source Gain from mortality - L = .... 2.09
Total surplus, --- ...-_- $6.60
This method of distributing the surplus can also be illus-
trated by opening a debit and credit account with the policy-
holder :*
Cr. Gross premium, -------- $22.70
Interest on net premium, 4^ per cent, ... - .68
Interest on loading, 6^ per cent, ------ .25
Surplus interest on reserves, 2 per cent, - - - - .15
Gain from mortality, -------- 2.09
$25.87
Dr. Reserve, ---------- $7.66
Expenses, ---------- 3.41
Cost of insurance, table rate, ------ 8.36
Dividend to balance, -------. 6.44
$25.87
This explanation shows that the policyholder is credited with
all the contributions he makes and is charged with only the nec-
essary expenses, mortality and reserves. What remains after
these deductions belongs to him.
By adding the net premium and interest together, $15.34+
.68=$ 16.02, we have the reserve and cost of insurance = $7. 66 +
$8.36=$i6.o2, which explains the presence of the .68 interest
in the above credit account.
The principal objection to the contribution plan is that under
certain circumstances it shows a deficiency in the assets. If
a deficiency actually exists, it would be difficult to show a
surplus. To illustrate how the plan operates in case of a defi-
ciency, take the example of a whole-life policy of $1,000, age
* For this illustration I am indebted to my friend, Mr. Henry W. Smith,
Actuary of the Hope Mutual Life Insurance Company, of New York.
5 3
30, annual premium $16.55, no gains from favorable mortality,
and the account will stand :
Cr. Gross premium, -.-...- $16.55
Surplus interest of 2 per cent on actual reserve of
$6.52, .13
Interest on net premium ------ .68
Total, $17.36
Dr. Reserve required by law, ----- $7.66
Cost of insurance, ------- 8.36
Expenses, 15 per cent, ------ 2.48
Total, $18.50
Balance against the company, - - - - 1.14
Here is a difference of $1.14, which equals the difference be-
tween the actual and the required reserve, $7.66 $6. 52=$!. 14.
There are other methods of distributing surplus, such as the
percentage plan, by a percentage on the gross premiums, or
a percentage on the reserves, or on the amount insured ; and
they are so simple as to require no particular explanation. But
none of these can be adapted to different kinds of policies and to
premiums with different percentages of loading, and make an
equitable adjustment of surplus, like the contribution plan.
Surplus may be applied in several different ways to benefit the
policyholder, but they may all be reduced to two : the reduction
of premium, and the increase of insurance. It may be deducted
from the next premium, the policyholder paying the difference,
or it may be applied to the permanent reduction of the premium
in the following manner : Divide the surplus by the present value
of an annuity of $i at the present age of the policyholder. If a
man aged 50 has a surplus of $100 on a continued-payment life
policy, divide $100 by 13.2358, the present value of $i at age
50, and the result is $7-5553, the annual reduction. To find
what would be the temporary reduction for ten years, we have the
present value of a temporary annuity of $i for ten years, which is
N *~P* + = A5o.io =7.7393 and $ioo-*-7.7393=$i2. 9 2i. To
find how much this surplus will give a permanent increase to the
policy, taking the net premium as a basis, we have the ratio, if
.43037 will purchase $i insurance, $100 will purchase $100-5-
.43037 =$23 2. 538 ; that is, we divide the surplus by the single
OF LIFE INSURANCE.
53
premium of $i for the given age. The temporary increase of
the policy for ten years is found by dividing the surplus by the
single premium of $i for ten years, or
TONTINES AND TONTINE DIVIDENDS.
Tontines are a kind of life annuity which were first brought
into public notice in Europe by Lorenzo Tonti, a Neapolitan, in
the year 1648. The members of a tontine were divided into
classes according to their ages, and each individual subscribed
a certain sum which was invested so as to produce an annual
revenue to be divided among the survivors. Each succeeding
year the numbers of the living became less and the revenue was
concentrated upon a smaller number of survivors until the last
one passed away, when the capital subscribed reverted to the
crown.
The first association of this kind in France was founded in
1653, under the administration of Cardinal Mazarin, and called
the "Royal Tontine." The total sum subscribed was 1,025,000
francs, and the members were divided into ten classes paying
102,500 francs each. Each individual subscription was 300
francs and the subscriber received the interest on this sum which
was annually increased by the dividend arising from the sub-
scriptions of other members who had died during the year.
In France in 1726, a widow, the last surviving member of a
tontine died at the advanced age of ninety-six. She had been
the wife of a poor surgeon who had invested her little capital of
300 francs in a tontine, and at her death she enjoyed a revenue
of 795000 francs.
The Tontine Association of New York was established in
1794 by several prominent merchants of that city, who were desi-
rous of having an exchange where they could meet and trans-
act business. They formed a Tontine Association and issued
203 shares of stock valued at $200 each, and with this fund,
amounting to $40,600, they purchased a piece of property on the
corner of Wall and Water streets and erected a building known
as the Tontine Coffee House. The members of the association
agreed that each could nominate some one person during whose
life the interest in the funds would be paid, and in most cases
the nominees were their own or a friend's children. By a recent
54
PRINCIPLES AND PRACTICE
arrangement, it was agreed by the 'surviving members that
when their number should be reduced to seven the property
would be divided among them and the old Tontine Associa-
tion be brought to ,a close. The members having been
reduced by death to the required number in 1870, the preliminary
steps were taken to have the property, amounting to $300,000,
divided among the survivors.
Life insurance and tontines are opposed to each other in the
advantages which they offer. In the former the gain, if we may
use the expression, is on the part of him who dies early, and the
earlier the policyholder dies the greater is the amount of insur-
-ance obtained on a given kind of policy. In the tontine the
advantage is altogether on the side of him who survives the
longest.
To illustrate the nature of tontines, we will suppose that
69,804 persons at the age of fifty, contribute one dollar each at
the beginning of each year to form a tontine fund, and this to be
equally divided among the survivors, at age 60. If the money
is placed at compound interest, 7 per cent, and the mortal-
ity is the same as the American Experience Table, the follow-
ing will be the result :
Living at the beginning of ist year - - 69,804x1.9672=137.318.10
4 4< 2d " - 68,842x1.8385=126,566.01
4 " 3d " 67,841x1.7282=116.564.42
' " 4th " - 66,797x1.6058=107,262.65
4 " 5th " 65,706x1.5007=98,605.00
4 " 6th " - 64.563 x 1.4026= 90,556.06
4 " 7th " 63,364x1.3108=83,057.54
4 " 8th " - 62.104x1.2250=76,077.40
4 44 gth " 60,779x1.1449=69,585.89
4 " loth " 59>3S5 x 1-07 =63,541.96
Total amount to be distributed ------ $969: 135.03
Survivors at the end of the tenth year, ... 57>9i7
Share of each surviving member, ----- $16.73
Amount of $i per annum at 7 per cent compound interest for
ten years --------- $14.78
Gain from the tontine system ----- $1-95
The application of the tontine principle to the distribution of
surplus or bonus in life insurance companies has long been the
subject of practical and scientific investigation in England, and in
a modified form it has been adopted by several companies in this
OF LIFE INSURANCE.
55
country. All the different methods of applying dividends, in
which the main idea is to defer them for a number of years, and
then tojsay them to those policyholders only who have persisted
in keeping their policies in force usually for ten or more years,
while all the premiums and surplus of those who have allowed
their policies to lapse, or who have died, is concentrated upon
those policies which remain in force, involve the principle of the
tontine system. Considering the large number of policies which
lapse after one or two premiums are paid, and the prospect
there is of realizing a much larger dividend than by the ordinary
method, it is not strange that this feature should have some
attractions, for those who can afford to assume the risk that they
will live to enjoy its benefits.
EXPECTATION OF LIFE.
" The Expectation of Life expresses the true average duration
in years of a certain number of individuals at a certain age."
Neison.
The calculation of a life expectancy is very simple. In the
American Experience Table of mortality, at age 95, there are
3 living at the beginning of the year, and all die during the
year ; and, therefore, assuming that the deaths of each year are
equally distributed throughout that year, we have the average
expectation of these 3 persons to be half a year each, or .50, and
the number of years which the aggregate of these three lives will
amount to will be 1.50. At the age 94 there are 21 living at the
beginning of the year, and 18 dying during the year. The 18
who die during the year live in the aggregate 9 years, and there
are 3 who live during the whole of this year and half of the next,
making the total number of years lived by these 21 to be
9 + 3 + 1.50=13.50, and this divided by 21 =.64, the expectation.
For the age 93 we have 79 living and 58 deaths during the year.
Hence, ( f + 21 + 13.50) -7 9 =63.5o-79=.So, or| + ( ~3 ) =.8o.
T> i /2i6 + 79 + 4i+3\ 319
ror age 01 we have +(- -}=.^o+^=i,ig.
2 \ 462 / J 462
To find the expectation of life for any age we have the follow-
ing rule :
Divide the sum of tH<* tabular numbers of the living at all the
PRINCIPLES AND PRACTICE
TABLE No. IX.
EXPECTATION OF LIFE BY DIFFERENT TABLES.
4
-k 5
l
Carlisle.
t*5
>M
$
4_
Combined
Experience.
American
Experience.
\
5
!
Carlisle.
fO
5
!
Combined
Experience.
American
Experience.
i
32-74
44.67
46.65
53
6-54
18.97
17.67
18-16
18.79
2
7*7 *7O
An r r
48 ST.
CA
ft ofi
18.28
1 7.06
TH ro
1 8 OQ
o/-/y
7O CC
4/-OO
Af\ 8?
iJ.U.0^
AT\ 61
i4
rr
J.W.VAJ
c c8
T7 eg
lf\ A r
1 7".S U
1 6. 86
T *7 /1O
oy-oi
/to c8
T-y- 01
CO Tfi
mj.\ji
A.Q 8 1
03
c6
5-5
5 TO
1 /-;> o
16-89
lu -4o
1C. 86
16.22
i /-4<J
16.72
T-w.^o
40.84.
i lj -/ u
r T 'j ^
Ty."- 11
Ac\ *7T
o u
C*7
.1U
A \1
16.2 1
Ij'W
T C 96
T C CO
T f\ OC
6
AT O*7
O 1 "'4
c, i . 1 6
T-y-/ 1
AO 7O
57
c8
14.03
4T r
T C CC
l^.^VJ
14.68
1 5-59
HO7
iu - u O
T C 7O
rj
T 1>u /
AT O7
CO *7O
T^y-oy
J.8 Q2
5
CO
' X 5
T-J AC
^D'OD
T/l O2
14. 10
y/
T A 7*7
1 5-o9
TA nA_
I
8
T 1>U O
^o *7n
o u- /y
CO 7^
^<j.y-
4.8 7.7
60
Ij.UO
1 *> T
1 T-y- i
HI A
T *2 C7
1 4.J/
T 7 ^7^7
1 4-/4
T A on
9
4 u -79
40-36
o'^4
49-57
T--O/
47-74
61
13.21
12.74
o4
13.82
1 6-56
12.96
1 3-77
13.18
14.09
13-47
10
39-78
48.82
47-05
48.36
48.72
62
12.28
I3-3I
12.41
12. 6l
12.86
II
39- H
48.04
46.31
47-68
48.08
63
II.81
12. 8-1
11-87
12.05
12.26
12
38.49
47.27
45-54
47-01
47-44
64
"35
12.30
H-34
11.51
11.68
13
37.83
46.50
44.76
46.33
46.82
65
10.88
11.79
10.82
10.97
II.IO
H
37-17
45-74
43-97
45-64
46.16
66
10.42
11.27
10.32
10.46
10.54
15
36.51
44.99
43.18
44.96
45-50
67
9-95
10.75
9-83
9.96
10.00
16
35-85
44.27
42.40
44.27
44-85
68
9-50
10.23
9-36
9-47
9.48
7
35-20
43-57
41.64
43.58
44.19
69
9-05
9.70
8.90
9.00
8.98
18
34-58
42.87
40.90
42.88
43-53
70
8.60
9.15
8-45
8-54
8.48
19
33-99
42-16
40.17
42.19
42.87
7i
8.17
8.6c.
8.03
8.10
8.00
20
33-43
41.46
39-48
41.49
42.20
72
7-74
8-16
7.62
7.67
7-54
21
32.90
40-75
38.80
40.79
41-53
73
7-32
7.72
7.22
7.26
7.10
22
32-39
40-03
38-13
40.09
40-85
74
6.92
7-33
6.85
6.86
6.68
23
31-87
39-31
37-46
39-39
40.17
75
6-54
7.00
6-49
6.48
6.28
24
3I-36
38-58
36-79
38.68
39-49
76
6.18
6-69
6.15
6.11
5-88
25
30-85
37-86
36.12
37-98
38-81
77
5.83
6-40
5-82
5-76
5-48
26
30-33
37- J 3
35-44
37-27
38.11
78
5-48
6.11
5-5i
5-42
5.10
27
29.82
36-40
34-77
36-56
37-43
79
5-u
5.80
5.21
5-09
4-74
28
29.30
35-68
34.10
35-86
36-73
80
4-75
5-5i
4-93
4.78
4-38
2 9
28.79
34-99
33-43
35-15
36-03
81
4.41
5-20
4.66
4.48
4.04
30
28.27
34-34
32-76
34-43
35-33
82
4-09
4-93
4.41
4.18
3-7i
V
27-75
33-68
32-09
33-72
34.62
83
3-8o
4-65
4.17
3-90
3-39
32
27.24
33.02
31.42
33-oi
33-92
84
3.58
4-39
3-95
3-63
3.08
33
26.72
32-36
30-74
32-30
33-21
85
3-37
4-13
3-73
3-36
2-77
34
26.20
3i-68
30.07
3I-58
32-50
86
3-i8
3-9
3-53
3.10
2-47
35
25.68
31-00
29.40
30-87
3I-78
87
3-oi
3-7i
3-34
2.84
2.19
36
25.16
30-32
28-73
30-15
31-07
88
2.86
3-40
3.16
2-59
i-93
37
24.64
29.63
28.06
29.44
30-35
89
2.66
3-47
3-00
2-35
1.69
38
24.12
28.95
27-39
28.72
29-62
90
2.41
3.28
2.84
2. II
1.42
39
23-60
28-27
26.72
28-00
28-90
9i
2.08
3.26
2.69
1.89
1.19
40
23.07
27.61
26.06
27.28
28-18
92
i-75
3-37
2-55
I6 7
.98
4i
22.56
26.97
25-39
26.56
27-45
93
i-37
3-48
2.41
1.47
.80
42
22.04
26.34
24-73
25-84
26-72
94
1.05
3-53
2.29
1.28
.64
43
21-54
2 5-7i
24.07
25.12
25-99
95
75
3-53
2.17
1. 12
50
44
21.03
25.09
23.41
24.40
25-27
96
5
3-46
2.06
99
....
45
20.52
24-45
22.76
23.69
24-54
....
3.28
i-95
.89
....
46
20.02
23.81
22.11
22.97
23-80
98
....
3-7
1-85
75
....
47
19-51
23.17
21.46
22.27
23-08
99
....
2-77
1.76
50
....
48
19.00
22. SO
20.82
21.56
22.36
100
....
2.28
1.68
....
....
49
CO
18.49
T *7 r\r\
2I.8I
*) T T T
20.17
T f\ C A
20.87
90 T&
21-63
2O*QI
IOI
1 02
....
1.79
....
....
....
5
si
17.99
17-50
i tj r\'j
^ i. 1 1
20.39
1r\ fiS
I 9-54
18.90
T C --,0
(J. 1 O
19.50
T<3 8l
20.20
T C\ Af\
103
VC\A
87
"*
i f *\j&
1U.UO
1O. ^O
1 O* O<
19.49
W
OF
INSURANCE.
57
ages greater than the given age by the given age, and increase
the quotient by one-half.
The expectation of life is never used in any exact calculations
in life insurance, but it is often referred to for the sake of making
off-hand estimates on the probable duration of a lifetime. Its
want of adaptation to the computation of premiums is easily
illustrated by the following table :
TABLE No. X.
A.
B.
c.
D.
E.
4f<.
Expectation
of Life.
Net Annual Pre-
mium, $1.000.
Amount o/"$i.oo,
per Annum during
Expectation, 45
per cent.
Net Annual Pre-
mium, multiplied bv
Annuity = C x D.
IO
49
9-973
I77-5030
1770.19
15
46
10.843
152.6726
I655-50
20
42
11.065
124.2764
1487.08
25
39
13-423
106.0303
1423.29
30
35
I5-336
85.1640
1306.07
35
32
17.877
71.7562
1282.75
40
28
21.301
56.4230
1201.84
45
25
25.986
46.5706
I2IO.2O
50
21
32.490
35-3034
1146.99
55
17
4I-527
25-855I
1073.68
60
14
54-I4I
19.7841
1071.13
65
II
71.898
14.4640
1039-93
Column A gives the age of the insured, B the expectation in
even years, C the net premium for $1,000 on the whole life rate,
D the amount of $i per annum at 4 1-2 per cent, and E the net
premium multiplied into the amount of $1.00 per annum, or
C x D. If the sum insured were equal to the net premium mul-
tiplied by the amount of $i per annum during expectation, as
many people suppose, then the amounts in the last column
would be $1,000 each, whereas they vary from it by considerable
differences.
EQUATION OF LIFE.
This is a term used by Mr. T. G. P. Neison to represent the
number of years for which there is an equal probability of living,
and which he regards as the best mode to determine the com-
parative value of life within this period, as the expression is
affected by the mortality within these years only. The expecta-
tion of life, which is often confounded with a chance of living an
equivalent number of years, merely expresses the true average
duration in years of a class of individuals at a certain age : it
PRINCIPLES AND PRACTICE
involves a consideration of the decrements of life at every superior
age, and, consequently, at even younger ages, it is affected by
the irregularities of mortality at the older ages.
The equation of life is illustrated by the following example:
At age 20, according to the American Experience Table of
mortality, there are 92,637 persons living, and the equation of
life represents the period when one half, or 46,318, will be sur-
viving. At age 66 there are 47,361 alive, and the difference
between these two numbers, 47,36146,318=1043; hence the
equation will fall between the ages 66 and 67. The number
dying between these ages is 2,070 ; hence we have the proportion,
^,070 : 1,043 : : I : .50 ; that is, the equation of life will be reached
TABLE No. XI.
EQUATION OF LIFE.
Age.
Amer-
ican Ex-
perience.
Com-
bined Ex-
perience.
^
Amer-
ican Ex-
perience.
Com-
bined Ex-
perience.
Affe.
Amer-
ican Ex-
perience.
Com-
bined Ex-
perience.
10
54-65
53-34
40
29.79
28.47
70
7-86
7-75
II
53-85
52-52
41
28.96
27.64
71
7-38
7.29
12
53-05
51.69
42
28.12
26.83
72
6.91
6.86
13
52-23
50-87
43
27.28
26.O2
73
6.48
6-44
H
51.42
50.06
44
26.46
25.21
74
6.0^
6.04
15
50.6l
49-23
45
25.62
24.40
75
5-65
5-66
16
49-79
48-38
46
24.79
23-59
76
5-26
5-30
*7
48.98
47-55
47
23-97
22.80
77
4-87
4-96
18
48.15
46.72
48
23-I4
22. OI
78
4-5i
4.64
19
47-33
45-89
49
22-33
21.23
79
4.16
4-33
20
46.50
45.06
50
21.52
20.46
80
3-83
4-03
21
45-68
44.22
5i
20.72
I 9 .70
81
3-52
3-77
22
44-85
43-39
52
I 9 . 9 2
18.95
82
3-21
3-5 1
23
44-03
42-50
53
19.14
18.21
83
2.92
3.26
24
43-19
41.72
54
18-35
17.48
84
2.64
3-ot
25
42.36
40.89
55
I7-58
16.76
85
2.36
2 -79
26
41-53
40.06
56
16.82
16.04
86
2.07
2-57
27
40.69
39-22
57
16.08
15-35
87
1.81
2-35
28
39-86
38.39
58
15-34
14.67
88
J -59
2.12
2 9
39-02
37-56
59
14.62
14.00
89
1.38
I.gi
3
38.18
36.73
60
*3-9 l
13-34
90
1.16
1.72
3i
37-34
35-90
61
13.22
12.70
9 1
94
i-54
32
36-51
35-07
62
12.55
12.08
92
79
i-35
33
35-67
34-24
63
11.69
11.47
93
.69
I-IS
34-
34-83
33-41
64
11.25
10.88
94
.58
97
35
33-99
32.58
65
10.63
10.31
95
50
So
36
33-15
31.76
66
10.03
9-76
96
77
37
32-31
30.93
67
9.46
9-23
97
....
72
38
3i-47
30.11
68
8.90
8.71
98
....
67
1 39
30.63
29.29
69
8-37
8.22
99
50
at 66.50 years of age ; and, subtracting the age of the person from
this quantity, we have 66.5020=46.50, the equation of life.
OF LIFE INSURANCE. 59
The expectation of life at age 20 is 42.20 years, and would
be reached at age 62.20, when there are 54,400 living, or
8,082 more than half the tabular number at the age 20.
The equation of life may be found by the following rule :
Take half the tabular number living at the given age, divide the
difference between this quotient and the tabular number of the
living at the next preceding age where the number of living is
greater than this quotient, by the number of dying in that age
where the equation occurs, the result is the fractional part of the
year required. The integral part of the equation may. be found
by subtracting the given age from the age in which the equation
is found, as in the preceding example.
JOINT-LIFE POLICIES.
Joint-life policies, as issued in this country, are made payable
to the survivor on the death of one of two lives, both parties
being insured under the same policy. In this class of policies
the probability that either one of two persons will survive a
given period of time is less than the probability that each
separate life will continue the same length of time. It is
evident, with very little demonstration, that if A aged 60 and B
aged 70 were insured on the same joint-life policy the proba-
bility that one of the two will die within a year is greater
than the probability that either of the two taken separately
will die during that time. If the probability that A will
live for one year be and B's probability of living is then
the probability that both of them will survive this period is
x = and the probability of one of the two dying during
10 10 100 *
year is i = -. In making this calculation we assume that
J IOO 100
A has only of a certainty of living one year and B only
Q
, therefore the chance of both living would be in A's case not
of a year but of B's = , and in B's case the chance
10 10 10 100
would be of = -?-. As the supposed mortality on A's single
life is only and on B's the risk on their joint lives would
J IOO IOO *
60 PRINCIPLES AND PRACTICE
be much greater than upon either life taken separately, and since
the premiums on policies increase with the probability of dying,
though not exactly in the same ratio, it is easy to see from this
illustration that the premiums on joint life policies should be
considerably larger than those on policies for single lives.
It is not intended in this place to enter upon a full explana-
tion of the intricate calculations involved in the computation of
joint life premium rates, but we propose to give only such tables
as will be of value to the public. As a general rule, joint-life
policies are not regarded with much favor by American compa
nies. Many of the most prominent companies have refused to
issue them or have abandoned them after a few years' trial, while
other companies have large numbers upon their books.
Required the probability that two lives aged 25 and 35 will
both live one year. The probability of the life age 25 =
89032 = '99 1 93 6 - The probability of the life aged 35 = |jg? =
.991054. Multiplying, .991936 x 991054 = .983062. The prob-
ability that one of the two will die within a year is i .983062
= .016938.
THE RETURN-PREMIUM PLAN.
By this plan a company contracts to return to the policy-
holder the whole amount of the sum insured at death or expira-
tion of the policy when the full number of premiums have been
paid, and also to return the whole amount of premiums without
interest.
We assume that the legitimate object of life insurance is to
obtain the greatest amount of insurance at the least cost, that is,
to throw as great a burden as possible upon the company with a
due regard to the length of the time in which the payments will
be made and exercising a reasonable caution against making the
payments too heavy in the unproductive period of old age.
In order to enable the company to afford to return the whole
amount of premiums paid when the claim is due, it is necessary
to charge a larger annual premium during the continuance of
the policy. The company cannot afford to return all the pre-
miums without being repaid for this obligation by a greater
reserve, a greater accumulation of interest, and a less amount at
risk for the same money than in the ordinary nnethods of insu-
OF LIFE INSURANCE.
6l
ranee. It is plain that he who chooses this form of policy seeks
a future good by paying a greater premium and obtaining less
insurance.
As an illustration of the workings of the return-premium
plan we take the columns as given in the following table :
TABLE No. XII.
RETURN PREMIUMS, AMERICAN EXPERIENCE, 4^ PER CENT.
A.
B.
c.
D.
E.
A re*
Net Annual Pre-
mium to insure
$ i .000 for whole
Amount of Insur-
ance for the first
Amount of Insurance
on the ordinary
whole life plan pur-
chased by a net an-
No. of
Premiums
Age.
lift;, premiums
returned at
death, -without
year on the Re-
turn-Pretn turn
Plan.
nual premium equal
to that charged in
the Return-Premium
to be paid
before C=D
interest.
plan at the same age.
IO
$I3-584
$1013.584
$1362.078
27
15
I5-247
1015.247
1406.161
27
2O
17.472
1017.472
1460.137
27
25
20.496
1020.496
1526.931
26
30
24.687
1024.687
1609.742
25
35
30.630
1030.630
I7I3-375
24
40
39.284
1039.284
I844-233
22
45
52.261
1052.261
2OII.I2I
2O
5
72-3*3
1072.313
2225.700
17
55
103.986
1103.986
2504.058
15
60
I55-365
"55-365
2869.637
13
65
241-331
1241.331
3356.575
IO
70
389-633
I389-633
4017.001
8
Column A gives the age of the policyholder ; B, the net annual
premium on the return-premium plan ; C, the amount of insur-
ance the first year on this plan ; D, the amount of insurance which
could be purchased by the premiums in column B if the party
were insured on the whole-life plan ; and E, the number of pre-
miums necessary to be paid in order that column C may equal
D. At age 30 the net annual return premium is $24.687
which secures for the first year $1024.687 insurance, but
insured on the whole-life plan with the same amount of premium
the policyholder would get $1609.742 insurance and the policy-
holder insured by the first method has to make 25 payments be-
fore his policy increases to $1609.742, the amount to be obtained
on the whole-life plan. At age 55 the policyholder in the
return-premium plan pays an annual premium $103.986 and
obtains the first year $1103.986 insurance but on the whole-life
plan he could have $2504.058 or $1400.072 more insurance the
62
first year and not till he has made 15 payments or till he has
reached the age of 69 will his policy be larger than if he had
adopted the whole life plan.
FORFEITURE OF POLICIES AND PAID-UP INSUR-
ANCE.
A policy of life insurance is a contract whereby the company,
for a certain consideration, agrees to indemnify the policyholder,
his heirs or assigns, in case of his death or at a certain period if
living, according to the terms expressed therein. One part of
the contract is that the premiums shall be regulai'ly paid during
the time specified. The company cannot violate this contract,
until the policy becomes payable, except by refusing to receive
the premiums and keep the policy in force upon the books. But
it is comparatively easy and a frequent practice for the policy-
holder to violate his part of the contract and to refuse or neglect
to pay the premiums due. In the meantime, the company holds
an unearned deposit or reserve, to accumulate and meet the
future claim. The neglect to pay the premium constitutes the
first violation of the contract, and the policyholder cannot legally
claim any favors from the company after this. But there may be
a moral injustice done to the policyholder in refusing to make
any compromise with him. Since he has paid money for insur-
ance which he has not got, it is but just that he should have all
the company can afford to restore.
With a limited payment life or endowment policy, the rule
usually adopted is to issue a paid-up policy for such a fractional
part of the sum insured as the number of payments made bears
to the whole number promised. But in the case of a continued
premium life policy, the case is different. In this form of insur-
ance, there is the least for the policyholder to sacrifice, and there-
fore the temptation to allow the policy to lapse is often very
strong. Although the policyholder, by violating the conditions,
has forfeited all claim upon the company unless otherwise
agreed upon, yet public opinion naturally frowns upon a company
which absorbs the unearned premiums for the benefit of other
policyholders. Beyond protecting itself from loss, the company
should derive no undue advantage from the inability of a policy-
hoMer to pay the annual premium. It is this which has made
OF LIFE INSURANCE. 63
the non-forfeiture law of Massachusetts and the non-forfeiture
regulations of some companies of other states, a means of remov-
ing, to some extent, one of the harsh features of life insurance.
In life insurance more than in almost any other business, the
public need the 'most perfect confidence, not only that the legal
obligations of the companies will be fulfilled, but that they or
their legal representatives will be equitably dealt by, and this
has become one of the first conditions to the prosperity of the
business.
The forfeiture of policies for the non-payment of premiums
was quite common ten years ago, when the whole-life plan of
insurance was the one usually adopted, and the sacrifices which
policyholders were sometimes compelled to make, in losing not
only the whole of the reserves, but reversionary paid-up insurance,
was a hardship which loudly demanded a reform. In the year
1859, the subject was first brought before the legislature of Mas-
sachusetts by Hon. Elizur Wright, the insurance commissioner,
which resulted, in 1861, in the passage of the non-forfeiture law
of that state.
In England also, previous to this time, non-forfeiture policies
had been strenuously advocated by Dr. Farr. It is highly
probable that this eminent actuary was the first to propose and
advocate the payment of a definite cash surrender value to a
policy. Many years ago he demonstrated what was the portion
of yearly premium which was necessary to secure the company
against loss and what might be withdrawn by the policyholder
in -anticipation of his future claim. The plans of Dr. Farr were
adopted by the British Imperial Life Association, where any
policyholder has a right to withdraw from the company a definite
proportion of the premiums he has paid. The Massachusetts
non-forfeiture law, above alluded to, compels the company, in
case the policyholder neglects to pay the premiums, to continue
the policy in force as a paid-up policy of temporary insurance so
long as four-fifths of the cash reserve computed according to the
Actuaries' Table of mortality and 4 per cent interest would sus-
tain it.
This law was intended to apply exclusively to whole life poli-
cies. At the time when the law was proposed in 1859, there were
very few endowment or limited-term life policies in force in the
6 4
PRINCIPLES AND PRACTICE
companies doing business in Massachusetts the policies issued
up to that time having been almost entirely confined to the whole-
life plan. The clause in the law which allows the companies to
deduct from the amount insured, when the policy became a claim,
the unpaid premiums and interest thereon at 6 per cent interest,
weakens its force to a great extent when applied to short term
endowments and life policies with a limited number of pay-
ments.
This peculiarity of the law is easily shown by taking the
example of a fifteen-payment endowment for $1,000, issued at
age 40, payable at death or 55, annual premium $69.49. Sup-
pose that after five annual payments have been made, the
payment of premiums is discontinued, and then, according to the
operation of this law, a term policy for twenty-two years is
allowed. At the end of the fifteen years from the date of the
policy, or ten years after the payment of premiums ceased, the
policyholder, in the event of death, would leave to his heirs
only the amount of $1,000 less the unpaid premiums and interest,
or $1,000 $970.89 = $29.11, and the greater (he loading on the
premiums the less the insurance which is obtained. That is, the
amount insured constantly decreases, and decreases faster under
mutual than under non-participating rates. In another part of
this work we give some tables for the calculation of insurance
due on lapsed policies, according to this law.
SURRENDER VALUES.
No subject in life insurance is more thoroughly discussed at
the present day than the proper rule for determining the surrender
value of a policy. The common method of computing the sur-
render value is to deduct from the reserve 25 to 50 per cent, as a
surrender charge, and pay the remainder as an equitable sur-
render value. But this method is held to be wrong in principle,
for the longer a policyholder remains in a company, and conse-
quently the less benefit he can confer upon it by the payment of
his annual premium, the greater will be his surrender charge.
In other words, the longer he stays in the company the more it
will cost him to get out.
Every policyholder when he comes into a company is expected
OF LIFE INSURANCE. 65
to confer a benefit upon it by his annual contributions ; and, if he
leaves the company by allowing his policy to lapse, he inflicts
an injury upon it equal to the present value of the future profit
which the company would receive from the transaction. What
is the measure of this injury, or what basis shall we adopt for
ascertaining it? Mr. Wright says that the present value of the
future cost of insurance, which he calls " insurance value," should
be the basis, and that the surrender charge should be a percent-
age on this insurance value. Prof. Bartlett, Actuary of the
Mutual Life, of New York, takes similar ground, when he
says that "the company's interest in any particular policy is the
present value of the sums the policy would, if continued in the
company in its present condition, contribute from year to year
to pay death claims on other policies." Upon this basis some
very ingenious formulae for computing surrender values have
been made. This theory of "insurance value" may be correct
so far as the policyholder is concerned, but it fails to do justice
to the companies. The " cost of insurance," as regards the
companies, is, in addition to the policyholder's contribution to
losses, as given in the cost-of-insurance tables, all his propor-
tion of office expenses, salaries, license fees, etc., everything re-
quired to sustain the company as an efficient working organiza-
tion. When the company receives an application for a policy of
insurance, it receives also a virtual pledge that the applicant will
make his annual contributions to the support of the company as
a corporation, besides what is necessary to pay death claims and
endowments. This view of the subject seems the more reason-
able, because under this new rule the company is supposed to
cut off all profits from lapsed policies as a source of income, and
make only such a surrender charge as will prevent the company
from incurring any loss. Now these two things are perfectly
clear, the policyholder has agreed to make certain contributions
towards the future losses of the company and the running ex-
penses, and by paying a percentage on the insurance value he
has recompensed the company for only one of them. A surrender
charge, made by taking a percentage of the present value of the
unexpired gross premiums from the reserve, has been proposed
as a method of finding an equitable surrender value for all kinds
of policies. Some of the advantages of this method are that it
gives a better practical adjustment of the surrender charges on
66 PRINCIPLES AND PRACTICE
whole-life and short-term endowment policies, than by taking a
percentage on the insurance value, and that the surrender charge
each subsequent year is less than the one preceding.
AVERAGE DURATION OF POLICIES.
This is a subject which has always been ignored in life insur-
ance calculations, since all policies are issued upon the assump-
tion that the future premiums are to be promptly paid, while in
practice the average duration of policies is much less than the
tabular duration. In every company a large number of policies
Ip.pse after a few payments, but as most companies give either a
surrender value on being released from the contract, or a paid-up
policy for a fractional part of the sum insured, this result makes
but little change in the ratio of liabilities and assets. But cases
sometimes arise when agents wish to know the present value of
their future commissions, and then the future duration of the
policies must be estimated. Unfortunately no statistics on this
subject derived from the experience of American companies
have been published.
The combined statistics returned by fifteen life offices in
England show that the average lifetime of a policy in these
companies, up to the year 1843, was less than five and-a-half
years ; in the Gotha Life, of Germany, it was a little over eight
years; and in the Equitable Life, of London, twelve and-a-half
years. In the seventeen life offices the average duration of life,
after insuring, of the policyholders who died was 6.413 years.
In the Massachusetts Report for 1861, we find that on 2,180
policies which had been forfeited in companies doing business
in that state, 7-646 premiums had been paid, making the average
duration of each lapsed policy 3.51 years.
68
PRINCIPLES AND PRACTICE
TABLE XIII.
AMERICAN EXPERIENCE MORTALITY TABLE.
Age.
Number survi-
ving at each age.
Deaths in each
year.
Age.
Number survi-
ving at each age.
Deaths in each
year.
10
100,000
749
55
64,563
> r 99
II
99.251
746
56
63,364
,260
12
9 8 '55
743
57
62,104
.325
13
97,762
740
58
60,779
,394
H
97,022
737
59
59'385
,468
15
96,285
735
60
57,9*7
,546
16
95-550
732
61
56,37i
1,628
i7
94,818
729
62
54,743
L7I3
18
94-089
727
63
53-030
i, 800
*9
93^62
725
64
5 I , 2 3
1,889
20
92>637
723
65
49,341
1,980
21
91,914
722
66
47,36i
2,070
22
91,192
721
67
45,291
2,158
23
90,471
720
68
43,133
2,243
24
89.751
719
69
40,890
2,321
2 5
89,032
718
70
38,569
2.39 1
26
88.314
718
7 1
36,178
2,448
27
87.596
718
72
33,730
2,487
28
86,878
718
73
3L243
2,505
29
86,160
719
74
28,738
2,501
30
85.441
720
75
26,237
2,476
3i
84,721
721
76
23,761
2,43i
3 2
84.000
7 2 3
77
21,330
2,369
33
83.277
726
78
18,961
2.261
34
82,551
729
79
16,670
2,196
35
81.822
732
So
H,474
2.091
36
81,090
737
Si
12,383
1,964
37
8o.353
742
82
10,419
1,816
38
79.611
749
83
8,603
1,648
39
78.862
756
84
6,955
1,470
40
78,106
765
85
5,485
1,292
4i
77.341
774
86
4,193
1,114
42
76,567
785
87
3,079
933
43
75-782
797
88
2,146
744
44
74-985
812
89
1,402
555
45
74,173
828
90
847
385
46
73-345
848
9 1
462
246
47
72.497
870
92
216
137
48
71,627
896
93
79
58
49
70-731
927
94
21
18
50
69.804
962
95
3
3
ri
68,842
I,OOI
06
O 1
C2
67.841
I O<1A
yu
O7
3*
C7
\j / '^"r*
66.7Q7
*' ( -"TT
I OOI
y/
oS
JO
C A
wv>. fyi
6c 706
i,^_/y i
T 147
y
no
64
J, /*-"-'
i .*4j
99
OF LIFE INSURANCE,
69
TABLE No. XIV.
COMBINED EXPERIENCE MORTALITY TABLE.
Age.
Number survi-
ving at fetch age.
Deaths in each
year.
Age.
Number survi-
ving at each age.
Deaths in each
year.
10
100,000
676
55
63,469
L375
ii
99,324
674
56
62,094
L436
12
98,650
672
57
60,658
L497
'3
97,978
671
58
59> l6 i
1,561
M
97.307
6 7 I
59
57,600
1,627
15
96,636
6 7 I
60
55.973
1,698
16
95.965
672
61
54,275
1,770
IT
95.293
673
62
52,505
1,844
IS
94,620
675
63
50,661
i,9i7
19
93.945
677
64
48,744
1,990
20
93.268
680
65
46,754
2,061
21
92,588
683
66
44.693
2,128
22
9 I '95
686
67
42,565
2,191
23
91,219
690
68
40,374
2,246
24
90,529
694
69
38,128
2,291
^5
89.835
698
70
35,837
2,327
26
89-I37
703
7i
33,5!0
2,35i
27
88-434
708
72
3i,i59
2,362
28
87,726
7'4
73
28,797
2,358
29
87,012
720
74
26,439
2,339
30
86.292
727
75
24,100
2,303
3i
85,565
734
76
21,797
2,249
32
84,831
742
77
*9.548
2,179
33
84,089
750
78
17-369
2,092
34
83-339
758
79
15,277
1,987
35
82,581
767
80
13,290
1,866
36
81,814
776
81
11,424
i,73o
37"
81,038
785
82
9,694
1,582
38
80,253
795
83
8,112
1,427
39
79.458
805
84
6,685
1,268
40
78,653
815
85
5,417
1,111
4i
77.838
826
86
4,306
_ _o
95"
42
77,012
839
87
3,348
811
43
76,i73
857
88
2,537
673
44
75.3i6
881
89
1,864
545
45
74.435
909
90
i,3i9
427
46
73.526
944
9i
892
322
47
72,582
981
92
57
231
4 8
71,601
1,021
93
339
155
49
70,580
.063
94
184
95
50
69.517
,108
95
89
5 2
5i
68,409
,156
96
37
24
52
67.253
,207
97
13
9
53
66,046
,261
98
4
3
54
64,785
>3 l6
99
i
i
PRINCIPLES AND PRACTICE
TABLE No. XV.
COMMUTATION COLUMNS, AMERICAN EXPERIENCE, 4^ PER CENT.
4
Dx.
NX.
Cx.
MX.
JR*.
IO
64,392-77
1,214,144.09
461.5329
12,109.051
322.708.03
II
61,158.34
1,149,751.32
439.8893
11,647-519
310,59898
12
58,084.84
1,088,592.98
419.2538
11,207.6:9
298,951 46
13
55,164.32
1,030.508.14
399-5799
10,788.375
287.743.83
52,389.25
975.343-82
380.8230
10,388.796
276-955-46
15
49,752-44
922,954.57
363-4350
10,007.973
266,566.66
16
* 873,202. 15
346-3651
9,644.538
256,558.69
17
. . O/" GSR^C*
4^pO53PrV
825,955.60
330-0915
9,298.173
246.914.15
18 ,
4jap-53
781,089.96
315.0104
8,968.081
237,615.98
19
V4&.453-9 3
738,486.43
300.6161
8,653.071
228,647.90
20
38,411.27
698,032.51
286.8773
8,352-455
219.994.83
21
36,470.32
659,621.24
274.1440
8,065.577
211,642.37
22
34,625.68
623,150.92
261.9754
7,79i-433
203,576.79
23
32,872.65
588,525-23
250-3465
7,529-458
195,785-36
2 4
31,206.73
555,652.58
239-2333
7,279.111
188,255.90
25
29,623.67
524,445-85
228.6130
7,039.878
180.976.79
26
28,119.40
494,822.18
218.7684
6,811.265
173-936-91
27
26,689.75
466,702.78
209.3478
6,592-497
167,125.65
28
25,331.08
440.013.04
200.3328
6,383- H9
160,533.15
29
24.039-93
414,681.96
191.9730
6,182.816
154,150.00 j
30
22,812.75
390.642.02
183.9617
5,990.843
147,967.19
31
21,646.42
367,829.28
176.2844
5,806.881
141.976.34
3 2
20,537-99
346,182.86
169.1612
5,630.597
136.169.46
33
19,484.42
325,644.86
162.5484
5.461.436
130,538.87
34
18,482.83
306,160.44
156.1915
5,298.887
125-077-43
35
17.530.73
287,677.61
150.0806
5,142.696
119.778.54
36
16,625.73
270,146.89
144.5988
4,992.615
114.635.85
37
15,765.20
253,521.15
139.3108
4,848.016
109.643.23
38
14,947.00
237.755.96
134-5695
4,708.706
104.795.22
39
14,168.78
222,808.96
129.9781
4,574-i36
100,0^6.51
40
13,428.66
208,640.18
125.8617
4,444.158
95-5 I2 -375
12,724-53
195,211.51
121.8588
4,318.296
91.068.217
42
12,054.73
182,486.08
118.2685
4,196.438
86.749-920
43
11,417.36
170.432.25
114.9057
4,078.169
82.553-483
44
10,810.79
159,014.90
112.0271
3,963.263
7S,475-3 I 4
45
10,233.23
148.204.10
109-3153
3,851.236
74.512.050
46
9,683.250
137.970.87
107.1347
3,741.921
70.660.814
47
9, '59- '33
128,287.62
105.1810
3,634-786
66.918.893
48
8,659.540
119,128.49
103-6597
3,529.605
63,284.107
49
8,182.981
110,468.95
102.6278
3,425.946
59-754-502
50
7,727.976
102,285.96
101.9164
3-323-318
56.328.556
7,293.276
94-557-9S9
101.4815
3, 221.401
53.005.239
52
6,877.730
87.264.712
101.2831
3.119.920
49-7S3-\17
53
6,480.277
80,386.982
101.2850
3,018.637
46.663.918
54
6,099.937
73,906.705
101.5431
2,917.352
43,645.281
OF LIFE INSURANCE.
TABLE No. XV (CONTINUED.)
COMMUTATION COLUMNS, AMERICAN EXPERIENCE, 4^ PER CENT.
4
D x .
N x .
c*.
M x .
Rx.
55
5.735-7 1 ?
67,806.768
101.9312
2,815.809
40,727.929
56'
5,386.794
62,071.052
102.5043
2,7i3-877
37,912.121
57
^052.322
56,684.258
103.1504
2,611.373 '
35,198.243
58
4.731-607
Si, 63 1. 936
103.8488
2,508.223
32,586.8/0
59
4,424.005
46,900.329
104.6523
2,404-374
30.078.647
60
4.128.846
42,476.324
105.4668
2,299.722 .
27,674.274
61
3,845-582
38,347-478
106.2782
2,i94-255-. . '
^5-374-552
62
3 073-704
34,501.897
107.0117
2,087.977
23 ,'1=80.297
63 3.312.801
30,928.193
107.6044
1,980.965
3-1,092. 320
64 3,062.540
27,615.392
108.0620
1,873-361
19,111.356
65 2,822.598
24>55 2 -85i
108.3902
1,765.299
17,237-995
66 2,592.661
21,730-253
108.4373
1,656.908
15.472.697
.67 2.372.578
19, 137-592
108.1792
1,548.471
13,815-788
68
2, -62. 230
16,765.014
107-5983
1,440.292
12.267.317
69
1,961.522
14,602.784
106.5454
1.332.694
10,827.025
70
1,770-509
12,641.263
105.0323
1,226.148
9,494-3319
7i
1,589.234
10,870.754
102.9055
1, 121.116
8,268.1839
72
i4 I 7-893
9.281.520
100.0430
1,018.210
7,147.0681
73
1.256.792
7.863.627
96.42778
918.1673
6,128.8578
74
1,106.244
6,606.834
92.12806
821.7395
5,210.6905
75
966.4790
5.500.590
87-27957
729.6114
4.388.9510
76
837.5807
4,534-m
82.00317
642.3319
3,659-3395
77
7 i 9- 5095
3,696.530
76.47059
560.3287
3,017.0077
78
612.0552
2,977.021
70.76821
483.8581
2.456.6789
79
514.9306
2,364.966
64.91260
413.0899
1,972.8208
80
427.8438
1,850.035
59.14724
348.1773
i'559-739
Si
350-2727
1,422.191
53-16253
289.0301
1,211.5536
82
282.0267
1,071.9185
47.03961
235-S675
9 22 -52352
33
222.8424
789.89177
40.84970
188.8279
6S6.6s =598
8 4
172.3966
567.04938
34.86844
147.9782
497.82805
85
130.1044
394.65274
29-3-659
1 13.-! 098
349.84982
86
95-I7523
264-54837
24.19736
83-783I9
236.74004
S7
66.87942
l6 9-373H
19-39314
59-5S5S3
152.95684
8S
44.60631
102.49372
14.79868
40.19269
93-37IOH
89
27.88676
57.88742
10.56396
25-3940I
53.178320
90
16.12194
30.00064
7.012586
14.83005
27.784310
9 1
8.415*04
13-87871
4.287819
7.8174590
12.954265
92
3- 7649 1 5
5.463611
2.285102
3.5296396
5. 1 368; .62
93
1.317687
1.698697
.9257566
'2445372
1.6071665
94
0.335 iss
0.381009
.2749318
.3187806
.36262938
95
0.045822
0.045822
.0438488
.0438488
.04384878
PRINCIPLES AND PRACTICE
TABLE NO. XVI.
COMMUTATION COLUMNS, COMBINED EXPERIENCE, 4 PER CENT-
Age.
D x .
N x . '
c x .
M.
10
67*556.41
1,381,771.74
439.1167
14.411.3725
II
64,519.00
1,314,215.33
420.9784
x 3,972-2557
12
61,616.50
1.249,696.33
403-5858
I 3>55 I - 2 772
J 3
58,843.07
1,188,079.83
387.4858
13,147.6913
H
56,192.36
1,129,236.76
372-5825
12,760.2055
IS
53,658-54
1,073.044.40
358.2524
12,387.6229
16
51,236.51
1,019,385.86
344.9868
12,029.3704
*7
48.920.90
968,149.35
332.2118
11,684.3835
18
46.707.10
919,228.45
320.3837
11.352.1716
19
44.59 -3o
872,521.35
308.9740
11,031.7878
20
42,566.31
827,931.05
298.4068
10,722.8137
21
40,630.73
785.364-74
288.1955
10,424.4069
22
38.779-81
744,734-01
278.3283
10,136.2113
23
37.009.94
705,954.20
269.1839
9,857.8830
24
35.3i7-3i
668.944.26
260.3311
9,588.6992
2 5
33-698.63
633,626.95
251.7611
9,328.3681
26
32,15076
599,928.32
243.8120
9,076.6069
27
30,670.39
567-777-56
236.1021
8 832.7948
28
29,254.65
537,107.17
228.9451
8.596.6926
2 9
27,900.53
507,852.52
221.9894
8,367-7475
30
26,605.44
479.951-99
215.5266
8,145.7580
31
25.366.64
453.346-55
209.2325
7,930.2313
32
24,181.76
427,979.91
203.3779
7,720.9987
33
23,048.32
403,798.15
197.6641
7,517.6207
34
21,964.18
380,749.83
192.0889
7,3i9-9565
35
20.927.31
358,785-65
186.8939
7,127.8675
36
I9-935-52
337,858.34
181.8143
6,940.9735
37
98.986.96
317,922.82
176.8491
6,759- J 59*
3S
18,079.84
298.935.86
172.2134
6,582.3100
39
17,212.25
280,856.02
167.6727
6,410.0966
40
16,382.57
263,643-77
163.2265
6,242.4238
41
15.589-24
247,261.20
159.0669
6,079.1972
4 2
14.830.58
231,671.96
155-3561
5,920.1302
43
14,104.82
216,841.38
152-5857
5,764-7740
44
13,40974
202,73606
150.8258
5,612.1882
45
12,743.16
189.326.82
149-6357
5,461.3623
46
12,103.41
176,583.66
149.4188
5,311.7282
47
11,488.47
164,480.25
149.3031
5,162.3094
48
10,897.30
152,991.78
149.4143
5,013.0062
49
10,318.76
112,094.48
149-5775
4,863.5918
50
9,781.92
131.765-72
149.9131
4,714.0142
5i
9- 2 55-78
121,983.80
150.3918
4,564.1010
S 2
8.749.40
112,728.02
150-9873
4.413.7091
53
8,261.90
103,978.62
i5 I - 6 753
4,262.7218
54
7,792.46
95,716.72
152.2026
4,111.0465
OF LIFE INSURANCE.
TABLE No. XVI. (CONTINUED.)
COMMUTATION COLUMNS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
D x .
N*.
a.
M x .
55
7-340-55
87,924.26
152.9100
3,958.8437
56
6,905.30
80,583.71
153-5515
3,805.9337
57
6,486.17
73,678.41
I53-9H75
3,652.3821
58
6,082.78
67,192.24
I54-3249
3,498.4644
59
5>694-5
61,109.46
154-6633
3>344-i394
60
5,320.82
55,414.96
155.2044
3,189.4760
61
4,960.97
50,094.14
155-5630
3,034.2715
62
4,614.60
45^33-i7
I55-8334
2,878.7084
63
4,281.28
40,518.57
I55-77I7
2,722.8749
64
3,960.85
36,237.29
155-4841
2,567.1031
65
3.653-02
32,276.44
154.8380
2,411.6189
66
3,357-68
28.623.42
I53-7227
2,256.7808
67
3,074.82
25,265.74
152.1862
2,103.0580
68
2,804.37
22,190.92
150.0063
1,950.8717
69
2,546.50
19,386.55
147.1266
1,800.8653
70
2,301-43
16.840.05
143.6909
1,653-7385
7i
2.069.22
14,538.62
I39-5893
1,510.0474
72
1,850.05
12,469.40
134.8485
1,370.4580
73
1,644.05
10,619.35
129.4424
1,235.6094
74
i,45i-37
8,975.298
123.4610
1,106.1668
75
1,272.087
7,523.928
116.8853
982.7057
76
1,106.275
6,251.841
109.7545
865.8203
77
953-972
5,145.566
102.2484
756.0657
78
815-0323
4,i9 J -594
94.3904
653.8171
79
689.2945
3,376.5616
86.2047
559.4266
80
576.5783
2,687.2671
77.8415
473.2219
81
476.5607
2,110.6888
69-3925
395-3803
82
388.8389
1,634.1281
61.0154
325.9878
83
312.8680
1,245.2892
52.9205
264.9724
84
247.9142
932.4212
45-2153
2i2.o=;i9
85
193-1637
684.5070
38.0931
166.8365
86
147.6411
491-3433
31-5838
128.7433
87
110.3786
343.7022
25.7091
97-1594
88
80.4243
233-3236
20.5139
7I-4503
89
56.81712
152.8993
15-9734
50-9363
90
38-65848
96.08221
12.0336
34-9630
9i
25-13852
57-42373
8.7255
22.9294
92
I5-44572
32.28521
6.0188
14.2039
93
8.83283
16.83949
3-8833
8.1851
94
4.60983
8.00665$
2.2885
4.3018
95
2.14399
3-396825
1.2045
2.0133
96
.85704
1-252835
5345
.8088
97
.28954
395795
.1927
2743
98
.085663
.106255
.0618
.0816
99
.020592
.020592
.0198
.0198
1
74
PRINCIPLES AND PRACTICE
TABLE No. XVII.
COMMUTATION TABLES, AMERICAN EXPERIENCE, 6 PER CENT.
Age.
Dx.
NX.
Cx.
M X .
Rx.
10
55-839-47
853.966.39
394-5637
7,501.7416
155.968.97
ii
52,284.18
798,126.92
370.7391
7,107.1779
148,467.23
12
48.953-97
745.842.74
348-3474
6,736.4388
141,360.05
13
45:834-65
696.888.77
327.3027
6,388.0914; 134,623.61
H
42,912.92
651.054.12
307-5243
6,060.7887 128,235.52
15
40,176.36
608.141.20
289.3300
5,753-2644 122,174.73
16
37,612.90
567,964.84
271.8388
5,463-9344
116,421.46
17
35.212.03
530-35I-94
255.4006
5,192.0956
"0,957.53
18
32,963.50
495 1 39- 9 *
240.2830
4,936-6950
105,765.43
19
30,857.35
462.176.41
226.0584
4,696.4120! 100,828.74
20
28,884.66
431,319.06
212.6743
4,47o-3536 96,132.327
21
27,037.00
402.434.40
200.3587
4,257.6793) 91,661.974
22
25,306.24
375,397-40
188.7558
4,057.3206
87,404.294
23
23.685.06
350,091.16
177.8245
3,868.5648
83-346-974
2 4
22,166.57
326,406.10
167.5260
3,690.7403
79,478.409
25
20,744-33
304,239-53
157.8236
3,523.2143
75,787.669
26
19,412.30
283,495-20
148.8902
3,365-3907
72,264.454
27
18,164.60
264.082.90
140.4624
3,216.5005
68,899.064
28
16,995.72
245.918.30
132.5117
3,076.0381
65,683-563
29
15,901.41
228,922.58
125.1852
2.943-5264
62,607.525
30
14,876.14
213,021.17
118.2635
2,818.3412
59,663.999
31
i3-9'5-S4
198.145.03
111.7243
2,700.0777
56,845.658
32
13,016.42
184,229.19
105.6926
2,588.3534
54,145.580
33
12,173-95
171,212.77
100.1237
2,482.6608
51,557.226
34
11,384.72
159,038.82
94.84670
2,382.537!
49,074-566
35
10,645.47
147,654.10
89.84627
2,287.6904
46,692.029
36
9-953-050
137,008.63
85-33960
2,197.8441
44-404-338
37
9-304-330
127,055.58
8i.os t ;22
2,112.5045
42,206.494
33
8,696.614
"7.75I-25
77.18859
2,031.4493
40,093.990
39
8,127.166
109,054.63
73-49997
1,954.2607
38,062.540
40
7.593-635
10,027.47
70.16506
1,880.7607
36,108.280
4i
7,093.643
93.333-S3I
66.67222
1,810.5956
34,227.519
42
6.625.144
86,240.188
64.07927
i,743-6234
32,416.923
43
6,186.057
79,615.044
61.37623
i,679-5442
,30.673.300
44
5.774-525
73.428.987
58.99186
1,618.1679
28,993-756
45
5,388.674
67,6154.462
56-74930
i559- 1 76i
27,375.5SS
46
5.026.906
62. 26*;. 788
54.83025
1,502.4268
25,816.412
47
4,687.532
57,238.882
53.06862
i,447-5965
24,313-985
48
4,369- *33
52,551.350
51.56092
i,394-5279
22,866.388
49
4,070.263
48,182.217
50.32530
1,342.9670
21,471.861
5
3-7S9-544
44,111.954
49.26926
1,292.6417
20,128.894
5i
3,525-773
40.322.410
48.36477
i,243-3724
18,836.252
52
3,277-836
36.796.637
47-587H
1,195.0077
17,592.879
53
3,044.711
33,5.8.801
46.91461
1,147.4205
16.397.872
54
2,825.455
30,474.090
46.36856
1,100.5059
15,250-45!
OF LIFE INSURANCE.
75
TABLE No. XVII (CONTINUED.)
COMMUTATION COLUMNS, AMERICAN EXPERIENCE, 6 PER CENT.
%
^
D x .
Ak
Ck
M x .
jR*.
55
2,619.154
27,648.635
45.88711
l > 54- 1373
14,149.945
56
2, 425.013
25,029.481
45-49213
1,008.2502
13,09^.808
57
2,242.257
22,604.468
45-13107
962.75810
12,087.558
58
2.070.205
20,362.211
44.79368
917.62703
11.124.800
59
1,908.230
18,292.006
44-50145
872-83335
10,207.173
60
i>755-7 l6
16,383-776
44.21317
828.33190
9-334-3394
61
1,612.122
14,628.060
43.92288
784.11873
8,506.0075
6211,476.947
i3>oi5-933
43.60014
740.19585
7,721.8887
63
I.349-746
11,538.991
43.22123
696-59571
6,981.6929
64
1,230.124
10,189.245
42.79084
653-3744S
6,285.0972
65
1,117.703
8,959.121
42.31342
610.58364
5,631.7227
66
1,012.124
7.841.418
41.73278
568.27022
5,021.1391
67
913.1013
6,829.2936
41.04427
526.53744
4,452.8688
68
820.3721
5,916.1923
40.24618
485-493I7
3.926.3314
69
733-6S97
5,095.8202
39.28841
445.24699
3,440.8382
70
652.8716
4,362.1305
38.18240
405-95858
2,995-59"
7i
577-7344
3,709.2589
36.87985
367.77618
2,589-6327
72
508.1524
3.I3I-5245
35-34659
330.89633
2,221.8565
73
444.0425
2,623.3721
33-58719
295-54974
1,890.9601
74
385-3208
2,179.3296
31-63543
261.96255
1,595.4104
75
33I-8748
1,794.0088
29.54641
230.32712
.!, 333-4479
76
283-5430
1,462.1340
27-36739
200.78071
1,103.1207
77
240.1261
1,178.5910
25-15983
173-4I332
902.3400
78
201.3741
938.4649
22.95417
148.25349
728.92670
79
167.0214
737.0908
20.75693
125.29932
580.67321
So
136.8105
570.0694
18.64571
104.54239
455-37389
Si
110.4208
433-2589
16.52192
85.89668
350.83150
82
87.64860
322.83809
14.41216
69-37476
264.93482
3
68.27522
235- 18949
12.33856
54.96260
195.56016
84
152.07201
166.91427
10.38290
42.62404
HO- 59756
85
38-74165
114.84226
8.609106
32.241142
97-9735 2 3
S6
27.93962
76.10061
7.002851
23-632036
65-73 2 3Si
87
i9-355 2 8
48.16099
5-533062
16.629185
42.100345
88
12.72664
28.80571
4.162468
11.096123
25.471160
89
7.843789
16.079072
2.929308
6-933655
I4-375037
90
4.470494
8.235283
1.917022
4.004347
7.441382
9 1
2.300426
3.764789
1.155568
2.087325
3-437035
92
1.014645
i-4 6 4363
.6071208
9317566
1.3497102
93
.3500915
.4497184
.2424804
3246358
4179536
94
.0877947
.0996269
.0709930
.0821554
0933 ' 78
95
.0118322
.0118322
.0111624
.0111624
.0111624
7 6
PRINCIPLES AND PRACTICE
TABLE No. XVIII.
NET PREMIUMS PER $1,000, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Single
lift.
Whole
life.
Ten
payment
life.
Endow-
ment 10
years.
Endow-
ment 15
years.
Endow- Endo-i'-
ment 20 ment 25
years, years.
Endow-
ment 30
years.
Endow-
ment 35
years.
20
21
22
23
24
25
26
27
28
2 9
30
31
32
33
34
3 I
36
37
38
39
40
4i
42
43
44
4 ?
46
47
48
49 *
50
5'i
52
53
54
55
56
57
58
I 9
60
61
62
?
64
65
66
67
68
69
70
217-45
221. l6
225.02
229.05
233.26
237-64
242.23
247.01
25I-99
257-I9
262.61
268.26
274.16
280.30
286.69
293-35
300.29
307-5I
3I5-03
322.83
330-95
339-37
348.12
357-19.
366.60
376.35
386.43
396-85
407.60
418.67
430-04
441.70
453-63
465.82
478.26
490.93
503.80
516.87
530-10
543-48
556.99
570-59
584.26
597-97
61 1.70
625.42
639.08
652-65
666.11
679.42
692.54
11-97
12.23
12.50
12.79
13.10
13.42
13-77
I4-I3
I4-5I
14.91
15-34
15-79
16.27
16.77
I7-3I
17.88
18.48
19.12
19.81
20-53
21.30
22.12
23.00
23-93
24.92
25-99
27.12
28.33
29.63
31.01
32-49
34-07
35-75
37-55
39-47
41-53
43-72
46.07
48-58
51-27
54-14
57-22
60.52
64.05
67.84
71.90
76.25
80.91
85.91
91.26
97.00
27.17
27.64
28.13
28.64
29.18
29-73
30.32
30.92
3 J -56
32.22
32.92
33-64
34-40
35-19
36.01
36.87
37-77
38-71
39-69
40.72
41.79
42.90
44.07
45-29
46.57
47.90
49-30
50.76
52.29
53-89
55-57
57-3i
59- "3
61.03
63.02
65.10
67.27
69-55
71.94
74-45
77.08
79-86
82.79
85.89
89.17
92.66
96.35
100.28
104.46
108.90
"3-63
81.90
8l. 93
81.96
81.99
82.04
82.06
82.10
82.14
82.19
82.24
82.29
82-35
82.41
82.48
82.55
82.64
82-73
82.83
82.94
83.07
83.21
83-36
83-54
83-74
83-97
84.23
84.52
84.86
85.24
85.67
86.17
86.69
87.30
87.97
88.73
89.55
90.48
9 r -5i
92.65
93-92
95-33
96.90
98.64
100.58
102.52
104.49
50-55
50.58
50.62
50.66
50.70
50-75
50.80
50.85
50.91
50.97
51.04
51.12
51.20
51.29
51-39
5I-5I
5I-63
51-77
5I-92
52.10
52.30
52.52
52.77
53-05
53-37
53-73
54- H
54.60
55-13
55-71
56.36
57-09
57-9
58.80
59.80
60.92
62.15
63-53
64.05
66.74
67.61
70.69
72-95
75-47
78.23
81.24
35-43
35-47
35-52
35-57
35-62
35-68
35-74
35-Si
35-89
2r22
36.06
36.16
36.27
36.39
36.52
36.68
36.85
37-04
37-25
37-49
37-76
38.06
38.40
38.79
39.22
39-70
40.25
40.86
4 l -52
42.30
43-15
44.09
45-H
46.30
4758
49.00
50.57
52.29
54.t9
-6 ->8
26.80
26.86
26.91
26.98
27.05
27.12
27.20
27.28
27.38
27.48
27.61
27.74
27.89
28.05
28.24
28.44
28.67
28.93
29.21
29-53
29.90
30-29
30.74
31-24
31.81
32.43
33-13
33-90
34-77
35-74
36.79
37.96
39-25
40.66
42.22
43-91
21.42
21.49
21.56
21.64
21.72
21.82
21.93
22.04
22.l6
22.31
2247
22.64
22.84
23.06
23-30
2 3-57
23-87
24.21
24.58
25.00
25.46
25-97
26.54
27.18
27.88
28.65
29-5I
30.46
3 J -5
32.64
33-89
17.89
1/-97
18.07
18.17
18.28
18.41
18.55
18.70
18.87
19.05
19.26
19.49
19.74
20.03
20.34
20.68
21.07
21.49
21.96
22.48,
23-05 ;
23-68
24-37
25.10
25.96
26.87
....
58.57
1
OF LIFE INSURANCE.
, I
TABLE No. XIX.
NET ANNUAL PREMIUMS PER $1,000, COMBINED EXPERIENCE, 4
PER CENT.
Affe.
Single
life.
Whole
life.
Ten
payment,
life.
Endow-
ment, IO
years.
Endow-
ment, 15
years.
Endow-
ment, 20
years.
Endow-
ment, 25
years.
Endow-
ment, 30
y.ars.
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
3
36
37
38
39
40
42
43
44
45
46
251.91
256.56
261.37
266.36
271.50
276.82
282.31
287.99
293.86
299.91
306.17
312.63
319.29
326.17
333-27
340.60
348-17
355-99
364.07
381.04
389.96
399.18
408.71
418.52
428-57
478.86
12.95
13.27
13.61
13.96
H-33
14.72
15-13
15-56
16.01
16.48
16-97
17.49
18.04
18.62
19.23
19.87
20.54
21.26
22.02
22.82
23-68
24-59
25-55
26.58
27.68
28.85
3O 08
30.81
31.40
32.00
32-63
33-27
33-94
34-64
35-35
36.09
36.86
37-66
38.48
39-33
40.21
41.12
42.06
43-04
44-05
46.20
47-33
48.53
49-77
51.08
52-44
53-86
CC 37
83-87
83.91
83-97
84.02
84.08
84.15
84.22
84.29
84-37
84-45
84-54
84.63
84.71
84.82
84-93
85-03
85-I5
85.28
85.42
8^76
85.97
86.22
86.51
86.84
87.02
87 61
52.27
52.33
52.40
52-47
52-54
52.62
52.70
52-79
52.88
52.98
53-oS
53-20
53-43
53-57
53-72
53-88
54-07
54-27
54-51
54-77
55-07
55-40
55-79
56-23
56.70
C7 22
36.97
37-05
37-12
37-21
37-29
37-38
37-48
37-59
37-7
37-82
37-95
38.09
38-25
38.41
38.59
38.80
39-02
39.28
39-55
39-87
40.22
40.60
41.05
41-53
42.08
42.68
47 74
28.19
28.28
28-37
28-47
28-57
28.68
2S.SI
28.94
29.08
29.24
29.40
29-59
29.79
30.04
30.26
30.52
30-Sl
3I-H
31.90
32-35
32.84
33-38
34-00
34-67
35-42
7fi 27
22.68
22.79
22.90
23.01
23-I5
23.29
23-44
23.61
23-79
24.00
24.21
24.44
24.70
24.98
25.29
26.OI
26.42
26.87
27-37
27.92
28-53
29.20
29.94
30.76
47
44Q.7C
71 7Q
c6 85
88 06
C7 80
77 12
48
460.02
32.77
cS 43
88 c5
cS 43
44. Rtr
78 OS
4O
470.88
34 ">7
80 O7
45-71
5O
481.01
95.78
6l.74
89.66
50.86
46.65
40. 27
CI
4Q3. II
37 41
67 4O
oo 20
60 68
47-68
52
CO4.46
7Q.IC
6c 70
OO O7
61 c.7
48.81
53
4I.OO
67.17
QI.73
62 cc
50.03
C27. C7
42 OC
69 12
02 cc
51-37
cc
C7Q.7I
4C.O2
71 14
O7 4C
64 80
152.84
56
47.23
73.25
Q4 43
66 09
563. io
4O C7
*7C 44
OC CI
67 CT
58
C7C. 14.
C2.O7
77 7 c
06 74
587.26
C.4.72
So 15
Q7 QQ
7O 77
6O
5QQ.43
C.7.C.6
82 68
QQ.47
72.64
61
6 1 1 .63
60. C.7
S^-34
IOI.O7
62
623.83
6*. 78
88.13
IO2 Si
63
635.00
67.2O
QI O7
IO4.73
64
6.48.12
7O.84
Q4. I 6
106.83
65
660.17
74-72
97 4 }
log 12
66
672.13
78.84
loo 88
67
683.06
83.24
IO4 C7
68
6Q $ . 65
87.01
1 08 59
69
7O7.IQ
02. 8q
I 12 48
70
718.57
98.20
II6.S5
78 PRINCIPLES AND PRACTICE
TABLE No. XX.
NET ANNUAL PREMIUMS PER $1,000 FOR TERM INSURANCE POLICIES.
Age.
AMERICAN EXPERIENCE, 4^ PER CENT.
COMBINED EXPERIENCE, 4 PER CENT.
Three
years.
Five
years.
Seven
years.
Ten
years.
Three
years.
Five
years.
Seven
years.
Ten
years.
20
7-50
7-55
7.61
7-68
7.09
7.18
7.27
7.41
21
7-57
7.61
7.66
7-74
7.18
7-27
7-36
7-51
22
7.62
7.67
7.72
7.80
7-27
7-37
7-47
7-63
2 3
7.67
7.72
7.78
7.87
7-37
7-47
7-58
7-75
24
7.72
7.78
7.84
7-94
7-47
7-58
7.69
7.87
2 5
7.78
7.84
7.91
8.01
7-58
7.70
7-82
8.01
26
7.84
7.91
7-98
8.10
7.70
7.82
7-95
8.15
27
7.91
7.98
8.06
8.19
7-82
7-95
8.09
8.30
28
7-99
8.06
8.15
8.28
7.96
8.09
8.24
8.46
29
8.07
8.15
8.24
8-39
8.10
8.24
8-39
8.62
30
8.15
8.24
8-34
8.50
8.25
8.40
8.^6
S.So
31
8.24
8-33
8. 44
8.63
8.41
8-57
8-73
8.98
32
8-34
8.45
8-57
8.77
8-57
8.74
8.91
9.17
33
8-45
8-57
8.69
8.91
8-75
8.92
9.10
9-38
34
8-57
8.70
8.84
9.08
8-93
9.11
9-3o
9-59
35
8.70
8.84
9.00
9.26
9.12
9-3i
9-50
9-83
36
8.84
9.00
9.17
9-47
9-3i
9-5i
9.72
10. 10
37
9.00
9.18
9-36
Q. 70
9-52
9-73 9-96
10.41
38
9.18
9-37
9-58
9-94
9-74
9.96
10.23
10.75
39
9-37
9-58
9.81
10.22
9.96
1O.2I
10.53
11.15
40
9-58
9.81
10.08
10.54
10.21
10. <;i
10.89
"59
4i
9.81
10.07
J o-37
lO.gO
10-49
10.86
11.31
12.09
42
10.07
10.36
10.70
11.29
10.83
11.28
11.80
12.67
43
10.37
10.69
11.08
11.77
11.25
11.77
12.35
13-30
44
10.69
11.07
11.50
12.29
11.76
12.34
12.98
14.03
45
11.06
11.50
12.00
12.88
12-34
12.98
13.68
14.81
4 6
11.49
11.99
12-57
13-55
12-99
13.69
1 4- 45
15.69
47
11.98
12-55
'3-19
14.30
I3-7I
14-47
15-29
16.63
48
12.55
13-19
13-91
15-13
14.48
i5-3i
16.20
17-65
49
I3-I9
13-9 1
14-73
16.07
I5-32
16.23
17.20
18.76
5
13.92
14.72
15.60
17.12
16.24
17-23
18.28
19.97
5*
1 4- 73
15.62
16.62
18.28
I7-25
18.31
'9-45
21.28
52
15-63
16.63
17-73
19.56
18.34
19.50
20.72
22.71
53
16.64
17-75
18.97
20.98
19-53
20.78
22.10
24.27
54
17.77
19.00
20.34
22.56
20.81
22.16
23.60
25.96
55
19.02
20.38
21.86
24.29
22.21
23.67
25-24
27.80
56
20.40
21.91
23-54
26.20
23-7I
25-3I
27.03
29.81
57
21.94
23.60
25-39
28.31
25-35
27.10
28.99
32.00
58
23.64
25-47
27.44
3- 6 3
27-I5
2Q.08
31-13
34-39
59
25-52
27-54
29.60
33-iS
29.13
3^24
33-47
36-99
60
27.60
29.82
32.19
35-99
31-31
33-62
36.04
39.81
_. __
VALUATION TABLES.
NET VALUES.
The following tables, from page 82 to 119 give the net values
of a policy of $1,000, according to various plans of insurance
and ages, and also according to the two standards of mortality
and interest generally adopted in the United States.
The states of New York, California, Kansas, Kentucky, Mis-
souri, Michigan, and Wisconsin, have adopted the American
Experience Table and 44 per cent interest, while Massachusetts,
Connecticut, Maine, New Hampshire and Illinois, use the Com-
bined Experience 4 per cent.
The net values are given to the end of each policy year, to the
1 5th and also of the 2Oth year, where the number of annual
premiums is sufficient.
Although there has been an endless amount of discussion
about the relative merits of the two standards of valuation, very
few persons have taken the trouble to investigate for themselves
the actual difference there is between the valuations of the
same policy made upon both of them. Thus the value of a
whole life policy issued at age 20, and having been in force
5 years, has a value 29 per cent greater by the Combined Ex-
perience 4 per cent standard than by the other. In the older
ages, and when the policy has been in existence a greater num-
ber of years this difference diminishes. A life policy with the
same conditions, issued at age 35, has a reserve 15 per cent
greater by the Combined Experience 4 per cent table, and at 50
only 4 per cent greater. Also, the longer a policy is in force
the less the difference, and we see that a policy issued at age 50,
and in force 20 years, has a larger reserve by the American Ex-
perience 4^ per cent standard than by the other. Similar differ-
ences, though in a less degree, are seen in the Ten payment Life
and Endowment policies.
The difference in the valuation of endowments by the two
standards is very slight. In the Ten Year Endowments it is
almost nothing, but increases with the length of the policy term.
OF LIFE INSURANCE.
8l
TABLE NO. XX. a.
SHOWING THE DIFFERENCE BETWEEN THE VALUES OF THE SAME POL-
ICY ACCORDING TO THE AMERICAN EXPERIENCE $\ PER CENT, AND
THE COMBINED EXPERIENCE, 4 PER CENT. STANDARDS.
WHOLE LIFE.
FIFTEEN- YEAR ENDOWMENT.
Age SO.
Age 2O.
Vf
1?
Premium
American
Experience,
4/^ /"" <*
Premium
Combined
Experience,
4 per cent.
Ratio.
*&
g
Premium,
American
Experience,
tf/2 per cent.
Premium,
Combined
Experience,
4 per cent.
Ratio.
i
5
10
15
20
4-74
25.81
57-71
97.00
145.04
6.22
3330
7253
118.56
I72.6l
I-3I
1.2 9
1.26
1.22
X.ZQ
I
5
10
45-37
251.86
577-52
47-42
26o.OI
586.80
1.045
1.032
1.016
Age 35.
Age 35.
I
5
10
45-27
251.09
575-69
47-02
257-94
583.58
1.039
1.027
1.013
I
5
10
15
20
982
53-20
"7-45
193.42
279-59
11.48
61.34
I33-4I
214.30
301-35
I.I7
I-I5
1-13
I. II
1.08
Age BO.
I
5
10
45-74
250.28
568.47
47.07
254.64
572.42
1.029
1.013
1.007
Age 5O.
I
5
10
15
20
20.45
106.83
222.74
342-79
460.56
21.62
110-79
226.84
344-07
456.79
1.05
1.04
i. 02
I.OO
99
TWENTY- YEAR EI'DOWMENT.
Age 2O.
I
5
10
29-45
163.27
373-82
31-39
171.80
386.71
1. 066
1.052
1.035
TEN PAYMENT LIFE.
Age 35.
Age 2O.
I
5
10
29.64
163.81
373-59
3I-36
171.29
385.17
1.058
1.045
1.031
I
5
20.75
114.91
24.94
136.30
i. 20
I JO
Age 35.
Age 5O.
I
5
29.85
164.99
34-78
190.23
1.16
i-i5
I
5
10
3i-74
170.88
377.08
33-"
175-76
382.92
1.043
1.028
1.015
Age 5O.
I
5
449
245-54
4906
265.87
1.09
1.08
TWENTY-FIVE-YEAR ENDOWMENT.
Age 2O.
TEN- YEAR ENDOWMENT.
I
5
10
2 '.36
112.72
257-57
22.19
121.18
271.90
1.089
1-075
1.056
Age 2O.
I
5
7.39
4.35-59
80.51
442.17
1.027
1. 01?
Age 35.
Age 35.
I
5
10
20-95
115-33
261.32
22.67
123.21
275.11
1.082
1.068
1.052
I
5
78.10
434-32
78.8 9
439-79
I.OIO
1.013
Age 5O.
Age 5O.
I
5
10
25.00
132.64
284.94
26-36
137-64
29 T -35
1.054
1.038
I.O22
I
5
77-31
42938
78.56
432.60
1.016
i. 008 :
S2
PRINCIPLES AND PRACTICE
TABLE No. XXI.
NET VALUE PER $1,000 OF AN ORDINARY LIFE POLICY, AT THE END OF
VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
4-74
9.68
14.83
20.20
25.81
31.66
37-77
44.14
21
4.96
10.14
15-54
21.17
27.06
33-19
39-59
46.17
22
5.20
10.63
16.29
22.2O
28.37
34-80
4I-5I
48.51
23
5-46
11.15
17.09
23.29
29.76
36.50
43-53
50.86
2 4
5-72
11.70
17-93
24-43
31.22
38-29
45-66
53-34
25
6.01
12.28
18.82
25.64
32-75
40.16
47.89
55-95
26
6.31
12.83
19-75
26.90
34-36
42.13
50.24
58.68
27
6.62
13-53
20.72
28.2 3
36.06
44.21
52-71
61-SS
28
6-95
14.20
2i-75
29.63
37-85
46.39
55-30
64-58
29
7-30
14.91
22.84
31.11
39-72
48.69
58-03
67-75
30
7.66
15-66
23-99
32.66
41.69
51.11
60.90
71.09
31
8.06
16.45
25.19
34-29
43-78
53-64
63.91
74-58
32
8.46
17.27
26.45
36.01
45-96
56-3I
67.06
78.24
33
8.89
18.14
27.79
37.82
48.26
59.10
70-37
82.08
34
9-34
19.07
29.19
39-72
50.67
62.04
73-85
86.11
35
9.82
20.04
30.67
41.72
53-20
6^.12
77-50
90-34
36
10.32
21.06
32.21
43.81
55-84
68.34
81.31
94-77
37
10.85
22.12
33-84
46.00
58-63
71-74
85-33
99.40
38
11.40
23.24
35-54
48.31
61.56
75-30
89.52
104.25
39
11.98
24.42
37-34
50-74
64.64
79-03
93-92
109.30
40
12.59
25.66
39-23
53-29
67.86
82.93
98.50
"4-57
4i
13.24
26.98
41.23
55-97
71.24
87.01
103.28
120.04
42
13.92
28.36
43-3i
58.78
74.76
91.25
108.23
125.67
43
14.64
29.80
45-49
61.70
78.42
95-64
"3-33
131.46
44
I5-38
31-3I
47-75
64.72
82.20
100.15
118.56
137-39
45
16.17
32.87
50.11
67.86
86.09
104.78
123.92
143-47
46
16.98
34-50
52-54
71.07
90.07
109.51
129.39
149.66
47
17.82
36.18
55-03
74-35
94.14
"4-35
134-98
155-98
48
18.69
37-88
57-56
77.70
98.28
119.28
140.66
162.40
49
19.56
39.61
60.14
8i.ii
102.51
124.30
146.45
168.92
50
20.45
4i-39
62.78
84.61
106.83
129.42
152-34
I75-56
5i
21-37
43.21
65-49
88.18
111.24
134.64
158-35
182.32
52
22.32
45.08
68.27
91.83
"5-75
139-97
164.46
189.18
53
23.29
47.00
71.11
95-56
120.34
145-39
170.67
196.14
54
24.28
48.96
74-00
99-36
125.01
150.90
176.97
203.17
55
25-30
50.96
76.95
103.24
129.77
156.49
183-34
210.28
56
26.33
53-oo
79-97
107.19
134.60
162.15
189.79
217-45
57
27-39
55-09
83-05
in. 20
I39-50
167.88
196.29
224.68
58
28.48
57-22
86.17
115.26
144.44
173.66
202.84
231.92
59
29.58
59-38
89.32
119.36
H9-43
179-47
209.40
239-14
60
30.70
61.56
92.51
123-50
154.46
185.29
215.94
246-33
OF LIFE INSURANCE.
TABLE No. XXI (CONTINUED.)
NET VALUE PER $1,000 OF AN ORDINARY LIFE POLICY, AT THE END OF
VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thirfnth
year.
Fourt'nlh
year.
Fifteenth
year.
Twentieth
year.
20
50.78
57-71
64-93
72.46
80.31
88.49'
97-00
145.04
21
53- -3
60.48
68.05
75-94
84-I5
92.70
IOI.OZ
151.78
22
5 5. So
63.40
71-33
79-58
88.18
97-13
106.45
158.84
23
5$- 5 1
66.47
74-77
83.41
92.41
101.78
111.52
166.21
24
6i-35
69.69
7S-3S
87-43
96-85
106.65
116.83
J73-9 1
25
64-34
73.08
82.18
91.65
101.51
111-74
122.39
181.94
26
67.47
76.63
86. 1 6
96.07
106.37
117.08
128.19
190.30
27
70.77
80.36
9-34
100.70
111.48
122.66
134.28
199.00
28
74-23
S4-27
94.71
105.56
116.82
128.51
140.64
208.03
2 9
77.86
88-37
99.29
110.63
122.41
134-63
147-30
217-39
30
81.67
92.67
104.10
115-96
128.26
141.03
154.24
227.05
31
85.67
97 .l8
109.13
121-53
I34.40
147.71
161.49
237.02
32
89.84
101.90
114.40
127-37
140.79
154.69
169.04
247.26
33
94- 2 3
106.84
119.92
I33-46
147-47
161.94
176.88
257-78
34
98-83
112.03
125.69
139-83
I54.43
169.50
185.02
268.56
35
103.66
"7-45
131.72
146.46
161.67
177-34
193.43
279-59
36
108.69
123.11
137-99
153-36
169.18
185.43
202.09
290.85
37
113.96
129.01
ifl-53
160.51
176.93
193.77
211. OO
302.32
38
"9-45
I35-I5
i5i-3i
167.91
184.92
202.34
22O.I4
3I3-99
39
125.18
141.52
158-31
175-53
193- *s
211. IO
229.53
325-85
40
131.11
148.11
165-53
183-36
201.59
220.18
239.11
337-86
4i
I37-25
154.89
I72-95
191.41
210.24
229.41
248.91
350.00
42
H3-55
161.86
180.56
1 99.64
219.07
238.83
258.87
362.25
43
150.02
168.99
188.34
208.05
228.08
248.40
268.99
374.58
44
156.64
176.28
196.28
216.61
237-23
258-13
279.26
386.96
45
163.41
183-72
204.37
225.32
246.54
268.00
289-65
399-37
46
170.30
191.29
212.58
234-I5
255-96
277-98
300.14
411.76
47
177-33
198.98
220.93
243.12
265-51
288.06
310.72
424.11
48
184.45
206.79
229.38
252.18
275-14
298.22
32L36
436-38
49
191.69
214.71
237-94
261.34
284.85
308.44
332.06
448.54
50
199.04
222.74
246.60
270.59
294.64
318.73
342-79
460.56
5i
206.51
230.87
255-36
279.92
304- 5 i
329.07
353-54
472.41
52
214.08
239.09
264.19
289.32
314.42
339-42
364-27
484.08
53
221.73
247.40
273.10
298.77
324-34
349-76
374-96
495.61
54
229.45
255-7 6
282.05
308.23
334-26
360.05
385-55
507.07
55
237-25
264.19
291.02
317-69
344-13
370.27
396.04
518.57
56
245.09
272.62
299.98
327.11
353-92
38o.37
406.37
530-21
57
25--9S
281.06
308.92
336.45
363-61
390.22
416.55
542.08
58
260.81
289.45
3I7-77
345-69
373-15
400.12
426.61
554-26
59
268.62
297-77
326.51
354-77
382-53
409.80
436-65
566.77
60
276.36
305-98
335-n
363-7I
391.81'
419.47
446.78
579.68
8 4
PRINCIPLES AND PRACTICE
TABLE No. XXII.
NET VALUE PER $1,000 OF A TEN-PAYMENT LIFE POLICY, AT THE
OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
20
20-75
42.56
65.48
89.58
114.91
21
21. 2O
43-47
66.89
9!-5i
"7-39
22
21.66
44-43
68.36
93-53
119.98
23
22.15
45-43
69.90
95-63
122.67
24
22.66
46.48
7I-5I
97.82
125.48
25
23.19
47-57
73-18
IOO.II
128.41
26
23-74
48.69
74.92
102.48
131.46
27
2432
49.88
76.73
104.96
I34-63
28
24.92
51.10
78.62
107-54
137-94
2 9
25-54
52-38
80.59
110.23
141.38
30
26.19
53-72
82.63
113.02
144-95
31
26.87
55-10
84.76
115.92
148.67
32
27.58
56.54
86.96
118.94
I52-53
33
28.30
58.02
89.26
122.07
156-54
34
29.06
59-58
91.64
125.32
160.69
35
29.85
61.20
94.12
128.68
164.99
36
30.66
62.86
96.66
132.17
169.45
37
3 I -5 I
64.58
99-31
J35-77
174.06
38
32-38
66.36
102.03
139-49
178-83
39
33-28
68.20 *
104.86
143-35
183.76
40
34-21
70.11
107.78
H7-33
188.84
4i
35-i8
72.08
no.Si
i5i-44
194.09
42
36-17
74.12
113.91
155-66
199.46
43
37.20
76.20
117.10
!59-99
204.98
44
38-25
78-34
120.36
164.41
210.60
45
39-33
80.53
123.70
168.93
216.32
46
40-43
82.76
127.08
173-49
222.09
47
4i-55
85.02
130.49
178.09
227.92
48
42.67
87.28
I33-9I
182.72
233-78
49
43-79
89-53
137-33
187-33
239.66
50
44.90
91.98
140.76
191.96
245-54
5i
46.02
94.04
144.18
196.58
251.41
52
47-13
96.28
I47-58
201.17
257-25
53
48.24
98.50
150-95
205-73
263.04
54
49-32
100.70
I54-27
210.22
268.76
55
50-39
102.85
157-53
214.64
274-39
56
51-44
104.96
160.73
218.95
279.89
57
52.46
107.02
163-85
223.17
285.25
58
53-47
109.02
166.86
227.23
290.42
59
54-42
110.93
169.74
231.11
295-39
60
55-33
112.75
172.48
234.82
300.13
OF LIFE INSURANCE.
TABLE No. XXII (CONTINUED.)
NET VALUE PER $1,000 OF A TEN-PAYMENT LIFE POLICY, AT THE END
OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Sixth
year.
Seventh
year.
Eighth
year.
Ninth
year.
Tenth
year.
2O
141.56
169.57
199.03
230.02
262.61
21
144.61
173.22
203.32
234-97
268.26
22
H7-79
I77-03
207.79
240.13
274.16
2 3
151.11
iSl.OO
212.44
245-5I
280.30
24
I54-56
185.14
217.30
25 1 . 1 2
286.69
25
158.17
189.46
222.36
256.96
293-35
26
161.92
193-95
227.62
263.04
300.29
27
165-83
198.62
233.10
269.37
307-5I
28
169.89
203.48
238.81
275-95
3I5-03
2 9
174.12
208.55
244.74
282.80
322.83
30
178.52
213.81
250.91
289.92
330-95
31
183.09
219.28
257-3I
297-3I
339-37
3 2
187.84
224.95
263.96
304-97
- 348.12
33
192.76
230.83
270.85
312.93
357-19
34
197.87
236.93
278.00
32I.I8
366.60
35
203- T 5
243-25
285.40
329-73
376.35
36
208.63
249.80
293.08
338.57
386.43
37
214.21
256.57
301.00
347-72
396-85
38
220.15
263.57
309.19
357-15
407.60
39 .
226.20
270.79
3I7-64
366.88
418.67
40
232.44
278.22
326.33
376.88
430.04
4i
238.85
285-87
335-25
387-I4
441.70
42
245.44
293.70
344-38
397-63
453-63
43
252.17
301.70
353-70
408.34
465.82
44
259- 3
309.84
363-I8
419.25
478.26
45
265.99
318.10
372.83
430.36
490.93
46
273-03
326.48
382.60
441.63
503-80
47
280.15
334-94
39 2 -49
453-04
516.87
4 8
287.31
343-46
402.46
464-57
53- I0
49
294.49
352.02
412.50
476.21
543-48
5"
301.68
360.61
422.58
487.92
556.98
5i
308.87
369.20
432.69
499.67
570.59
52
316.03
377-77
442.78
511.46
584.26
53
323-13
386..J8 iy2.84
523-23
597-97
54
330. 16
394-71
462.82
534-95
611.70
55 337-07
403-03
472.69
546.60
625.43
56
313-84
411-19
482.43
558.14
639.08
57
3.SO-44
419.17
491.98
569-53
652.65
58
35683
426.94
501.31
580.73 666.11
59
362.99
434-4*
5>-36
191 -(ft
679.43
60
368.86
441-60
5I<).II
602.34
69254
86
PRINCIPLES AND PRACTICE
TABLE No. XXIII.
NET VALUE PER$I.OOO OF A TEN- YEAR ENDOWMENT POLICY, AT THE
END OP VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Aff*.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
20
78.39
160.91
247.78
339-26
435-59
21
78.39
160.90
247.76
339.22
435-55
22
78.37
160.87
247.72
339-17
43549
23
78.34
160.82
247.68
339- i 2
435-43
24
78.32
160.78
247.63
339.06
435-36
25
78.31
160.76
247.58
339-00
435-29
26
78.29
160.71
247-53
338.94
435-22
27
78.27
160.68
247.48
338.88
435-4
28
78.26
160.65
247.42
338.82
435-o6
29
78.23
160.61
24737
338-74
434-9S
30
78.22
160.58
247-3I
338.66
434-89
31
78.20
160.53
247.25
338.58
434-79 .
32
78.17
160.49
247.18
338-49
434-68
33
78.14
160.42
247.11
338.40
434-56
34
78-12
160.38
247.03
338.29
434-44
35
78.10
160.33
246.94
338.18
434-32
36
78.07
160.^6
246.84
338.05
434.18
37
78.03
160.18
246.73
337-9 1
434-02
38
77-99
160. 1 1
246.62
337-75
433-83
39
77-95
160.02
246.50
337-6o
433-64
40
77.91
159.96
246.38
337-44
433-44
4i
77-88
159.88
246.25
337-27
433-21
42
77-83
I59-78
246. 1 1
337-07
432-95
43
77-79
I5Q-68
245.96
336.85
432.67
44
77-75
159.60
245.81
336-64
432.45
45
77.72
I59-50
245.64
336-41
432.11
46
77-65
15937
24544
336 13
43L76
47
77-59
159.20
245.18
335-76
431.29
4 8
77-52
159-05
244.85
335-31
430.72
49
77-43
158.84
244.50
334-So
430. 10
50
7'7-3i
is8.$8
244.10
33424
429-38
5i
77-15
158-28
243-63
333 59
428.54
C2
77-Qi
15793
243.09
33^88
427.58
53
76.84
I57-56
242.47
33 I -9 6
426.53
54
76.63
157.12
241.81
33i-o8
425-47
55
76.42
156.66
241.10
330.15
424-35
56
76.17
*5 6 13
240.30
329.07
423.00
57
75-90
x 55-56
2.39-39
32783
42r.53
58
75.60
I54-9 2
238.36
326.42
419.79
59
75,28
154-23
237.24
324-93
417.92
60
74.92
I53-46
236.08
323-35
4I5-99
OF LIFE INSURANCE.
8 7
TABLE No. XXIII (CONTINUED.)
NET VALUE PER $ 1,000 OF A TEN-YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Sixth
year.
Seventh
year.
Eighth
year.
Ninth
year.
Tenth
year.
20
537-04
643.89
756-45
875.04
I,OOO.OO
21
536.99
643.83
756.40
875.01
IjOOO.OO
22
53693
643-77
756.35
874.98
IjOOO.OO
2 3
536.86
643-7I
75630
874-95
I,OOO.OO
2 4
536-79
64365
756.25
874.92
I,OOO.OO
25
536.72
643-59
756.20
874.88
1,000.00
26
643.52
756.14
874.84
I.OOO.OO
27
536-57
643-44
756.07
874.80
IjOOO.OO
28
536-49
756.00
874.76
I,OOO.OO
29
536.40
643.27
755-92
874.71
I.OOO.OO
30
536.29
643-I7
755-84
874.66
1,000.00
3 1
536-I8
643.06
755-75
874.60
1,000.00
32
536.06
642.94
755-65
874-54
I,OOO.OO
33
535-94
642.82
755-54
874.47
IjOOO.OO
34
535-Si
642.69
755-42
874.40
I,OOO.OO
35
535-66
642.54
755-29
874-3I
I.OOO.OO
36
535-49
642.37
755-H
874.21
I,OOO.OO
37
535-31
642.18
754-98
874.10
IjOOO.OO
38
535-"
641.97
754.80
873-99
1,000.00
39
534-90
641.76
754-62
873.87
I,OOO.OO
40
534-69
64I-55
754-42
873-74
I,OOO.OO
534-44
641.30
754.18
873-59
I,OOO.OO
42
534-1.5
641.01
753-90
873-4I
IjOOO.OO
43
533-88
640.67
753-58
873.20
1,000.00
44
533-53
640.31
753-25
872.97
1,000.00
45
533-13
639.90
752-00
872.72
1,000.00
46
53^-68
639.42
752-46
872.43
1,000.00
47
532-"
638.85
752.03
872.09
1,000.00
48
531-44
638-17
871.68
1,000.00
49
530.77
6.37-44
750.70
871.25
1,000.00
50
529.99
636.64
749.98
870.79
I,COO.OO
51
529.12
635.72
749-15
870.27
1,000.00
52
528.10
634.66
748.20
869.64
1,000.00
53
526.94
633.46
747.07
868.98
1, 000.00
54
525-71
632^8
745-94
868.19
1,000.00
55
524-33
630.83
744.81
867-39
1,000.00
56
522.79
629.27
743-44
866.50
1,000.00
57
520.96
627.46
741.82
865.45
1,000.00
58
518.95
625.38
739.96
864.24
1,000.00
59
516.91
623.29
738.o6
862.98
1,000.00
60
514.86
621.09
736-09
861.64
1,000.00
83
PRINCIPLES AND PRACTICE
TABLE No. XXIV.
NET VALUE PER $1.000 OF A FIFTEEN-YEAR ENDOWMENT POLICY,
AT THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Aft.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
45-37
93.10
143-34
196.21
251.86
310.45
372.13
437.08
21
45-36
93.08
H3-3I
196.17
251.82
310.40
372-07
437-02
22
45-35
93.06
143.28
196.13
251.76
310.34
372.00
436.94
23
45-34
93-04
143.26
196.10
25I-72
310.29
371-94
436.87
24
45-33
93-03
H3-23
196.06
251.68
310.23
37I-87
436-79
25
45-33
93-02
143.20
196.03
25I-63
310.16
371.80
436-7I
26
45-32
93.00
143.18
J 95-99
25I-58
310.11
371-73
436.62
2 7
45-3i
92.99
J 43-i5
195-95
25I-53
310.04
37I-65
436.53
28
45-30
92-97
143.12
I95-92
251.48
309.98
371-57
436.44
2 9
45-29
92-95
143.10
195.88
251.42
309.90
37I-48
436.34
30
45-29
92.94
143.08
I95-83
25I-37
309.84
37I-40
436.24
31
45-29
9 2 '93
143-05
195-79
25I-32
309-77
37I-3I
436.12
32
4 .;.28
92.91
143.02
I95-76
251.26
309.69
371.2!
436-00
33
45-27
92.89
143.00
I95-72
261.20
309.61
371.10
435-87
34
45-27
92.89
142.98
195.69
251.14
309-53
370-99
435-74
35
45-27
92.88
142.96
I95-65
251.09
309.44
370.88
435-6o
36
45-27
92.88
142.94
195.61
251.02
309-35
370-76
435-46
37
45-27
92.87
142.92
195-57
250.96
309.27
370.66
435-31
38
45-27
92.87
142.91
195-54
250.91
309.19
370-55
435-17
39
45.28
92.88
142.92
195-54
250.88
309-I3
370-45
435-02
40
45-29
92.89
142.93
195-54
250.87
309.09
370.36
434.89
4i
45-32
9 2 -93
142.97
195-57
250.88
309-05
370.28
434-74
42
45-35
92.98
143.02
195.61
250.89
309.02
370.18
434-56
43
45-39
93-04
143.09
195.66
250.91
308.98
370.06
434-35
44
45-43
93.12
143.16
I95-72
250.92
308.92
369.91
434-09
45
45-49
93-20
H3-25
I95-78
250.92
308.83
369.70
433-77
46
45-54
93.28
143-33
195.81
250.87
308.68
369-44
43338
47
45.60
93-37
143.40
195.82
250.80
308.50
369-13
432-93
48
45-66
93-43
M3-43
195-79
250.67
308.25
368.74
432-39
49
45-70
93-47
H3-43
I95-72
250.50
307-94
368.27
431-75
5
45-74
93-51
143.42
I95-63
250.28
307-58
367-73
43I-07
5'
45-78
93-54
i43-4i
195-52
250.04
307.16
367-13
430-24
52
42.81
93' 57
143-37
I95-3S
249-75
306.70
366.46
429.34
53
45.86
93-59
H3-33
195.22
249-43
306.18
365-72
428.36
54
45-89
93.61
143.28
195.04
249.08
305-6I
364.90
427.26
55
45-93
93-63
143.22
194.85
248.69
304.98
363-99
426.06
56
45-97
93-65
143.16
194.64
248.27
304-3
363.00
424.76
57
46.03
93-69
143.10
194.42
247.82
303-56
361-95
423-35
53
46.09
93-73
I43-05
194.19
247-34
302.78
360.81
421.81
59
46.16
93-78
142.98
193-93
246.82
301-93
359-55
420.12
60
46.23
93-83
142.92
I93-67
246.28
301.00
358.18
418.27
OF LIFE INSURANCE.
TABLE No. XXIV (CONTINUED.)
NET VALUE PER $I,OOOOF A FIFTEEN-YEAR ENDOWMENT POLICY, AT
THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4$- PER CENT.
4g*
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thirteenth
year.
Fourteenth
year.
Fifteenth
year.
20
505 4S
577-52
653-40
733-35
817.60
906.40
1,000
21
505-4I
577-45
653-33
733-28
81754
906-36
1,000
22
505-32
577-36
653-25
733-21
817.48
906.32
1. 000
23
505-25
577-28
653-I6
733-13
817.4.2
906.28
I.OOO
2 4
505-I7
577-19
653-07
733-05
817-35
906.24
1,000
25
505-07
577-09
652.88
732.96
817.28
906.20
1,000
26
504.98
57699
652.87
732.86
817.20
906.15
I.OOO
27
504.88
576.88
6:52.76
732-76
817.12
906.09
1,000
28
504-78
576.78
652-65
732-65
817.02
906.03
1,000
2 9
504.66
576.64
652.52
732-52
816.92
905-97
1,000
30
504-54
576.51
652.38
732-39
816.80
905.90
1,000
31
504.41
576-37
652.24
732-25
816.68
905-83
1,000
32
504.26
576.21
652.07
732.10
816.55
905-74
I.OOO
33
504.12
576.05
651.90
73* -93
816.41
905-65
1,000
34
503-96
575-88
651.72
73* -75
816.25
905-55
1,000
35
503.80
575-69
65L5 2
731-56
816.08
905.44
1,000
36
503-63
575 49
651-31
731-34
81^.89
9 5-3I
1,000
37
503-45
575-29
651.08
73-
815.68
905*17
1,000
38
503.26
575-07
650.84
73 -85
8*5-45
905.02
1,000
39
5 3-07
574-83
650.56
730-56
815.19
904.84
1,000
40
502.88
574-58
650.26
73024
814.89
904.65
1,000
4i
502.66
574-29
649.91
72987
814 16
904.43
I.OCO
42
502.40
573-94
649.51
729.46
814.18
904. 18
1,000
43
502,09
573-55
649.06
72898
813-76
903.89
I/JOO
44
501.72
573-09
648-53
728.44
813.27
9357
1,000
45
501.29
572-55
647-93
727.82
812.72
903.21
1,000
46
500.77
5/i 93
647.23
727.11
812.01}
902 So
1,000
47
500. i S
571.22
646.44
726.30
811.38
902.34
1,000
48
499.49
570.40
64S-54
72S 39
Sio.sS
901.82
1,000
49
498.70
569-47
644.52
724-37
809.68
901.23
1,000
50
497.84
568.47
643-38
723-23
808.68
900.58
1,000
5i
490-. 8 1
567-27
642.11
721-95
807.56
899.86
I.OOO
52
49v7o
565-97
640.69
720.54
806.32
899.05
I.OOO
'53
494.48
564-54
639-13
718.97
804-93
898.14
1,000
54
493-^2
562.96
637.42
7'7-23
803.40
897.14
I.OOO
55
491.63
561-23
635-5I
715 31
801.72
896.03
1,000
56
490.01
560.32
633-4'
7T3 20
79983
894.79
1,000
57
488.24
557-24
631-13
7IO.S6
797-75
893.42
1,000
<8
486.31
5 5* -06
628.58
708.28
7<J5 44
891.88
1,000
59
484.18
552-43
625-79
705.42
792.89
890. 20
1,000
60
481-83
549-64
622.68
702.24
790.05
888.34
1,000
PRINCIPLES AND PRACTICE
TABLE No. XXV.
NET VALUE PER $1,000, OF A TWENTY- YEAR ENDOWMENT POLICY, AT
THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4 PER CENT
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
29-45
60.41
92.98
127.23
163.27
2OI.2O
241.10
283.10
21
29.44
60.40
92.97
127.22
163.26
201. IS
241.07
283.06
22
29.44
60 40
92.96
127.22
163-25
201.16
241.06
283.03
23
29.44
60.40
92.97
127.22
163.25
201.16
241.04
283.01
2 4
29.44
60.41
92.97
127.22
163-25
201.15
241.02
282.99
25
29-4>
60.42
92.98
127.23
163.26
2OI.I5
241.02
282.98
26
29-45
60.42
92.99
127.24
163.26
2OI.I5
241.01
282.95
27
29.46
60.44
93.01
127.25
163.27
201.16
241.01
282.94
28
29.47
60.45
93.02
127,28
163.30
201.17
241.02
282.94
2 9
29.48
60.47
93-05
127.31
163-32
201.20
241.04
282.95
30
29.50
60.50
93-09
127-34
163-36
2OI.24
241.07
282.96
31
29.52
60.54
93-13
127-39
163.42
2OI.29
241.12
283.00
32
29-54
60.57
93.18
127.46
163.48
201.36
241.17
283.04
33
29.56
60.61
93-25
127-53
163.57
201-43
241.24
283.10
34
29-59
60.68
93-33
127.64
163.68
201-55
24I-35
283.20
35
29.64
60.76
93-44
127.76
163.81
201.68
241.49
283.33
36
39.68
60.84
93-55
127.90
163.96
201.85
241.65
283.49
37
29.74
60.94
93-69
128.06
164.15
202.06
241.87
283.69
33
29.79
61.05
93-84
128.26
164.39
202.32
242.14
283.96
39
29.87
61.19
94-05
128.52
164.69
202.64
242.47
284.27
40
29-95
61.36
94.29
128.82
165-03
203.01
242.84
284.64
4i
30.06
61.^6
94-58
129.17
165.44
203.44
243.29
285.06
42
30.18
61.80
94.90
129.58
165.89
203.93
243-77
285-50
43
30-33
62.06
95.28
130.03
166.41
204.47
244.29
285.96
44
30.48
62.36
95-69
I30.54
166.97
205.04
244.83
286.45
45
30.66
62.69
96.15
131.09
167.56
205.63
245.40
286.95
46
30-85
63.04
96.63
I3I-65
168.16
206.24
245-97
287.45
47
31.06
63-43
97.14
I32-25
168.80
206.88
246.57
287.97
48
31.29
63-83
97-67
I 3 2.86
169.46
207-54
247.18
288.50
49
Si-Si
64.23
98.21
133-49
170.15
208.23
247.83
289.04
50
31-74
64.66
9S-79
134.18
170.88
208.96
248.51
289.62
5i
32.00
65.12
99.41
I34-9 1
171.67
209.75
249.24
290.25
5 2
32.27
65-63
100.09
I35-7 1
172.52
210.61
250.05
290.94
53
32-58
66.17
100.83
I36-57
173-45
2H-55
250 93
291.69
54
32.89
66.76
101.62
'37-50
174-47
212.58
251.89
292.51
55
33-25
67.40
102.48
138-53
175-59
213.70
252.94
293-4I
56
33-62
68.09
103.42
J39- 6 5
176.79
214.91
254.08
294-39
57
34-03
68.84
104.44
140.85
178.09
216.22
255-3 1
295.46
58
34.48
69.66
105-54
142.14
179-48
217.63
256.64
296.58
59
34-95
70.52
106.70
H3-5I
180.97
219.13
258-03
297-75
60
35-45
71.44
107.94
144.98
182.57
220.71
259.48
298.96
OF LIFE INSURANCE.
TABLE No. XXV (CONTINUED.)
NET VALUE PER $1,000 OF A TWENTY- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Affe.
Ninth
year.
Tenth
year.
Eleventh
year.
T-uielfth
year.
ThirPnth
year.
Fourteenth
year.
Fifteenth
year.
20
327.29
373-82
422.80
474-37
528.68
-Or CO
505.0O
646.14
21
327.24
373-75
422.74
474-30
528.60
585-79
646.05
22
327.21
373-72
422.68
474-23
528.52
585-70
645.96
23
327.18
373-67
422.62
474.16
528.44
585-6I
645.86
24
327-I5
373-63
422.56
474.09
528.35
585.52
645-76
25
327.12
373-59
422.51
474.02
528.27
585-42
645-65
26
327.08
373-54
422.45
473-95
528.18
585-32
645-53
27
327-07
373-51
422.40
473.S7
528.0 9
585.20
645.41
28
327-05
373-48
422.35
473.80
527.99
585."
645.28
29
327-05
373-45
422.29
473-72
527.89
5S4-97
645.14
3
327-03
373-42
422.25
473-65
527.80
584-86
645.01
3 1
327.06
373-42
422.22
473-59
527-72
584.74
644.86
32
327.08
373-42
422.19
473-54
527-63
584.63
644.72
33
327.12
373-44
422.19
473-51
527-56
584.52
644.58
34
327.20
373-50
422.22
473-50
527-5I
584.42
644-43
35
327-32
373-59
422.27
473-50
527.46
584-32
644.27
36
327-47
373-71
422.34
473-53
527.42
584.20
644.09
37
327-65
373-85
422.45
473-57
527-39
584.09
643.88
38
327-88
374-05
422.58
473.62
527-34
583-94
643-65
39
328.17
374-29
422.73
473-67
527-29
583-78
643.40
40
328-50
374-54
422.89
473-72
527.21
583-59
643. 10
4i
328.86
374-Si
423.05
473-76
527-I3
583-37
642.75
42
329.23
375-o8
423.21
473-79
527-00
5S3-IO
642.35
43
329.61
375-35
423.36
473-78
526.84
582.78
641.89
44
330.01
375-64
423.49
473-75
526.63
582.40
64L35
45
330-4*
375-9 1
423.60
473-68
526.37
581.95
640.74
46
330.80
376.15
423-67
473-56
527-05
581.43
640.04
47
331-20
376.39
423.73
473-40
525-67
580.83
639^3
4 8
33!-6o
376-62
423.75
473-20
525-22
580.14
638.33
49
332.00
376.84
42376
472-95
524-71
579-36
637.32
50
332-43
377.08
433.74
472.67
524.I3
578.50
636.20
5i
332-89
377-32
423.73
472-35
523.52
577-56
634-97
52
333-40
377-59
423.7I
472.02
522.83
576.53
633.62
53
333-95
377-89
423.74
471.67
522.21
575-41
632.15
54
334-57
378.24
423.72
471.29
521.40
574'lS
630.52
55
335-25
378.63
423-74
470.88
520.42
572.82
628.72
56
335-99
379-03
423-74
470.41
519.42
571.30
626.70
57
336.78
379-46
423.72
469.85
518.29
569.57
624.43
58
337-6o
379-87
423.62
469.17
516.97
567.60
621.88
59
338.43
380.24
423-43
468-34
5I5.43
565.39
619.09
60
339-26
380.57
423-I3
467-34
5I3-7I
563.00
616.13
9 a PRINCIPLES AND PRACTICE
TABLE No. XXVI.
NET VALUE PER $1,000. OF A TWENTY-FIVE YEAR ENDOWMENT POLICY,
AT THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
20.36
4*-75
64.24
87-87
112.72
138-85
166.33
195.22
21
20.37
41-77
64.26
87-QO
112.76
138.89
166.37
195.27
22
20.37
41.78
64.29
87.94
112. 8l
138.95
166.43
I95-32
23
20.39
41.81
6 4-33
87.99
112.86
139.01
166.49
195-39
24
20.41
41.85
64.38
88.05
112.94
139.09
166.58
195.48
25
20.43
41.89
64-43
88.13
113.02
139.18
166.68
195-59
26
20.45
41-93
64.50
88.21
113.12
I39-30
166.81
I95-7I
27
20.48
41.99
64.58
88.31
113.24
139-43
166.95
I95-87
28
20.51
42.05
64.67
88.43
"3-38
!39-59
167.12
196.06
2 9
20-55
42.12
64.78
88.57
"3-54
139-77
167.33
196.28
30
20.59
42.21
64.91
88.73
"3-74
140.01
167.58
I96-55
31
20.65
42-32
65-05
88.91
ii3-97
140.27
167.88
196.86
32
20.71
42.43
65.22
89.14
114.23
M0.57
168.21
197.22
33
20.77
42.56
65.42
89-39
"4-55
140.93
168.61
197.64
34
20.85
42-73
65-65
89.70
114.91
i4!-35
169.07
198.15
35
20.95
42.91
65-93
90.05
"5-33
141.83
169.61
198.74
36
21.06
43.12
66.23
90.44
115.80
142.38
170.23
199.42
37
21. l8
43-36
66. s 8
90.89
116.36
H3-03
170.96
2OO.22
38
21.31
43.62
66.97
91.41
116.99
J43-77
171.79
2OI.I2
39
21.47
43-93
67-43
92.01
"7-73
144.62
172.74
202.15
40
21.65
44.29
67-95
92.70
118.56
H5-58
173.81
203.30
4i
21.86
44.70
68.56
93-48
119.51
146.67
175.02
204.59
42
22.09
45.16
69.23
94-36
I2 o-55
147.87
176-34
205.99
43
22.36
45.68
69-99
95-33
121.72
149.20
177.78
207.50
44
22.65
46.25
70.82
96-39
122.99
150.62
I79-3I
2O9.II
45
22.98
46.88
7i-73
97-55
124-35
152.15
180.97
210.85
46
23-32
47-56
72.71
98-79
1215.80
153-77
182.73
212.17
47
23-71
48.30
73-76
IOO. IO
127-35
I55-5I
184.62
214.69
48
24.12
49.08
74.87
101.50
129.00
157-37
186.63
216.82
49
24-55
49.89
76.03
102.98
U0.75
159-35
188.79
212.08
50
25.00
50-77
77-29
104.58
132.64
161.48
191.10
221-53
5i
25-49
5 J -7i
78.64
106.30
I34-67
163.76
193-59
224.17
52
26.02
52-72
80.09
108.14
I34-85
166.22
196.27
227.OO
53
26. sS
53-So
81.65
IIO. 1 1
139.18
168.86
199.14
230.03
54
27.18
54-95
83-30
112. 21
141.67
171.67
202.20
233-25
55
27.82
56.18
85.06
114.46
H4-33
174.67
205.46
236.69
56
28.50
57-49
86.95
116.85
147.16
I77-S5
208.92
240.35
57
29.23
58.89
88.96
"9-39
150.14
iSz.23
212.60
244.24
58
30.01
60.38
91.09
122.19
153-34
184.82
216.50
248.34
59
30.82
61.95
93-33
124.92
156.70
188.61
220.60
252.64
60
31.68
63-59
95-69
127.92
160.25
192.59
224.91
257.I7
OF LIFE INSURANCE.
93
TABLE No. XXVI (CONTINUED.)
NET VALUE PER $1,000 OF A TWENTY-FIVE YEAR ENDOWMENT POLICY,
AT THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Ninth
year.
Tenth
year.
Eleventl
year.
T-velfth
year.
ThirPnt
year.
Four'ntl
year.
Fifteent)
year.
; Twenfth
year.
20
225.61
257-57
291.20
326.57
363-79
402.96
444.19
685-59
21
225-65
257.61
291.23
326.60
363-80
402.96
444.18
685.50
22
225.71
257.66
2QI.28
326.63
363-83
402.98
444.18
685.41
23
225-77
257-73
29 1 -33
326.68
363-87
403.01
444.20
685-31
24
225.87
257.81
291.41
326.75
363-93
403-05
444-21
68 5 .22
25
225.97
257-9 1
291.51
326.84
364.01
403.10
444.24
685.13
26
226.IO
258-05
291.64
326.96
364.10
403.18
444.29
6^5.04
27
226.26
258.21
291.79
327.10
364-23
403.28
444-37
684.95
28
226.46
258.41
291.98
327-27
364-38
403.42
444-48
684.87
29
226.69
258.64
292.21
327-49
364.59
403-59
444-63
684.80
30
226.97
258.92
292.48
327-75
364.84
403-83
444-S3
684-73
31
227.29
259.24
292.81
328.08
365-I5
404. 1 1
445.08
684.65
32
227.66
259-63
293.21
328.48
365-53
404.46
445-37
684.57
33
228.12
260. 10
293-69
328.95
365-98
404.88
445-75
684.47
34
228.65
260.67
294.26
329-52
366-52
405-37
446.19
684.37
35
229.29
261.32
294.93
330.17
367-I4
405-94
446.67
684.26
36
230.01
262.08
295.68
330.91
367-85
406.58
447.22
684.12
37
230.86
262.95
296.56
33I-76
368.64
407.28
447-78
683.96
38
231.82
263.94
297-54
332-70
369-50
408.04
448-44
683.78
39
232.89
265.04
298.63
333-74
370-45
408.88
449.14
683.58
40
234.10
266.21;
299.81
334-86
371-49
409-79
449-89
683-33
4i
235-43
267.58
301.10
336-08
372.61
410.77
450.70
683.05
42
236.86
269.01
302.49
337-40
373-Si
411.83
45I-58
682.73
43
238.40
270.55
33-99
338.82
375-10
412.95
452.49
682.35
44
240.07
272.21
305.60
340-33
376.48
4H-I5
453-48
681.92
45
241.84
273.98
307-32
341-95
377-95
4I5-44
454-53
681.44
46
243-74
275-87
309.16
343-68
379-53
416.81
455-65
680.89
47
245-77
277.90
311.14
345-55
381-23
418.29
456-85
680.28
48
247-95
280.07
313-26
347-56
383.06
419.87
458-14
679.60
49
250.28
282.42
3I5-53
349- y
385-01
421-57
459-53
678.83
50
252.80
284.94
318.00
352-03
387-13
423.42
461.04
677-97
5i
255-5I
287.64
320.64
354-53
389.42
425.42
462.66
676.97
52
258.42
290.57
323-48
357-22
391.88
427-54
464-38
675.82
53
2 6l.53
293.68
326.52
360.10
394-48
429-79
466.18
674-5I
54
264.85
297.00
329-76
363-14
397-24
432.16
468.04
673.06
55
268.38
300.55
333-19
366.36
400.14
434.62
469.97
67I-53
56
272.14
304.29
336-81
369-75
403-17
437-i8
471.94
670.00
57
276.28
308.24
340-63
373-31
406.35
439-85
473-98
668.60
58
280.31
312.41
344.64
377-05
409.67
442.64
476. 19
667-44
59
284.71
316.77
348-85
380.95
413.16
445-66
478.69
666.62
60
289.31
321-34
353-24
395-05
416.91
449.03
481.66
666.25
94 PRINCIPLES AND PRACTICE
TABLE No. XXVII.
NET VALUE PER $1,000 OF A THIRTY- YEAR ENDOWMENT, AT THE END
OF VARIOUS YE\RS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
rft-f/
year.
Second
\ear.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eiffhtli
year.
20
14.69
30.11
46.30
63-30
8l.I7
99-94
119.66
140.38
21
17.71
30.15
46-36
63-39
81.28
100.07
119.80
HO- 54
22
14-73
30.20
46.44
63.50
81.41
IOO.22
119.98
H - 73
23
14.76
30.26
46-54
63.62
81.56
100.40
120.18
MO- 95
2 4
14.80
30-34
46.65
63-77
81.74
100.61
120.42
141.22
25
14.85
30-43
46.78
63-94
81.94
100.85
120.70
HtoS
26
14.89
3-52
46.92
64.12
82.18
101.13
121. 01
141.88
27
H-95
30.63
470S
64-34
82.45
101.45
121.38
142.27
28
15.02
30.76
47.28
64.60
82.77
101.82
121. 80
142.77
2 9
15.09
30.91
47-50
64.89
83.12
102.24
122.30
H3-32
30
I5-I7
31.08
47-75
65.22
83-54
102.74
122.86
143.96
31
15.28
31.28
48.04
65.61
84.02
103.31
I23-52
144.68
32
15-39
31-49
48-37
66.05
84-56
103.95
124.24
I45-50
33
I5-50
31-74
48.74
66.54
8S-I7
104.67
125.08
146.44
34
15-65
32.03
49.18
67.11
85.88
105.51
I26.O4
*47-52
35
15.82
32-36
49.66
67-75
86.67
106.44
127.12
148-73
36
16.00
32.72
50.20
68-47
87-55
107.50
128.33
150.11
37
16.21
33-13
50.81
69.27
88-55
108.69
129.72
151.65
38
16.43
33-58
51.48
70.17
89.68
110.03
131.26
J 53-39
39
16.69
34-09
52.26
71.20
90-95
111.54
I32. 99
J55-33
40
16.97
34-67
53-12
72-35
92-37
113-23
134.92
157.48
4i
I7-30
35-32
54.10
73.63
93-97
115.10
I37-05
159.84
42
17.66
36-05
55-17
75-05
95-71
117-15
139.28
162.41
43
18.06
36.84
56.35
76.61
97.62
119.38
141.90
165.17
44
18.50
37-71
57-64
78.30
99.68
121.79
144.60
168.14
45
18.99
38.66
59-05
80.14
101.91
124.36
I47-50
' I 7 I -32
46
19.50
39-69
60.52
82.09
104.26
127.10
150.58
174.71
47
20.06
40.69
62.15
84.15
106.77
130.01
153-86
178.31
48
20.66
41.94
63-83
86.33
109.42
133-09
157-33
182.13
49
21.27
43-^3
65.60
88.63
112.22
136.35
161.01
186.17
50
21.93
44-43
67.48
91.08
115.19
139.81
164.90
190.46
5i
22.62
45-79
69.49
93-67
"8.35
143-47
169.03
195.01
52
23-36
47-23
7i-59
96.42
121.68
147-35
I73-40
199.81
53
24-I5
48.78
73-83
99-33
125.21
151.45
178.03
204.89
54
24-95
50-35
76.17
102.36
128.90
155.75
182.86
210.20
55
25.82
52.05
78.64
105.58
132.81
160.28
:
187.96
215-79
OF LIFE INSURANCE.
95
4, TABLE No. XXVII (CONTINUED.)
NET VALUE PER $1,000 OF A THIRTY- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YKARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thirfnth
year.
Fourfnth
year.
Fifteenth
year.
Twentieth
year.
20
162.15
185.02
209.05
234-32
260.88
288.80
3I8.I5
489.36
21
162.32
185.20
209.25
234-53
2bi.o8
28Q.OO
318.36
489.46
22
162.53
185.43
209.49
234-77
261.33
289.25
318.60
489.60
23
162.77
185.69
209.76
235.05
261.63
289-55
318.89
489.79
2 4
163.06
l86.00
210.09
235-39
261.97
289.90
3!9-23
490.03
2.5
163.40
186.36
210.47
235-79
262.38
290.31
3^9-64
490.32
26
163.78
186.78
210.91
236.26
262.85
290.79
320.1'
490.68
27
164.24
187.27
211.44
236.79
263.41
29 I -33
520.68
491. II
28
164.76
187-83
212.03
237-42
264.05
292.0"
.**I-3!)
49^63
29
165.37
188.48
212.72
238.14
264.80
292.73
322.13
492.22
30
166.06
189.23
213-53
238.98
265.68
293.68
323-03
492.90
31
166.86
190.09
214.44
239-95
266.69
294.71
324.08
493.66
32
167.76
191.07
2I5-5 1
241.07
267.84
295.90
32^.27
494.48
33
168.79
192.20
216.70
242.31
269.17
297.24
326.62
405.42
34
169.99
193-49
218.07
243-78
270.66
298.77
328.15
496.45
35
I7I-33
194-95
219.63
24^.42
272.35
300.48
329.84
497-57
36
172-85
196.60
221-37
247.24
274.23
302.36
33 I -7'J
498.79
37
174-55
198.43
223.33
249.28
276.30
304-43
333-73
500.14
38
176.45
200.48
225.49
25I-5I
278.56
306.70
335-96
501-59
39
178.57
202.75
227.87
254.00
281.05
3oq,i8
338.40
503-19
40
180.93
205.25
230.46
256.62
283.75
311.87
341.04
504.92
4*
183.47
207.94
233-28
259-52
286.68
314.80
3*3-9i
506.80
42
186.23
210.87
236.33
262.65
289.85
3I7-95
347-01
508.83
43
189.21
215.02
239.62
266.03
293.26
32136
350-35
511.03
44
192.40
217.40
243.14
269.65
296-93
325-01
353-05
513-41
45
195.84
221.04
246.93
273-53
300.84
328.04
3 7-81
5I5.97
46
199.48
224.89
250.95
277.67
305.06
333- '3
361.92
518.68
47
203.36
229.00
255-24
282.09
309-53
337-6
366.31
521.56
4 8
207.48
233-37
259.80
286.77
314.28
342.3;5
370-96
524.59
49
212.84
237-99
264.63
29I-73
3I9-30
347-35
375-90
527-74
50
216.47
242.90
269.74
296.98
324.62
352-66
381.12
531-01
5i
221.36
248.09
275-15
302.54
330.25
358-28
386.62
534-43
52
226.54
253 55
280.86
308.42
336.20
364.20
39 2 .4i
537-99
53
232.01
259-35
286.89
314.60
342-45
370.42
398-50
54178
54
237-72
265.40
293.20
321.07
348.98
376.92
404.84
545-8y
55
243-75
271.78
299.82
327-85
355-82
383-70
411.47
550.50
9 6
PRINCIPLES AND PRACTICE
TABLE No. XXVIII. %
NET VALUE PER $1,000 OF A THIRTY-FIVE YEAR ENDOWMENT POLICY, AT
THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 47 PER CENT.
Agt.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
10.97
22.48
34-55
47.21
60.50
74-45
89.08
104.44
21
1 1. 01
22.56
34-67
47-38
60.72
74.71
8 9 . 3 S
104.79
22
II. 06
22.65
34.82
47-58
60.96
75-oo
89-73
105.18
23
n. ii
22-77
34-99
47.81
61.23
75-34
90.12
105.63
24
n. 18
22.90
35- J 9
48.07
61.58
75-73
90-59
106.16
25
11.26
23-05
35-4i
48.37
61.95
76.18
91.11
106.75
26
"34
23.21
35-66
48.70
62.37
76.69
91.69
107.41
2 7
"43
23.41
35-95
49.08
62.85
77.27
92.36
108.18
28
"54
23.62
36.27
49-52
63-39
77.91
93.12
109.05
2 9
11.66
23.86
36.64
50.01
64.00
78.65
93-99
110.03
30
11.79
24.14
37-05
50.56
64.70
79-49
94-97
111.15
31
"95
24-45
37-52
5I-I9
65-49
80.44
96.07
112.40
32
12.12
24.79
38.04
51.89
66.36
81.49
97.29
113.80
33
12-31
25.18
38-63
52.68
67-35
82.67
98.67
"5-37
34
12-53
25.62
39-29
53-56
68.45
84.00
IOO.2I
"7- J 3
35
12.78
26.11
40.03
54-54
69.68
85-47
101-93
119.10
36
13.04
26.65
40.83
55-62
71.04
87.11
I03-85
121.29
37
13-34
27.24
41.74
56-83
72.56
88.93
105.99
123.72
38
13.66
27.90
42-73
58-17
74-23
90.96
108.34
126.41
39
14.03
28.63
43-84
59-65
76.11
93-20
110-95
129.36
40
14-43
29-44
45.06
61.29
78.15
95-65
"3-79
132.58
4i
14.88
30-34
46.42
63.09
80.41
98.33
116.90
136.06
42
I5-36
3I-32
47-88
65.06
82.84
101.24
120.21;
139.84
43
15.90
32-39
49.48
67.17
85-47
104.36
123-83
143-85
44
16.47
33-54
51.20
69-45
88.29
107.68
127.63
148.10
45
17.10
34-78
53-4
71.88
91.28
in. 20
131-65
152.60
46
17-75
36.09
54-99
74-44
94.42
114-90
135-88
157-34
47
18.46
37-49
57-05
77-H
97.72
118.80
140.34
162 32
48
I9.2O
38-94
59- * 9
79-95
101.17
122.88
149.88
167 54
49
19.96
40.44
61.42
82.88
104.81
127.14
145.00
172.98
50
20.76
42.03
63-77
85-97
108.59
131.61
154.98
178.69
OF LIFE INSURANCE.
97
TABLE No. XXVIII. (CONTINUED.)
NET VALUE PER $1,000 OF A THIRTY-FIVE YEAR ENDOWMENT POLICY, AT
THE END OF VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thir-
teenth
year.
Four-
teenth
year.
Fifteenth
year.
Twentieth
year.
2O
120-57
137-49
I55-25
173-88
193.46
214.01
235-58
360-80
21
120.95
I.37-9 1
I55-70
I74-38
193.98
214-55
236.15
361.39
22
121.39
138.40
156.23
174.96
I94-58
215.19
239.81
262.09
23
121.89
I3S95
156-83
175-59
I9.v27
215.92
237.58
362-91
2 4
122.48
U9-59
I57-52
I /6-34
196.07
216.76
238.45
363-87
25
123.14
140.32
158.32
177.20
196.99
217.72
239.46
36497
26
123.88
141.14
I59-23
178.18
igS.02
218-82
240.60
366 23
27
^4-75
142.09
160.26
179.28
199.21
22O.O6
241,91
2G/.67
28
125.72
I43-I7
'161.43
180.55
200.55
221.49
24342
3693'
2 9
126.82
I44-38
162.75
181.97
202.08
223.11
245.11
37I-I5
30
128.07
I45-76
164.25
183-59
203.80
224.94
247-03
37320
31
129.47
I47-30
165.94
185.41
205.75
227.0:
249 2O
375-46
32
1.3 -03
149.04
167.84
187.47
207.95
229.33
251.63
377-95
33
132.80
15099
169.97
189.77
210.41
231.92
254-33
380.69
34
I34-7S
153-lS
172.36
i9 2 -35
2I3-I5
234.81
257.32
383-69
35
136.99
i 55-6 1
175.02
195.20
216.19
237-99
260.62'
386.96
36
'3943
158.32
177.96
198-35
219. S2
241.47
264.21
390.52
37
142.16
161.32
lSl.20
201.83
223.18
245-27
268.12
394-39
33
145-15
164.60
184.76
205.60
227.15
249.40
272.36
398.58
39
I48-45
16^.21
lSS.62
209.70
23I-45
253.86
276.96
403.11
40
1152.02
172.09
192.79
214.12
236.08
258.68
281.90
407.99
4i
155 89
176.28
197.28
218.87
241 06
263 84
287.21
4t3 23
42
160.02
180.76
202.08
223-95
246.38
269.35
292.87
418.81
43
164.42
185-54
207.19
229.36
2S2.04
275.22
298.89
424-73
44
169. 10
190.60
2I2.6O
235.08
258.02
281.42
305-27
431.00
45
174-05
195.96
218.33
241.13
264-35
287.99
312.00
437-61
46
17925
201.59
224-34
247.49
271.OI
294.88
319.08
444-54
47
184.70
207.5;
230.67
254. 18
2/S.OI
302.13
326.49
451-79
48
190.45
213.71
237,30
261.19
2S.S-33
30971
334-28
-159-36
49
196.43
220.20
244-23
268.50
292. 9 7.
317.61
342-39
467.22
50
202.71
226.98
25I-47
276.14
300.95
325-87
350.85
475-38
COMBINED EXPERIENCE TABLE OF
MORTALITY.
This table of mortality, which was the result of the united
efforts of the actuaries of seventeen life offices of England and
Scotland, and for this reason is often termed the " Actuaries "
table, is a far better criterion of mortality than any which pre-
ceded it. Heretofore, all tables of mortality were made from
the average population of certain towns or countries, which
included large numbers of persons who were not proper sub-
jects for insurance, and consequently, the mortality record was
much greater than was needed for the successful determination
of the mortality of insured lives. But in this case, none but
selected and insured lives were taken. It comprises the recorded
experience of the Amicable, Alliance, British Commercial,
Crown, Economic, Eqetitablc, Guardian, Imperial, Law
Life, London Life, Norwich Union, Promoter, Scottish
Widows' Fund, Sun, Universal, and University offices. The
data of these offices was collected under the superintendence of
a committee of actuaries, who availed themselves of all the
experience and research of those who had preceded them, in
order to get a reliable table to measure the average mortality of
assured lives. It was first published by Jenkin Jones, in 1843,
and from that time till the present, it has been highly appreci-
ated by the actuaries of England and America. The statistics
upon which this table was founded have never yet been made
public, only a few copies of them were printed, and they only
for private circulation.
An objection has been raised against this table, that the aver-
age age of the policies was only 8^ years, and that for lives
which continue long in the company, this table would be found
defective. The experience of many of the companies in this
country is that this table gives results more nearly accurate than
any other in use, and that it is far better adjusted. Another
objection against it is, that some of the lives were assured in
OF LIFE INSURANCE,
99
two or more different companies, and in the compilation of the
table they would count as so many seperate lives. Neither of
these objections appear to have had much practical influence.
The fact still remains that for many years it was regarded as the
best table of mortality in use, that it has done excellent s<j vl-e
during the last thirty years and for some time to come will
probably be the standard table in use in the New England
states.
In compiling this table some curious and unexpected results
were obtained. It was found that the mortality from town life
taking all ages together, was more favorable than country life,
and that the mortality among assured females was greater than
among assured males. The first of these results does not appear
to have been noticed in this country, and the latter may be
attributed to defective medical examination, or that members of
this class were induced to insure because they were conscious
that they were relatively short-lived. The fact is clearly estab-
lished by all writers on vital statistics that the average longevity
of females is fully equal to that of males, and many companies
make no distinction whatever in the risk.
100
PRINCIPLES AND PRACTICE
TABLE No. XXX.
NET VALUE PER $1,000 OF AN ORDINARY LIFE POLICY, AT THE END OF
VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
//Vrf i
year.
\
Stcond
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
6.22
12.66
I9-3I
26.19
33-30
40 64
48.23
<;6.o7
21
6.47
13-17
20.09
27.24
34-64
42.27
50.16
58-31
22
6.74
I3-7 1
20.90
28-34
3 6 -03
,43-97
5 2 -i7
60.64
23
7-OI
14.26
21-75
29.49
37-48
45-74
54-26
63.07
24
7-3
14.84
22.64
30.69
39-0
47-59
56.45
65.60
2S
7.60
i.v45
23-56
3*-94
40.58
49- 5 i
58.73
68.24
26
7.91
16.09
24.52
33-24
42.24
5I-52
61.11
71.00
27
8.24
16-75
25-53
34-6o
43-96
53-62
63-59
73-89
28
8-58
17-43
26. =;S
36.02
45-76
55-Si
66.20
76-92
2 9
8-93
18.16
27.68
37-50
47.64
58-12
68.93
80.09
30
9-31
18.91
28.83
39.06
49-63
60.54
71.80
8345
31
97
19.70
30-03
40.70
5i-7i
6308
74.84
86.98
32
IO.II
20.54
3*-3!
42 43
53-9'
65.78
78.04
90.72
33
10.54
21.42
32-65
44-25
56 25
68.63
81.43
94.67
34
1 1. CO
"35
34-07
46.20
58-71
7I-65
85-03
98.86
35
11.48
23-33
35-59
48.25
61.34
74-86
88.84
103.29
36
11.99
24-39
37-19
50-43
64.11
78.26
92.87
107.92
37
12-55
25-51
38.90
52-75
67.08
St. 87
97.09
112.71
38
13.12
26.69
40.72
55-22
70.20
85.62
101.43
117.61
39
13-74
27.96
42.65
57-83
73-46
89.48
105.88
122.59
40
14.41
29.31
44.70
60.55
76.79
93-42
110.36
127.60
4 1
15.12
30-73
46.81
6^.29
So. 1 6
97-35
114.85
132.64
42
15-85
32.18
48.91
66.04
83-49
101.26
119.32
137-69
43
16.59
33-59
51.00
6873
66.78
105.11
123.80
142-74
44
17-30
3499
53-02
71-38
90.04
109.02
128.28
147.80
45
18.01
36-36
55-04
74-03
93-34
112.94
132.80
152.91
46
18.69
37-71
57-05
76.72
96.67
116.90
I37-3S
158.08
47
iQ-39
39.10
59- i 4
79-47
100.09
120.95
142.05
163-37
48
2Q.IO
40-54
61.28
82-30
103-57
125.09
146-83
168.78
49
20.86
42.02
63-47
85.19
107.14
129.34
I5I-73
I74-30
5
21.62
43 S2
6v7o
88.13
110.79
I33-67
156.72
179-95
5 1
22.39
4vo6
67.98
91.14
"4-53
138.09
161.84
185.74
S.2
23.19
4663
70.33
94.24
118.34
142.64
167.09
191.66
53
24.00
48.26
72.74
97.42
122.29
I47-32
172.47
i 07. 66
54
24.85
49-94
75-22
100.70
126.35
152.12
177-93
203-75
55
25.72
51-65
77-78
104.08
130-51
156.98
183.46
209.87
06
26.61
53-43
80.42
107-55
1.34-72
161.90
189.01
216.02
57
27-56
55-29
83-15
ii 1.07
138.99
166.84
194-59
222.18
5S
28.52
57-iS
Ss.88
II4-59
142.23
171.76
200. 14
228.28
59
29.50
59-05
88.60
118.08
147.46
176.66
205.63
23^-30
60
30-45
60.90
91.28
121.54
I 5 I -63
181.49
211.02
240.21
OF LIFE INSURAMV&.
101
TABLE No. XXX (CONTINUED.)
NET VALUE PER $1,000 OF AN ORDINARY LIFE POLICY, AT THE END OF
VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thir-
teenth
year.
Four-
teenth
year.
Fifteenth
year.
T-wentieth
year.
20
64.17
72-53
81.16
90.07
99.27
108.75
118.56
172.61
21 '
66.72
75-41
84-37
93.62
103.17
113.04
123.22
179-43
22
69.38
78.41
87.72
97-33
107.26
"7-5i
128.09
186.57
23
72-I5
8l.
91.20
IO1.2O
111.52
122.17
I33-I9
194-03
24
75-04
84-78
94-S5
105.24
"5-97
127.07
138.52
20I.8o
25
78.06
88.20
98.67
109.47
120.65
132.19
144.12
209.84
26
81.22
91.76
IO2.65
113.92
125-54
137-56
149.99
218.13
27
84.52
95-50
106.85
118-57
130.69
143.22
156.17
226.62
28
87.99
99-43
111.25
123.46
136.10
149.16
162.65
235.31
29
91.64
103.56
115.88
128.62
141.80
155-40
169.41
244.20
30
95-48
107.91
120.77
134.06
J47-79
161.93
176.42
253.29
31
99-53
112.51
125.93
139-79
154-05
168.68
183-65
262.57
3^
103.82
"7-37
131-36
M5-77
160.54
175.66
191.06
272.02
33
108.36
122.50
137-05
I 5 I -97
167.24
182.80
198.65
281.65
34
"3-15
127.86
142.94
158-38
174.10
190.11
206.39
291.42
35
118.16
133-41
149.02
164.92
181.11
197-57
214.30
301.35
36
123-35
i39-'3
155-22
171.60
188.25
205.13
222.36
311.42
37
128.69
M4-97
161.54
178-39
'95-53
212.92
230.54
321.60
33
134.10
150.89
167.95
185-31
202.92
220.76
238-83
33L9I
39
139.60
156.89
174.47
192.32
210.40
228.71
247.22
342-33
40
I45-H
162.97
181.06
199.40
217.96
236.73
255.70
352-84
4i
150 73
169.09.
187.69
206.53
225-57
244.82
264.25
363-37
42
156.33
175-22
194-35
213.68
233-23
252-95
272.83
373-90
43
161.94
181.37
201. 02
220 87
240.92
261.11
281.47
384-39
44
167.56
187.54
207.73
228.11
248.65
269.36
290.19
394-86
45
I73-24
193-79
214-53
235-43
256.50
277-7
299.01
405-30
46
179.12
200.13
221.41
242.86
264.45
286.15
307-S7
415-71
47
184.90
206.59
228.45
250.45
272.56
294.71
316.86
426.07
48
190.90
213.19
235-63
258.18
280.76
303.35
325.89
436 37
49
197.06
219.95
242.96
266.01
289.07
312.06
334-98
446.62
50
203-34
226.84
250.38
273.9 2
297.41
320.81
344-07
456.79
5i
209.76
223.82
257.88
281.89
305-81
329-58
353-18
466.88
52
216.27
240.88
265.44
289.91
3H-23
338.36
362.24
476-87
53
222.86
248.00
273.05
297-95
322.65
347- 19
37I-25
486.76
54
229.51
255-18
280.68
306.00
33I-04
355-7
380.21
496-55
55
236.19
262.35
288.31
3I3-99
339-37
364.42
389.11
506.21
56
242.87
269.52
295.88
321-93
347-63
372-98
397-9 2
5I5-79
57
249-54
276.63
303.39
329.80
355-84
38i.47
406.65
525-16
58
256. 13
283-65
3IO.8l
337-59
363-94
389-84
415.26
534-43
59
262.63
290.58
318.14
345-27
371-93
398.09
423-74
534-53
60
269.02
297.42
325-37
352-84
379-8o
406.22
432.09
552-49
102
PRINCIPLES AND PRACTICE
TABLE No. XXXI.
NET VALUE PER $1,000 OF A TEN-PAYMENT LIFE POLICY, AT THE END
OF VARIOUS YEARS. COMBINED EXPERIENCE, 4 PER CENT.
Agt,
First
year.
Second
year.
Third
year.
Fotirth
year.
Fifth
year.
20
24.94
50.98
78.19
106.61
136.30
21
y"
25.46
52.06
79.84
108.85
I39-I7
22
26.01
53-17
81.54
111,17
142,13
23
26.57
54-31
83.29
"3-56
H5 19
24
27.14
55-49
85.10
116.03
148.34
25
27.74
56-7I
86.97
118.57
I5I-59
26
2S-35
57-96
88.89
121.19
154-94
27
28.99
59-26
90.87
123.90
158.40
28
29.64
60.59
92.91
12668
161.95
29
30-3I
61.96
95.01
129.54
165.61
30
31.00
63-37
97.17
13249
169.40
31
3I-7I
64.82
99.40
135-53
17330
32
3 2 -44
66.32
101.70
138.68
I77-32
33
33-20
67.87
104.08
141.92
181.48
34.
33-93
69.46
106.53
H5-27
185.79
35
34-7S
71.11
109.06
148.74
190.23
36
35-6i
72.81
111.69
I52-33
194.84
37
36.48
74-58
114.41
156.05
199.61
33
37-37
76.42
"7-23
I59-9I
204.55
39
38-30
78.32
120. l6
163.90
209.6!
40
39- 2 7
80.31
123.20
167.99
214-75
4i
40.28
82.36
126.30
172.13
219.96
42
4^-32
84,44
129-39
176.27
225.14
43
42.35
86.48
132.46 .
180.36
230.29
44
43-35
88.49
135-47
184.40
235-4I
45
44-34
9-45
138.44
188.41
240.52
4 6
45-29
9 2 -37
141-37
192.40
245.62
47
46.25
94-31
144.31
196.41
250./3
48
47-18
96.22
147.24
200.35
255.80
49
48.11
98.12
150.15
204-33
260.84
50
49.06
1 00.02
153.03
208.25
265.87
5i
49-97
101.88
155-86
212 12
270-83
52
50.87
103 70
158 67
215-94
275-74
53
51-75
105.51
161.42
219.70
280.60
54
52-63
107.28
164.13
223.43
285.37
55
53-49
109.01
166.81
227.05
290.07
56
54-? i
110.73
169.40
230.62
294.62
57
<8
55- *6
55-92
112.39
113.98
171.96
174-35
23406
23730
299.02
33-i3
59
56-71
"5-51
176.63
240.38
3^7-13
60
57-39
116.88
178.70
243-20
310.78
OF LIFE INSURANCE.
103
TABLE No. XXXI (CONTINUED.)
NET VALUE PER $1.000 OF A TEN-PAYMENT LIFE POLICY, AT Tire
END OF VARIOUS YEARS. COMBINED EXPERIENCE, 4 PER CENT.
4**
Sixth
year.
Seventh
year.
Eighth
year.
Ninth
year.
Tfnth
year.
20
167.33
199-75
233-65
269.10
306.17
21
170.85
203.96
238.58
274-77
312.62
22*
174.49
208.30
243-66
280.62
319.29
23
178.24
212.78
248.90
2S6.66
326.17
24
182.12
217.40
254-3I
292.90
333-27
25
1 86. 10
222.17
259.88
299-33
340.60
26
190.21
227.08
265.63
305-97
348.17
27
194-45
23^15
27I-57
312.82
355-99
28
198.82
237-37
277.70
319.90
364.07
29
20333
242.77
284.02
327.20
372.42
30
207.98
248 33
290.56
334-76
381.04
3 1
212.78
25408
297-3 1
342-56
389.96
32
217.74
260.03
304.28
350.63
399.18
33
222.87
266.17
3"-5
358.97
408.71
34
228.16
272.52
318.96
367-59
41852
35
233- 6 4
279.08
326.66
376.45
4*3-57
36
239-32
285-87
334-58
3S5-53
438.86
37
245. 8
292.85
342.68
394-81
449-35
38
251.21
299-97
350-95
404.25
460.02
39
257-35
307-23
359-33
4I3-83
470.88
40
263.59
3M-56
367.82
423-54
481.91
4i
269.85
321-94
376.40
43338
493-"
42
276.12
329-37
385-04
443-34
504.46
43
282.39
336.8i
393-75
453-38
5I5-95
44
288.65
344-29
402.50
463-51
527.57
45
294.92
35I-78
411.29
473-71
539-31
46
301.18
354-28
420.12
483-98
551.16
47
307-45
366.78
428.98
494-3^
563-10
48
3t3-7o
374-29
437-85
504.68
574- H
49
3i99 3
381.78
446.71
515-09
587-26
5
326.12
389-25
455-62
525-52
599-43
51
33 2 -26
396-71
464-45
535-95
611.63
52
33 36
404 08
473-26
546-33
623-83
53
34437
411.38
481.97
556.65
636.00
54
350-32
418.57
490.58
566.88
648. 1 2
55
356-12
425-62
499-05
576.98
660.17
56
36i.77
432-49
507-32
586.92
672.13
57
367.22
439- * 4
515.39
596.68
683.96
53
372-41
445-53
523-18
606.22
695.66
59
377-35
451-63
530-72
615-50
707.19
60
38196
457-40
537-89
624.51
718.57
xo 4
PRINCIPLES AND PRACTICE
TABLE No. XXXII.
NET VALUE OF A TEN- YEAR ENDOWMENT POLICY, AT THE END OF
VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Agt.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
20
80.51
164.79
253.02
345-41
442.17
21
80.49
164.74
252-95
345-32
442.07
22
.80.46
164.69
252.87
345-23
441.97
23
80.43
164.63
252-79
345^3
441-85
24
80.40
164.57
252.71
345-02
441-73
25
80.37
164.51
252.62
344-9 1
441.60
26
So-33
164.44
252.53
344-79
441-47
27
80.30
I64.37
252.43
344-66
44' 32
28
80.27
164.30
252.31
344-53
441.16
29
80.22
164.21
252.20
344-3S
440.99
30
80.17
164.12
252.06
344.21
440.81
31
So. 1 2
164.03
25I.93
344.05
440.63
32
80.06
163.92
251.78
343-87
440-43
33
80.OI
163.82
251-63
343-68
440-22
34
79-95
163.70
25L47
343-49
440.00
35
78.89
163.61
5.'-3
343.29
439-79
36
79-83
163.48
*5MS
343-"
439-57
37
79.76
16336
251.00
342.92
439-37
33
79.72
163.27
2SC.88
342-77
439- -'- 1
39
79.68
163.20
250.78
34 2 -65
439-5
40
79- 6 5
163.16
250.71
342-54
438.87
4i
79-65
I63-I3
250.64
342-39
438-65
42
79-65
163.09
250.51
342-17
438.33
43
79.62
162.98
250.32
341-85
437 -9
44
79-55
162.82
250.02
341-43
437-38
45
79-45
162.58
249.63
340.92
436.77
46
79-30
162.27
249 17
340-33
436-07
47
79.14
161.94
248.68
339.69
435-32
48
78.96
161.58
248.14
338.99
434-49
49
78-77
161.19
247-56
338-23
433-58
50
78.56
160.80
246.92
337-39
432.60
5i
78-33
160.29
24(1.21
336-48
43I-52
52
78.07
159-77
245-45
335-49
430-3.5
53
77-79
159-22
244.62
334-42
429. 10
54
77-51
158.64
243-75
333-29
427.78
55
77.20
IijS.OO
242 82
332-10
426.36
56
76.86
157-35
241.86
330-84
424.84
57
76.55
156.69
240.85
329.48
423-19
58
76.20
I55.98
239-74
327-99
421-36
59
75-84
I55-I9
238.50
326.33
4I9-35
60
75-40
154.29
237.12
324-50
417.14
OF LIFE INSURANCE.
I0 5
TABLE No. XXXII (CONTINUED.)
NET VALUE PER $1,000 OF A TEN- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
Sixth
year.
Seventh
year.
Eighth
year.
Ninth
year.
Tenth
year.
20
543-53
649-72
761.01
877-67
1,000.00
21
543-42
649.62
760.92
877.62
1,000.00
22
543-32
649-5I
760.84
877-57
1,000.00
23
543-19
649.42
760.77
877-53
I,OOO.OO
24
543-07
649.30
760.67
877-47
I,OOO.OO
25
542-93
649.21
760.55
877-40
1,000.00
26
54^-79
649. 1 1
760.42
877-31
1,000.00
2?
542-64
648.87
760.30
877.24
I,OOO.OO
28
54 2 -47
648.71
760.18
877.16
1,000.00
29
542-30
648.55
760.04
877.08
I,OOO.OO
30
542.11
648.38
759-90
876.99
I,OOO.OO
31
54I-92
648.24
759-80
876.90
I,OOO.OO
32
54i-7i
648.00
759-59
876.81
I,OOO.OO
33
54I-50
647.80
759-43
876.71
1,000.00
34
541.28
647-59
759-25
876.60
1,000.00
35
541.06
647.38
759.09
876.49
1,000.00
36
540.84
647.18
758.91
876.38
1,000.00
37
540.64
646.98
75- 73
876.25
I.OOO.OO
33
540-45
646.77
758.53
876.11
1,000.00
39
540.24
64653
758-30
875-95
1,000.00
40
540.00
646.24
758.02
S75-76
1,000.00
4
539-70
645.92
757-71
875.56
I.OOO.OO
42
539-31
645 48
757-32
8-5-30
I.OOO.OO
43
538.82
644.98
756-87
875 " x
I.OOO.OO
44
538-23
644.40
756.37
874-69
1,000.00
4.5
S37-56
643-73
755-79
874-32
1,000.00
46
536-8i
642.99
755-15
873-92
1,000.00
47
53.S-98
642.15
7.) 4- 43
873-44
1,000.00
48
535 8
641 29
7^-69
872.99
I.OOO.OO
49
534-10
6-JO-3I
752-84
S72-45
1,000.00
50
533-03
639-23
75I-9 2
871.86
I.OOO.OO
5i
53-85
638.08
750-94
871.25
1,000.00
52
530-59
636.85
749-87
870.^6
1,000.00
53
529-24
635-.SO
748.70
869.80
I.OOO.OO
54
527.80
634.06
747-44
868.99
1,000.00
55
526.23
632.54
746.11
868.15
I.OOO.OO
56
524-54
630.76
744-53
867.10
1,000.00
57
522.68
628.88
742.88
866.02
1,000.00
53
520.65
626.80
74I-03
864.81
1,000.00
59
518.41
624-54
739-04
863-51
1,000.00
60
5I5-94
622.02
736.80
862.05
1,000.00
io6
PRINCIPLES AND PRACTICE
TABLE No. XXXIII.
NET VALUE PER $1,000 OF A FIFTEEN- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
47.42
97-oi
148.90
203.19
26O.OI
319.48
3^-75
446.95
21
47.40
96.98
148.85
203.12
259.91
3I9-37
381.62
446.80
22
47-38
96.94
148.79
203.04
259.82
319.26
381.49
446.66
23
47-36
96.90
I4S-73
202.96
259-7 l
319-13
3Si-34
446.50
24
47-34
96.86
148.66
202.87
259.61
319.00
381.19
446-33
25
47-32
96.82
148.60
202.78
259.49
318.85
381-03
446.15
26
47-30
96.77
148.52
202.68
259-35
318.69
380.84
4-15-95
27
47.27
96-72
MS-44
20.2.56
259.21
3 I 8-52
380.74
445-72
28
47-25
96.66
I4S35
202.44
259- 5
318.34
380.43
445-50
2 9
47-22
96-59
148.25
202.30
258.89
318.14
380.30
445-25
30
47-18
96.52
148.14
202.16
258.71
3I7-94
379-96
444-99
31
47-15
96-45
148.03
2O2.OI
258.53
3I7-72
379-75
444-74
32
47.11
96-37
147.92
201.87
258.36
3 J 7-52
379-51
444-50
33
47.07
96.31
147.82
201-73
258.19
3i7-3i
379-30
444.28
34
47-05
96.25
147-73
201.62
258.05
3I7-I7
379-13
444.10
35
47.02
96.20
147.66
201.52
257-94
3^7-05
378.99
443.96
36
47.00
96.17
147.61
201-47
257.88
316.99
378-94
443.88
37
47-00
96.16
147.61
201.46
257.88
316.99
3/891
443-79
33
47.01
96.18
147.64
2OI.52
257-94
317.02
378.88
443.69
39
47.04
96.24
H7-73
201.63
258.04
317.06
378.85
443-35
40
47.08
96-34
I47-87
201.76
2158.12
317.06
3/S.72
443-31
4i
47.16
96.47
148.02
201.87
258.16
316.99
378.54
443-ot
42
47.24
9 6 -.S9
148.11
201.92
258.09
316.80
378-23
442-58
45
47-30
9665
148.14
201.84
257.90
3 l6 -50
377-So
442.04
44
47-33
96.66
148.06
201.66
257.61
316.09
377-27
441-39
45
47-33
96.60
147.91
201.41
257-24
315-59
376.64
440.63
46
47.28
96.48
147.70
201.09
256.80
3i5-oi
375-92
439-77
47
47-23
96-35
147.48
200.75
256.32
3I5-38
375-13
438-84
48
47.18
96.22
147.24
200.38
255.80
313-69
374-2t
437-75
49
47.12
96.08
146.98
199.98
255-23
312.98
373-36
436.74
50
47.07
95-93
146.70
199-54
254.64
312-18
372-39
435-62
5i
47-oo
95-76
146.40
199.09
254.00
3ii-34
37I-3S
434-41
52
46-93
95-58
146.10
198.62
253-33
310.48
370.32
433-i6
53
46.86
95-42
H5-78
198.13
252.67
309.61
369.24
431-S3
54
46.81
95-25
H5-43
197.66
252.01
308.73
368.08
430.40
55
46.75
95.08
M5-I9
197.21
25I-35
307.80
366.86
428.87
56
46.69
94.96
H4-93
196.78
250.65
306.81
365-54
427.22
57
46.68
94.87
144.71
I96-33
249.92
305-74
364.12
425.43
58
46.67
94-79
H4-45
195.82
249.10
304-58
362.56
423-47
59
46.67
94-67
144.14
195-24
248.20
303.28
360.83
421.31
60
46.63
94-51
M3-76
194.58
247.18
301.84
358.93
418.93
OF LIFE INSURANCE.
107
TABLE No. XXXIII (CONTINUED.)
NET VALUE PER $1.000 OF A FIFTEEN- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Aft.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Tlu'rPnlk
year.
Four 1 nth
ytar.
Fifteenth
year.
20
5I5-24
586.80
661.78
740-39
822.8l
909.28
1,000.00
21
5I5-09
586.64
661.62
740.21
822.70
909.20
1,000.00
22
5H-93
586.48
661.47
740.11
822.59
909.14
1,000.00
23
5I4-76
586.30
661.30
739-95
822.47
909.07
1,000.00
24
514-58
586.12
661.12
739.80
822.35
909.00
I,COO.OO
25
514-39
585-9 2
660.93
739-62
822.19
908 90
I.OOO.OO
26
514.18
5S5-7I
660.73
739-44
822.07
908.80
1,000.00
2 7
5I3-94
585.46
660.49
739-23
821.90
908-73
1,000.00
28
5I3-70
585-22
660.27
739-03
821.74
908.64
1,000.00
29
513-44
584-97
660.02
738-80
821.59
908.56
1,000.00
30
5I3-I7
584.70
659-77
738-59
821.39
908.43
1,000.00
31
512.91
584-44
659-52
738-37
821.22
908.31
I.OOO.CO
32
512.68
584.21
659-31
738.i8
821.06
908.23
1,000.00
33
512.45
583-99
659.09
737.96
820,86
908.09
1,000.00
34
512.27
583-79
658.87
737-73
820.66
907-95
1,000.00
35
512.10
583-58
658.63
737-47
820.42
907.79
1,000.00
36
5"-97
583-4I
658.40
737-22
820.19
907.65
1,000.00
37
511.81
583-I6
658.10
736-91
819.90
907.46
I.OOO.OO
33
511.61
582.88
657.76
736.55
819.59
907.25
1,000.00
39
5"-37
582.56
657.40
736-17
819.26
907.01
1,000.00
40
5"-03
582.23
6156.91
735-68
818.82
906.75
1,000.00
4i
5to.63
582.66
656-39
735-16
818.37
906.48
1,000.00
42
510.10
582.05
655-73
734-51
817.81
906.12
1,000.00
43
509.46
580.33
654.98
733-79
817.20
95-74
1,000.00
44
508.70
579-49
654.11
732-96
816.50
905-30
1,000.00
45
507.82
578.54
653-I4
732.03
815.73
904.81
1,000.00
46
506.86
577-50
652.06
731.02
814,89
904.30
1,000.00
47
505.80
576.35
650.89
72991
8I3-97
903.72
1,000.00
48
504-56
575-01
649.51
728,58
812.90
903.11
1,000.00
49
503-43
573-So
648.32
727-46
811.88
902.40
1,000.00
50
502.16
572.42
646.86
727-05
810.70
901.66
1,000.00
5i
500.80
570-91
645.29
724-53
809.41
900.84
1,000.00
52
499-33
569-30
643-59
722.89
SoS.oo
899^5
1,000.00
53
497-78
567-56
641.77
721.11
806.48
898.99
I,COO.OO
54
496. 10
565-68
639-77
719-15
804.80
897.91
1,000.00
55
494-29
563-64
637.61
7I7-03
802.97
896.74
1,000.00
56
492.32
561.41
635-24
714.70
800.915
895^5
1,000.00
57
490.19
559-oo
632.66
712.16
798.76
894.03
1,000.00
58
487.84
556.34
629.82
709-37
79 6 -35
892.48
1,000.00
59
485.26
553-43
626.73
706.33
793-70
890.77
1,000.00
60
482.44
550.26
626.36
703.01
790.82
888.87
1,000.00
io8
PRINCIPLES AND PRACTICE
TABLE No. XXXIV.
NET VALUE PER $i,coo OF A TWENTY- YEAR ENDOWMENT POLICY. AT
THE END OF VARIOUS YEARS, COMBINED EXPERIENCE. 4 PER CENT.
Age.
First
year.
Second
year
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
20
31-39
64.19
98.48
I34-32
171.80
210.99
251.98
21
3I-38
64.18
98.46
134.28
I ?i-75
210.92
251.89
22
3I-38
64.16
98.43
134-25
171.69
210.85
251.80
2 3
31-37
64.14
98.40
134.20
171.63
210.76
251.69
2 4
3I-36
64.13
98-37
134-I5
171.56
210.68
25I-58
25
31-35
64.11
9S-34
134.10
171.49
210.58
2.SI-45
26
3!-34
64.09
98.30
134.04
171.40
210.47
25I-32
27
3i-34
64.06
9S-25
I33-98
171-32
210.36
251.18
28
3!-3 3
64.04
98.21
I33-92
171.23
210.25
25^05
29
3I-32
64.02
98.17
133-86
171-15
210.15
250.94
30
3i-3i
64.00
98.14
I33-80
171.09
210.06
250.82
3 1
3i-3i
63-98
98.12
I33-78
171.04
2IO.OO
250.7?
32
3i-3o
63-9S
98.11
I33-76
171.03
209.99
250.73
33
3KV
64.00
98.13
133-79
171.06
2IO.O2
250.78
34
31-33
64.03
98.18
133-86
171.14
210.13
250.90
35
3I-36
64.09
98.27
133-97
171.29
210.31
251.11
3 f >
31.40
64.18
98.40
I34-I5
171.52
210-59
251.40
37
31-47
64.30
9S-59
I34-4I
171.84
210.97
25I-85.
38
3'-54
64.47
98.84
134-75
172.26
211.42
252.24
39
3I-65
64.69
99.17
135-lS
172.74
211.89
252.80
40
31-79
64.06
99-57
I35.65
173-23
212.36
253.09
4i
31.96
65.28
99.99
136.12
173-73
212.77
253-42
42
32-14
65.60
100.98
136.54
174.08
213.09
253^5
43
32-31
65.87
100.71
136-85
174-36
2I3-3 1
253-Sl
44 '
32-44
66.10
100.96
137.10
'74-57
213-47
253.87
45
32-57
66.27
101.16
I37-29
174-74
213-58
253-9
4 6
32.61
66-37
101-33
137-47
174.89
213.67
253-90
47
32.75
66. s 8
101.53
I37-67
175.06
213-78
253.90
48
32-85
66.76
101 76
I37-90
175.26
213.91
253-95
49
32.98
66.96
IO2.OI
138.16
175-49
214.08
254.01
50
33-"
67.19
IO2.29
138.45
175.76
214.29
254.13
5 l
33-25
67.44
102-59
138.77
17608
214-55
254.32
5--
33-44
67.71
102-95
139.18
176.46
214.90
254-59
53
33-58
68.03
103.36
J39- 6 4
176.94
215.36
254-96
54
33-So
68.40
103.84
140.20
177-54
215-92
255-40
55
34-03
6S.8o
104.40
140.86
178.24
216.55
255.90
56
34-28
69.30
105.07
141.64
179.02
217.26
256.46
57
34.60
69.87
105.84
142.49
179.87
218.03
257.07
58
34-95
70-5I
106.64
143-40
180.76
218.84
257-70
59
35-33
7i-i5
107.47
144.30
181.68
219.67
258.35
60
35-70
71.80
108.30
145.24
182.62
220.52
259.01
OF LIFE INSURANCE.
109
TABLE No. XXXIV (CONTINUED.)
NET VALUE PER $1,000 OF A TWENTY- YEAR ENDOWMENT POLICY, AT
THE END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
4r*
Eighth
year.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thirfnth
year.
Four 1 nth
year.
Fift'enth
year.
20
294.86
339-73
386.71
435-87
487.36
541.29
597.82
657-05
21
294-75
339-6i
386.55
435-70
487.17
541.09
597-60
656.84
22
294.6 \
339-47
386.40
435-52
486.98
540.89
597-39
656.64
23
294-5I
339-3'
386.21
435-32
486.75
540.65
597-15
656.39
24
294.38
339-i6
386.03
435-12
486.54
540-45
596-92
656.18
25
294.21
33S-97
385.82
434-88
486.28
540.15
596.64
655-90
26
294.06
33^-79
385.62
43466
486.05
539-9 3
596.41
655.68
27
293.80
338.60
385.40
434-42
485.80
539-65
596-I5
655-43
28
2 93-73
338.41
3Sv20
434-21
485-57
539-43
565-93
655-2I
2 9
293.61
338.27
385.04
434.04
485.40
539-26
595-76
655-04
30
293-43
338.13
384.89
433-89
485.24
539-09
595-59
654.86
31
29339
338-04
3S4-76
433-8o
4S5-I5
538.98
595-43
654.64
32
293-37
338.02
384-79
433-79
485.12
538-90
595-29
654.44
33
293-43
338.io
384-87
433-84
485.12
538.84
595-15
654-23
34
29^.58
338-25
385.0I
433-93
485.14
538.76
594-98
653-98
35
293.81
338.47
385-I7
434-02
485.12
538.64
594-75
653.68
36
294.21
338.83
385.37
434-14
485.10
538-52
594-56
653-4I
37
294.50
339-0?
385.58
434-20
485.06
538.37
594-28
6.53-04
38
294.86
339-20
385.72
434.22
484.97
538.I4
593-94
653.60
39
295.22
33968
385-97
434-34
484-85
537-89
593-59
652.14
40
295-5I
339-74
385-90
434-H
484.62
537-52
593-07
65I-54
4i
295-75
339-86
385-9
434-oo
484.34
537-io
59 2 -54
651.90
42
295.88
339-87
385-77
433-72
483.90
536-53
59 r - 8 3
650.09
43
295-93
339-8o
385.56
433-36
483.40
535-S7
59 l -5
649.22
44
295.89
339-63
385-24
432-89
482.76
53507
590.12
648.21
45
295-79
339-40
384-86
432-34
482.04
534-21
589-13
647.11
46
295.68
339-6
384.47
43I-7S
481-32
533-33
588.11
645-97
47
295-57
338-90
384-03
431.18
480.54
532-38
586.97
644.69
48
295-49
338.66
383-53
430.60
479.78
53I-40
5S5-79
643-34
49
295.42
338.45
383.23
430.02
478-95
530-34
584-50
641.86
50
295.42
338.30
382.92
429-45
478.13
529-24
583-15
640.32
5i
295-49
338.21
382.60
428.87
477-2.5
528.08
581.71
638.64
52
295.68
338.14
382.28
428.25
4/6-33
526.82
580.15
636.82
S3
295-83
33S-I2
38I-97
427-63
475-35
525-48
578.46
634 84
54
296.09
338.12
381.67
426.98
474-31
524-05
576-65
632.71
55
296.38
338.14
381.36
426.28
473-20
522-50
574.69
630.42
56
296.72
338.18
381.04
425.54
472.00
520-85
572.6o
627.96
57
297.09
338.23
380.70
424.74
470.72
519.08
570.38
625.33
58
297.46
338.26
380.30
423.88
46936
517.20
567-99
622.51
59
297-83
338-26
379-8?
422.98
467-93
5^5-22
565- <17
619.42
60
298.19
333.25
379-44
422.04
466.43
5I3-I3
562.80
616.32
no
PRINCIPLES AND PRACTICE
TABLE No. XXXV.
NET VALUE PER $1,000 OF A TWENTY-FIVE YEAR ENDOWMENT POLICY,
AT THE END OF VARIOUS YEARS, COMBINED EXPERIENCE. 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
22.19
45.36
69.55
94 Sl
I2I.I8
148.74
I77.52
207.60
21
22.20
45-37
69-56
94.81
I2I.I8
HS-73
'77-50
207.56
22
22.21
45.33
69-57
94.82
121.19
1^8.72
177-48
207-53
23
22.21
45-39
69.58
94.84
1 2 1. 2O
HS.73
177-48
207.51
24
22.22
45-41
69.61
94.86
121.22
148.74
177-48
207.50
25
22.23
45-43
69-63
94.88
121.23
148.74
177-47
207.47
26
22.25
45-46
69.66
94.92
121.27
148.78
I77-50
207.49
27
22.27
45-43
69.70
94.96
121.32
148.82
'77-54
207,52
28
22.29
45-52
69.74
95-03
121.39
148.90
177.61
207.60
29
22.32
45-57
69.52
95-10
121-47
149.00
177.72
207.72
30
22-34
45-63
69.90
95-21
121. 6l
149- 15
177.89
207.92
3
22-39
45-71
70.01
95-36
121-79
149.36
178.14
2OS.2O
3-2
22-43
45-8o
70.15
95-54
122. OI
149.63
178.46
208.56
33
22.49
45-93
70-34
95-S4
122-39
150.08
178.99
209.16
34
22.58
46.09
70.58
96.12
122.64
150.51
179.49
209.76
35
22.67
46.27
70.86
96.49
123.21
151.08
180.17
210.52
36
22.78
46.50
71.20
9 6 -95
123-79
51-79
180.99
211.41
37
22.92
46.78
7I-63
97-53
I2 4-53
152.66
181.95
2i2.4r
$
23.08
47.12
72-I5
98-23
125.40
I53-65
183.01
213-49
39
23.28
47-52
72.76
99-03
126.34
154.69
184.09
214-55
40
23-52
48.00
73-47
99.92
127.36
155-79
185.20
215-6=;
4i
23-79
48-53
74-20
100.80
128.34
156.80
186.23
216.66
42
24.08
49.07
74-94
101.67
129.31
157-74
187.18
217.60
43
29-39
49.61
75-67
102.54
130-25
158.72
188.30
218.73
44
24-65
50.10
76-31
103.30
131.10
'59-75
189. -8
219.72
45
24-93
50-57
76.96
104.09
132.02
160.76
190.34
220.81
46
25.16
51.02
77.69
104.93
132-95
161.78
191.42
221.90
47
25-43
5KS2
78-30
105.78
133-97
162.91
192.61
223.13
48
25-7I
52.06
79.07
106.74
'35-09
164.14
'93-93
224.49
49
26.03
52.66
79-9 1
107.79
136-31
165.50
'95-39
225.99
50
26. 3 6
53-30
80.82
108.92
I37-64
166.99
106.98
227.68
5i
26.73
54.00
8 1. So
110.17
139.10
168.61
198.76
229.56
52
27.12
54-74
82.88
"2.53
140.69
170-43
200.74
23 ! -65
53
27.54
55-56
84.05
113.00
142.47
172.44
202.93
233-92
54
28.02
56.46
85-33
114.66
144.44
174.67
205.29
2 3 6.38
55
2S52
57-4J
86-75
116.46
146.^8
177-05
207.86
239.01
56
29.06
58-50
88.30
118.45
148.89
179.60
210.58
241.83
i7
29.69
59-71
90.01
120.56
I5L34
182.31
213-47
244.81
5S
30.34
60.96
9'-77
122.76
'53-88
185-13
216.49
247.91
59
SI-OS
62.25
93.60
125.03
156-53
188.05
219-59
251.13 i
i
60 31.74
63-57
95-46
127.36
I59-24
191.06
222.80 254.44
OF LIFE INSURANCE.
Ill
TABLE No. XXXV (CONTINUED.)
NET VALUE PER $1,000 OF A TWENTY-FIVE YEAR ENDOWMENT POLICY,
AT THE 2ND OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Ag<.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thir-
teenth
year.
Four-
teenth
year.
Fifteenth
year.
Twentieth
ytar.
20
239.04
271.90
306.25
342.18
379-76
419.09
460.27
697.64
21
238.97
271.81
306.14
342.04
379.60
418.91
460.06
697-3S
22
238.92
27I-73
306.04
34I-9 1
379-45
418.74
459-87
697.17
23
238.89
271.68
305-97
34I-83
379-35
418.63
459-74
697.03
24
238.86
271.62
305.88
34i-7i
379-23
418.48
459-59
696.84
25
238.81
271-5?
35-34
341.66
379-17
418.37
459- 4 *
696.70
26
238.82
27I-57
305.80
341.62
379- o
418.32
459-4 2
696.54
27
238.85
27I-59
3o.vS2
34I-63
379- 10
418.34
459-43
696.39
28
23S.93
271.68
305-9 1
34i-7i
379-21
418.46
459-55
696.21
29
239.06
271.81
306.06
341.89
379-39
418.63
459-7 *
696.01
30
239.27
272.05
306.32
342.18
379-69
418.92
459.94
655.80
3 1
239-59
271.41
306.72
342.60
380.10
419.29
460.24
695-59
32
240.01
272.87
307.22
343-io
380.56
419.68
460.^2
695-36
33
240.69
273.62
307.89
343-73
381.15
420.15
460.88
69^.12
34
24I-35
274.30
308.66
344-47
381-78
420.69
461.30
694.84
35
242.15
275.11
309.42
345-13
382.33
42I.IO
461. 58
%4 -5 1
36
243-7
276.00 i 310.21
345-82
382.90
421-54
461.88
694.05
37
244.05
276.93
311.07
346-58
3S3-54
422.05
462.24
693.63
33
245.10
277.91
3 lI -97
347-39
384-23
422.60
462.63
693.24
39
246.13
278.87
312.82
348.12
384-83
423.04
462.88
692.67
40
247.17
279.84
3I3-75
348-94
.3S5-48
423-54
463.21
692.08
4i
248.15
280.76
314-56
349.62
386.03
423.92
463.41
691.31
42
249.06
281.62
3I5-46
350.26
386.63
424-35
463-67
690.63
43
250.17
282.65
316.26
35i-oS
387-21
424.76
463.88
689.77
44
251.14
283.58
3I7-"
351-82
387.81
425.21
464.15
688.89
45
252.19
284.58
318.01
352.58
388.42
425-64
464.36
687-77
4 6
253-29
285.62
318.97
3.S3-46
389.16
426.19
464.68
686.68
47
254-5I
286.79
320.09
354-46
390.00
426.81
465.04
685.48
48
255.86
288.13
321-35
355-6i
390.96
427.53
465.46
684.17
49
257.40
289.65
322.80
356-89
392.04
428.34
465-96
682.78
50
259.12
?9*-3S
324-39
358.32
393-23
429-24
466.51
681.29
5
261.04
293.22
326.14
359-88
394-54
430.24
467.14
679.71
52
263.14
295.26
328.05
361.60
395-9S
431-34
467-83
678.05
53
265.42
297.48
330-13
363-46
397-55
432-54
468.59
676.29
54
267.89
299.88
332.38
365-47
399-25
433-84
469.44
674-47
55
2"o-54
302.44
334-78
367.62
401.06
435-3S
470.41
672.56
56
273-35
305-17
337-34
369-92
403.02
436.82
471.49
670.60
57
276-33
308.07
340.06
372-37
405.16
438.54
472-72
668.61
53
279-44
311.09
342.90
374-99
407.44
440.40
474.08
666. 56
59
282.66
314.24
345-92
377-77
409.89
442.43
475-61
664.46
60
286.00
3^7-55
349-09
380.71
412.52
444.65
477-30
1662.31
112
PRINCIPLES AND PRACTICE
TABLE No. XXXVI.
NET VALUE PER $1,000 OF A THIRTY- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
A?<.
First
year.
Second
year.
Third
rear.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eiffhth
year.
2O
16.42
33-54
51-39
7O.OO
89.41
109.66
130.78
152.81
21
16.45
33-6o
51.48
7O.II
89-55
109.87
130.90
J52-95
22
16.47
33-64
51-53
70.l8
89.62
109.88
I3I-03
153.08
23
16.50
33-69
51.61
70.28
89-75
1 10.03
131.19
r 53--4
24
16.54
33-77
5I-7I
70.41
89.90
110.21
I3I-37
153-44
25
16.58
33-35
5I-S3
70.56
90.08
110.41
131.60
153-68
26
16.63
33-94
51-97
70.74
90.29
110.65
131.87
I53-98
2 l
16.68
34-04
52.12
70.93
90.52
110.92
132.19
J 54-33
28
16.74
34-15
52.28
71.14
90.77
III. 21
I32-5I
J54-70
2 9
16.82
34-31
52-5I
71-45
91.16
1 1 1. 66
I33-03
I55-27
30
16.89
34-46
52.73
71-73
9L5I
112. IO
*33-54
155-87
31
16.99
34-65
53-oi
72.11
91.98
112.67
I33-2I
156.64
32
17.09
34.86
53-33
72-54
92.52
"3-32
134-97
*57-52
33
17.22
35-"
53-7i
73-05
93-17
114.10
!35-S9
158.59
34
17-37
35-4i
54.16
73-66
93-93
"5.03
136.99
159.86
35
1753
35-74
54-67
73-34
94.80
116.09
138-24
161.29
36
J7-73
36-15
55-28
75-17
95-85
ii7-39
J 39- 8 3
162.95
37
17.96
36-61
55-98
76.11
97-05
118.80
141.36
164.72
3$
lS.22
37-13
56.78
77.20
98.41
120.37
143.11
166.61
39
18.52
37-75
57-73
78.46
99-93
122.06
144.96
168.54
40
18.87
38.45
58-77
7980
101.52
123.91
146.95
17065
4i
19.26
39- 2 3
59-89
81.20
103.16
125-73
148.92
J 72-75
42
19.68
40.03
61.02
82.61
104.79
I2 7-55
150.91
174.84
43
2O. II
40.82
62.14
83-99
106.41
129.38
152-93
177.07
44
20.52
41.61
63.22
85-37
108.04
131-25
i55-oi
I79-3I
45
20.94
42.38
64-33
86.77
109-73
133-21
I 57- I 9
181.69
46
21-34
43-i6
65-45
88.24
111.51
135-26
!59-4S
184.19
47
21.76
43-99
66.68
89.83
"3-43
137-47
162.01
186.90
48
22.22
44.88
67.99
91.52
115.48
I39-84
164.62
189.82
49
22.72
45-85
69.40
93-36
117.67
H2-39
167.49
192.96
50
23-25
46.88
70.90
95.28
1 20.02
145.12
170.^6
196.36
5i
23.81
47-97
73-49
97-35
122.54
148.04
173-87
200.02
5-'
24.40
49-13
74.19
99-56
12^.22
151.19
J 77.45
203-95
53
25-03
50.37
76.01
101.91
128.11
J54-57
181.26
208.13
54
25-7I
5I-70
77-94
104.46
131.21
158.18
185.30
2 ' -'.53
55
26.42
53-o8
So.oi
107.16
I 34-5 1
161.97
189.53
217.12
a
1
1
OF LIFE INSURANCE.
TABLE No. XXXVI. (CONTINUED.)
NET VALUE PER $1,000 OF A THIRTY- YEAR ENDOWMENT POLICY, AT THE
END OF VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CEXT.
4e*.
Ninth
year.
Tenth
year.
Eleventh
year.
Twelfth
year.
Thir-
teenth
year.
Four-
teenth
year.
Fifteenth
year.
Twentieth
year.
20
175.81
199.81
224.87
25I-03
278.34
306.89
336.72
507.81
21
175-93
199.92
224.97
251.11
278.42
306.95
336.77
507.80
22
176.08
2OO.O7
225.12
251.26
278-56
307.08
336.8 9
507.90
23
176.24
200.24
225.28
251.42
278.72
307-23
337-04
508.03
2 4
I76-45
200.45
225.50
251.64
278.94
307.46
337-27
508.26
25
176.71
200.73
225.79
251.94
279.26
307-79
337-61
508.57
26
177.04
2OI.O8
226.18
252.36
279-72
308.29
338.15
509.08
27
177.42
201.49
226.51
252.82
280.20
308.80
339-02
509.35
28
177.89
202.03
227.14
253-47
280.90
309-55
339-49
509.84
29
178.47
202.66
227.89
254.22
281.72
310.43
340-35
510.31
30
IK-IZ
203.42
228.64
255-I6
282.72
311.46
341-39
510.86
31
l8o.O2
204.40
229.82
256.34
283.95
312.70
342.60
511.42
3 2
181.03
205.52
231.06
257-63
285.27
3I3-99
343-8i
5"-99
33
182.24
206.87
232.49
259. 1 1
286.74
3*5-40
345-15
512.65
34
183-67
208.42
234.10
260.75
288.34
316.95
346-61
5I3-40
35
185.24
210.06
235-79
262.41
289.97
318.50
348.08
514.11
36
iSy.OI
211.91
237-65
264.26
291.78
320.26
349-75
5i4-9i
37
188.88
213.81
239-56
266.15
293-63
322.04
35^-43
5I5-70
33
190.86
215.84
241.60
268.19
295-63
323-98
353-27
516.68
39
192.91
217.94
243-73
270.31
297.72
326.00
355-i8
5I7-68
40
I95-03
220.12
245.94
272.152
299.89
328.04
357-19
518.75
4i
I97-23
222-39.
248.25
274.83
302.17
333-32
359-32
519.90
42
199.48
224.72
250-63
277.22
304-54
332-63
361.27
521.10
43
201.79
227.12
253.08
279.70
307.01
335-04
393-44
522.34
44
204 18
229.62
255.66
282.31
309.62
337-67
366.39
523-65
45
206.70
232.27
258.40
28^.10
312.42
340.42
369.20
525-05
46
209.40
235-10
261.32
288.11
3I5-47
343-44
372.03
526.56
47
212.30
238.16
264.51
291.40
318.80
346.72
375-20
528.19
48
215-43
241.50
268.01
294.97
322.38
350.25
378.60
529.96
49
218.84
245.11
271.78
298.82
326.24
354-04
382.26
53I-87
50
222.51
249.02
275.81
302.94
330-35
358-09
386.17
533-97
5i
226.47
253-I8
280.13
307-3I
334-73
362.39
370-31
536-25
52
230.68
257.61
284.70
311.96
339-37
366.95
394-71
538.74
53
235-H
262.28
289.45
316.85
344.26
371-75
399-34
541.46
54
239.84
267.20
294.59
321.99
349-39
376.78
404.22
544-4 1
55
244-74
272.32
299.86
327-34
354-72
382.04
409-34
S47-6i
PRINCIPLES AND PRACTICE
TABLE No. XXXVII.
NET ANNUAL PREMIUMS PER $1,000 FOR JOINT LIFE POLICIES, COM-
BINED EXPERIENCE, 4 PER CENT.
Younger
Age.
Equal
ages.
Difference
in ages.
$ years.
Difference
in ages.
10 years.
Difference
in ages.
15 years.
Difference
in ages.
20 years.
Difference
in ages.
25 years.
Difference
in ages.
30 years.
!i
17
18
19
2O
21
22
23
24
a
27
28
29
30
3 1
32
33
34
3 I
36
37
38
39
40
4i
42
43
44
%
I 9 .I7
19.52
19.90
20.30
20.71
21.14
21. 60
22.O7
22-57
23.10
23-65
24-23
24.84
25.48
26.16
26.87
27-63
28.42
29.25
30.14
31.08
32.07
33-'3
34-25
35-45
36.73
38.11
39-58
41.17
42.87
44.69
46 62
20.20
20.61
21.04
21.48
21.96
22-45
22-97
23-52
24.10
24.70
25-34
26.01
26.71
27.46
28.24
29.07
29-95
30.88
31.86
32.91
34-03
35-22
36.49
37.85
39-31
40.86
42.52
44.29
46.18
48.20
50.35
C.2 67.
21. 6l
22.09
22.59
23.12
23.68
24.26
24.88
25-53
26.21
26.93
27.69
28.50
29-35
30.25
31.21
32-23
33-32
34-47
35-70
37.02
38-42
39-9
41.48
43.16
44-94
46.84
48.87
5I-03
53-34
55-So
58.43
6l 27
23-5I
24.09
24.71
25-35
26.03
26.75
27-5I
28.31
29.16
30.06
31.02
32.04
33-13
34-29
35-52
36.83
38.23
39-70
41.26
42.91
44.67
46.53
48.50
50.62
52.86
55-25
57-80
60.53
63-45
66.57
69.92
77 48
26.09
26.82
27-59
28.41
29-27
30.20
3I-I7
32.22
33-33
34-52
35-78
37-"
38.53
40.02
41.61
43-29
45.06
46.95
48.95
51.08
53-33
5.5-74
58-30
61.02
63-94
67.06
70-39
73-95
77-75
81.83
86.17
29-62
30.58
31-59
32.68
33-83
35-06
36.36
37-73
39-^9
40-73
42.36
44.10
45-93
47-88
49.94
52-13
54-46
56-94
59-58
62.39
65-38
68.58
71.98
75-6i
79.48
83-61
34-55
35-82
37-i8
38.61
40.13
41-73
43-43
45-24
47-15
49.18
5i-33
53-62
56-05
58.64
61.40
64-34
67-47
70.78
74-35
78-13
82.15
4.7
48.68
cc 06
64.21
77. 2O
is
TO. 86
JJ
C.7 6C
67.7Q
8l 14
4.0
c,7.i8
60 40
7O.78
8s. 67
CQ
cc.64
67 7.2
74 41
90.28
CT
c.8 26
78 27
C2
61 o?
60 76
82 40
C3
64 02
T7 7O
86 79
C.4.
6?.i7
77 08
01.48
ce
7O C4
8l 17
06 48
c6
7 A 17
C7
77 06
82 oc
CQ
86 44
y^-y/
ino 27
6?
OI 17
Tor Rc
61
62
TOI CO
67.
IO7 22
64
117 77
6c
OF LIFE INSURANCE. 115
TABLE No. XXXVIII.
NET VALUE PER $1,000 OF AN ORDINARY JOINT-LIFE POLICY, ( EOJJAL
AGES,) COMBINED EXPERIENCE, 4 PER CENT.
Aft.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7-57
15-39
23-47
31.80
40.40
49.29
58.46
67.92
21
7.88
1 6. 02
24.42
33-09
42.04
51.28
60.8 1
70.64
22
8.21
16.67
25.41
34-44
43-74
53-35
63.26
73-48
23
8-53
17-34
26.45
35-83
45-* 2
55-51
65.81
76.44
24
8.87
18.07
27-53
37-31
47.3S
57-77
68.47
79-5 1
2.5
9.26
18.81
28.67
38.84
49-32
60.12
71.26
82-73
26
9.64
19-59
29-85
40-43
51-34
62.58
74-15
86.09
26
10.05
20.41
31.09
42.10
54-45
65.14
77.20
89-63
2S
10.46
21-25
32-37
43-84
55- r '5
67-83
80.39
93-35
2 9
10.90
22.14
33-73
45-67
57-97
70-67
83.76
97.28
30
11.36
23-08
35-H
47.58
60.42
73-66
87.33
101.44
31
11.85
24.05
36.64
49- 6 3
63.02
76.84
91.12
105.86
32
12.35
25.09
38-23
5I-78
65-77
80.22
95- 14
110.57
33
12.89
26.20
39-92
54-9
68.72
83-83
99-45
115.62
34
13.48
27.38
41-73
56-55
71.86
87.68
104.07
1 2 I. O2
35
14.09
28.63
43-66
59.18
75-22
91.82
109.01
126.76
36
14-75
29.99
45-73
62.00
78.84
96.27
114.28
132.80
3S
15-47
3i-44
47-96
65-05
82.74
101.02
119.82
I 39-4
3
16.23
33-oo
50-36
68-33
86.90
105.99
I25-5 1
145.40
39
!7-o5
34-70
52-96
71.84
91.24
111.09
'3I-3 1
I5I-79
4
17-95
36-53
55-73
75.48
9S-67
II6.24
137.08
158.16
4i
18.92
38-47
58.57
79- *3
100.08
121.30
142.77
164.45
42
'9-93
40.42
61.37
82.73
104-35
126.23
148.34
170.64
43
20.91
42-29
64.08
86.14
io8.<ji
131.02
153-78
176.71
44
21.83
44.09
66.62
89-43
112.46
I35-7I
I59.I3
182.69
45
22.75
45-79
69.10
92.65
116.41
140.36
164.44
188.63
46
23-58
47-43
71-52
95-S4
120.33
144.99
169.74
I94-56
47
24-43
49.11
74.01
99.10
124-35
149.70
I75-"
200.59
4 8
25-29
50.82
76-54
102.42
128.41
154.46
180.57
206.69
49
26.19
52-58
79-13
105-79
132-51
I59-3I
186.10
212.86
50
27.10
54-36
81.74
109.18
I3' 1 "?!
164.21
191.69
219.16
5*
28.02
56-16
84-37
112 65
140.93
169.18
197.41
225-57
52
28.95
57-97
8707
Il6.l7
145-23
174.28
203.25
232.10
53
29.89
59-86
89.82
119.74
149 66
I7 9 .49
209.21
238.66
54
30.89
61.77
92.62
123.46
154.22
184.84
215.21
245.25
55
31-87
63.70
95-52
127.26
158.86
190.27
221.20
251.77
56
32.88
65-75
98-53
131.18
163.53
195.56
227.14
258.25
57
33-98
67.88
101.63
135- I 3
168.21
200.87
233-03
264.61
58
35-09
70.02
104.67
I38-95
172.76
206.05
238-74
270.75
59
36.22
72.11
107.64
142.67
177.16
211.06
244-23
276.65
60
37-25
74.11
110.46
146.26
181.41
215.69
249-47
282.23
n6
PRINCIPLES AND PRACTICE
TABLE No. XXXIX.
NET VALUE PER $1,000 OF AN ORDINARY JOINT-LIFE POLICY (DIFFER-
ENCE IN AGES, FIVE YEARS), COMBINED EXPERIENCE, 4 PER CENT.
Is
"<5
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eiffhth
year.
20
6.92
14.08
21.48
29.13
37-03
45-19
53-62
62.32
21
7.21
14.66
22.37
30.32
38-54
47-02
55-78
64.82
22
7-51
I5-27
23.28
3 I -5 6
40.11
48-93
58.03
67.42
23
7-82
15.89
24.23
32.86
41-73
50.90
60.36
70.13
24
8.14
16.55
25.22
34.18
43-43
52.96
62.80
72-95
25
8.48
17.22
26.26
35-58
45-19
55-"
65-34
75-89
26
8.82
17-93
27-33
37-03
47.04
57-35
67.99
78.96
27
9.19
18.67
28.46
38-55
48.96
59- '9
70.76
82.18
28
9-57
19.44
29.63
40.14
50-97
62.14
73-66
85-54
2 9
9-97
20.26
30.86
41.80
53-o8
64.71
76.71
89.09
30
10.39
21. IO
32.15
43-54
55-30
67.41
79.91
92.81
31
10.83
21.98
33-50
45-38
57.62
70.25
83.29
96-75
32
11.29
22.92
34-93
47-3 !
60.08
73.26
86.86
100.91
33
11.77
23.91
- 36.43
49-35
62.68
76.44
90.65
105-33
34
12.29
24.96
3803
5i-52
65-44
79-82
94.68
1 10.04
35
12.83
26.06
39-72
53-8i
68.37
83.42
98.97
115.04
36
i3-4i
27.24
41.52
56-27
7 I -5 I
87.26
103-54
120.32
37
14.02
28.49
43-44
58.89
74-86
91.36
108.34
125-83
38
14.68
29.84
45-51
61.70
78.40
95-69
114.40
I3I-58
39
15-39
31.29
47-73
64.71
82.22
IOO.2O
118.65
I37.5I
40
16.15
32.85
50.10
67.87
86.14
104.88
124.03
143.61
4i
16.97
34-50
52-57
7i-i3
90.18
109.66
129-55
149.80
42
17.84
36.22
55-io
74.48
94-29
114.52
i35-*3
156.05
43
18.71
37-94
57-67
77-84
98.44
119.42
140.72
162.29
44
19-59
39-70
60.25
81.25
102.63
124-33
146.32
168.50
45
20.51
4i-47
62.89
84.69
106.83
129.26
151.89
174.69
46
21.40
43-27
65-53
88.13
111.03
I34-I3
I57-4I
180.83
47
22.34
45-09
68.19
91.58
115.19
138.98
162.91
186.98
48
23.27
46.89
70.82
94-97
119.30
I43-78
168.40
193.10
49
24.19
48.69
73-41
98.32
123-38
148.59
173-88
199.22
50
25.11
50.44
75-97
101.65
127.48
I53-40
179-37
205.39
5i
25-99
52-17
78.52
105.01
131.60
158.24
184.92
211. 60
52
26.89
53-93
81.13
108.43
I35-78
163.18
I90-57
217.94
53
27-79
55-75
83.80
111.90
140.06
168.20
196.32
224.30
54
28.75
57.60
86.51
"5-47
144.42
173-35
202.13
230.73
55
29.71
59-47
89.29
119.10
148.87
178.51
207-95
237.64
56
30.68
61.41
92.13
122.82
I53-36
183.71
213.82
243.64
57
3i-7o
63.40
95.06
126.56
157-87
188.94
219.71
250.11
58
32-73
65-43
97-97
130.30
162.38
194.16
225.56
2:56.48
59
33-So
67.44
100.87
134.04
166.89
199-35
231.32
262.74
60
34-82
69.41
103-74
137-74
I7I-34
204.43
236.94
268.79
OF LIFE INSURANCE.
117
TABLE No. XL.
NET VALUE PER $1,000 OF AN ORDINARY JOINT-LIFE POLICY, ( DIFFER-
ENCE IN AGES, TEN YEARS,) COMBINED EXPERIENCE, 4 PER CENT.
Older
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
25
7-93
16.14
24-59
33-34
42-35
51.69
61.31
71.24
26
8.26
16.80
25.61
34-70
44.11
53-81
63.82
74.14
27
8.61
I7-50
26.66
36-16
45-93
56.02
66. 43
77-18
28
8.97
18.21
27.78
37.65
47.82
58.32
69.16
So-35
2 9
9-32
18.99
28.94
39.21
49.80
60.72
72.03
83-69
30
9.76
19.80
30.17
40.86
51.90
63-30
75-07
87.22
31
10.14
20.61
3I-4I
42.56
54-07
65-95
78.23
90.90
3 2
10.58
21.49
32-75
44-3S
56-38
68.78
81.58
94.82
33
11.03
22.41
34.16
46.30
58.81
71.77
85.14
98.96
34
11.51
23.40
35-66
48-34
61.42
74-94
88.91
103-35
35
12. 02
24-43
37-25
50-49
64.17
78.30
9 2. 9 I
108.00
36
12.56
25-54
38.94
52.78
67.07
81.87
97.14
112.88
37
I3-H
26.71
40-73
55-22
70.19
85.68
101.58
117.92
38
13-75
27-95
42.64
57-81
73-50
89.61
106.18
123.14
39
14.40
29.29
44.68
60.59
76.92
93-72
110.91
128.46
40
15.10
30.72
46.84
63-43
80.47
97.92
115.72
133-89
4 1
I5-S5
32.22
49.07
66.37
84.08
102.16
120.61
I39-4I
42
16.63
33-75
51-33
69-33
87.70
106.44
125-54
145.01
43
17.41
35-29
53-59
72.27
9'-33
110.75
130.55
150.71
44
18.19
36.82
55-83
75-23
95-oo
115.14
135-66
156.53
45
18.98
38-34
58.10
78.22
98.75
119.64
140.90
162. ijo
46
19.74
39-88
60.40
81.32
102.61
124.29
146.31
168.61
47
20-55
41.48
62.82
84-55
106.65
129.12
151.87
174.87
4 8
21-37
43.16
65-34
87.92
110.85
134.08
I57-56
181.23
49
22.26
44-98
67.99
9*-43
"5-i7
139.16-
i63-35
18765
50
23.19
46.78
70.74
95.02
"9-57
144.30
169.15
194-13
51
24-15
48.69
73-54
98.67
123-99
H9-43
175.00
200.63
52
25.14
50.61
76.36
102.31
128.38
I54-58
180.84
207.15
53
26.13
52-54
79.16
105.90
'32-77
I59-72
186.70
213-63
54
27.12
54-45
81.92
109.51
I37-I7
164.88
192.53
220.08
55
28.10
56-32
84.46
113.12
141.60
170.02
198.34
226.47
56
29.04
58.22
87.48
116.78
146.03
175.16
204. 1 1
232.83
57
30-05
60.19
9-37
120.48
150.49
180.30
209.88
239-17
58
31-07
62.18
93-23
124.17
154-yi
185.40
215-59
245-4 1
59
32.11
64.16
96.08
127.81
159-28
190.46
221.22
251-56
60
33-"
66.10
98.87
I3I-39
163-59
I95-38
226.73
257-59
Il8 PRINCIPLES AND PRACTICE
TABLE No. XLI.
NET VALUE PER $1,000 OF AN ORDINARY JOINT-LIFE POLICY, (.DIFFER-
ENCE IN AGES, FIFTEEN YEARS,) COMBINED EXPERIENCE, 4 PER CENT.
Old-
tr
age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eiffhth
year.
30
9.28
18.88
28.80
39-04
49.62
6o-55
7I-85
83-52
3 1
9.69
19.70
30.03
40.72
51-75
63-I5
74-93
87.10
3 2
IO. II
20.54
3 J -33
42.47
53-9S
6c.88
79.17
90.88
33
10.54
21.44
32.70
44-32
56.34
68.76
Si. 60
94.89
34
11.02
22.39
34- 14
47.29
59-84
71.82
85-25
99.14
35
II.50'
23-38
35-66
48.35
61.48
75.06
89.11
103.63
36
I2.O2
24-45
37-29
50.56
64.30
78-51
93.20
108-33
37
12.58
25-54
39.01
52.92
67.30
82.17
97 48
113.20
38
13.16
26.77
40.85
55-42
70.48
85-99
101.90
118.20
39
13-79
28.06
42.82
5 8.08
73.80
89.92
106.44
123.28
40
14.47
29.44
44.91
60.85
77-20
93-94
111.02
128.43
4 1
I5-I9
30.89
47-05
63-65
80.64
97-97
115.72
133-60
42
15-94
3 2 -36
49.21
66.46
84.06
101.99
120.24
138.82
43
16.68
33-Si
5i-34
69.22
87.44
105.99
124.87
144.06
44
17.41
35-24
53-43
71.96
90.82
1 10.03
129.54
H9-35
45
18.15
36-65
55-51
74.71
94-25
114.11
134.28
154-75
46
18.85
38.06
57-6i
77-51
97-74
118.28
139.12
160.25
47
19.58
39-5
59-79
80.40
101.34
122.59
144.12
165-95
48
20.33
41.01
62.04
83.40
105.07
127.03
149.30
171.84
49
21.12
42.58
64-38
86.50
108.92
131-65
154.66
177-94
50
21-93
44.20
66.80
89.69
112.91
136.42
160.21
184.27
5i
22.77
45-87
69.29
93-03
117.06
141.38
165.98
190.80
S 2
23.64
47.60
71.89
96.49
121.38
146-55
171-95
197.49
53
24-54
49.42
74.61
100.10
125.89 151.90
178.09
204.26
54
25-5I
51-33
77-46
103.90
130-56
I57-38
184.24
211.06
55
26.50
53-31
80.44
107.80
135-32
162.89
190.41
217.81
56
27-54
55-41
83-52
in-79
140. 10
168.37
196.52
224.51
57
28.66
57-56
86.63
"5-75
144.81
I73-76
202.54
232.10
58
29.76
59.68
89.66
"9-59
149-39
179.02
208.41
237-5I
59
30.84
61.74
92-59
123.30
I53-84
184.14
214.12
243-74
60
31.88
63.70
95-40
126.91
158.17
189.11
219.67
249.78
61
32.87
65.61
98.16
130-45
162.41
193.98
225.08
255.68
62
33-85
67-5I
100.89
!33-94
166.58
198.74
230.38
261.50
63
34-84
69-39
103-59
I37-30
170.67
203.42
235.63
267.23
64
35-80
71.24
106.25
Ho.73
174.67
208.04
240.78
272.86
65
36.75
73.06
108.83
144.02
178.63
212.59
245.68
278.42
COST OF INSURANCE.
COST OF INSURANCE.
These tables for the cost of insurance, give the tabular value
of carrying the risk of a policy of $1.000 for various ages and
conditions, and during the first eight years it is in force, and
they are computed on the American Experience Table of Mor-
tality, 4 per cent interest, and on the Combined Experience
4 per cent.
Since the Contribution Plan for dividing the surplus has been
generally adopted, the cost of insurance has become one of the
most important subjects of computation. It shows the tabular
expense a company incurs in carrying a policy a year, and is an
important aid in finding what should be the surrender charge.
By comparing the cost of insurance for a given age in different
classes of policies for a series of years, one is enabled to judge
pretty correctly of their relative insurance value.
By running the eye over these tables, it will be noticed that
the cost of insurance in a whole life policy increases from year
to year, while that of a ten payment life and short term endow-
ment decreases until we get among the older ages. The reason
of this that the tabular cost of insurance depends upon two vari-
able quantities which are multiplied into each other, the proba-
bility of dying which is continually increasing and the amount
at risk which is continually decreasing. If the amount at risk
decreases with sufficient rapidity, as in a ten year endowment,
the cost of insurance is annually lessened, until the last year it
is nothing. In a twenty year endowment, the cost of insurance
increases or decreases each successive year? according to the
age of the policy-holder at the time he was insured.
OF LIFE INSURANCE,
121
TABLE No. XLII.
COST OF INSURANCE PER $1,000 OF AN ORDINARY LIFE SINGLE-PRE-
MIUM POLICY, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Cost of Insurance.
Age.
Cost of Insurance.
Age.
Cost of Insurance.
20
6.11
40
6-55
60
11.83
21
6.12
41
6.61
6l
12.40
22
6.13
42
6.68
62
13.01
23
6.14
43
6.76
63
I3-65
2 4
6.14
44
6.86
64
14.32
25
6.15
45
6.96
65
I5-03
26
6.16
46
7.09
66
15-78
27
6.17
47
7.24
67
16.55
28
6.18
48
7.41 .
68
I7-36
2 9
6.20
49
7.62
69'
18.20
30
6.21
50
7.86
70
19.06
31
6.23
5i
8.12
7i
19-93
32
6-25
52
8.41
72
20.78
33
6.27
53
8-73
73
21. 60
34
6.30
54
9.08
74
22-39
35
6.32
55
9-45
75
23-I3
36
6.36
56
9.87
37
6.40
57
10.31
38
6.44
58
10.78
39
6.49
59
11.29
TABLE No. XLII (CONTINUED.)
COST OF INSURANCE PER $1.000 OF AN ORDINARY LIFE SINGLE-PRE-
MIUM POLICY, COMBINED EXPERIENCE, 4 PER CENT.
Age.
Cost of Insurance.
Age.
Cost of Insurance.
Age.
Cost of Insurance.
20
5-42
40
6.33
60
11.78
21
5-45
41
6.38
6l
12.27
22
5-48
42
6.44
62
12.78
23
5-5i
43
6-54
63
I3-32
24
5-54
44
6.68
64
13-87
25
5-58
45
6-85
65
H-45
26
S-63
46
7.07
66
15-05
27
5-65
47
7-30
67
*5-67
28
5-70
48
7-54
68
16.29
2 9
5-74
49
7.80
69
16.91
3>
5-79
50
8.08
70
17-55
31
5-84
5i
8-37
7i
18.19
32
5-89
52
8.69
72
18.83
33
5-95
53
9.02
73
19.48
34
6.00
54
9-36
74
20.13
35
6.05
55
9.72
75
20.77
36
6.11
56
' IO.II
37
6.16
57
10.49
38
6.22
58
10.89
39
6.27
59
11.32
For net value of an Ordinary Life Single-Premium Policy, see Tables No. XVII I and XIX.
122
PRINCIPLES AND PRACTICE
TABLE No. XLIIL
COST OF INSURANCE PER $1,000 OF AN ORDINARY LIFE POLICY, DURING
VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7-77
7-78
7-79
7.80
7.80
7.81
7.82
7.84
21
7.82
7-83
7.84
7-84
7-85
7-86
7.87
7-88
22
7.87
7-87
7.88
7.89
7.90
7.91
7.92
7-94
23
7.92
7.92
7-93
7-94
7-95
7.96
7-98
8.00
2 4
7-97
7-97
7-98
S.oo
8.01
8-03
8.04
8.06
25
8.02
8.03
8.04
8.t5
8.07
8.09
8.10
8.13
26
8.08
8.09
8.10
8.12
8.14
8.I 5
8.18
8.21
27
8.14
8.15
8.17
8.19
8.20
8.23
8.26
8.29
28
8.21
8.23
8.24
8.26
8.28
8. 3 I
S-34
8-37
29
8.28
8.30
8-32
8-34
8-37
8.40
8-43
8.47
30
8.36
8.38
8.40
8-43
8.46
8-49
8-54
S.s8
31
8. 44
.8.48
S.so
8-53
S-s6
8.60
8.64
8.71
32
8-53
8.56
8.60
8.62
8.67
8.71
8.78
8.84
33
8.64
8.67
8.70
8-75
8-79
8.85
8.91
8.99
34
8-75
8.78
8.82
8.87
8.92
8-99
9.07
9-i5
35
8.86
8.91
8-95
9.02
9.08
9.16
9-23
9-33
36
9.00
9.04
9.11
9.17
9-25
9-32
9.42
9-52
37
9-i3
9.20
9.26
9-34
9.42
9-52
9.62
9-75
38
9-3o
9-36
9-45
9-52
9.62
9-73
9.86
10.00
39
9-47
9-56
9- 6 3
9-73
9-84
9-97
10.12
10.30
40
9.67
9-75
9-85
9.96
10.09
10.24
10.42
10.63
4i
9.88
9.98
10. 08
IO.22
10.37
10.56
10.76
II.OI
42
IO.II
10.22
10.36
10.51
10.70
10.91
ii. 16
11.46
43
10.36
lO.SI
10.66
10.85
n. 06
11.31
11.62
11.97
44
10.66
I0.8l
II. OI
11.22
11.48
11.79
12.15
12.54
45
10.98
II. IS
11.40
11.66
11.98
12.34
12.74
13.18
46
"37
"59
11.85
12. IS
12.54
12.95
13-40
13.89
47
11.79
12.06
12.39
12.76
i3-!7
13-63
14-13
1468
48
12.28
12. 6l
12.99
13-41
13.88
H-39
H-95
15-56
49
12.85
13.24
13-67
14.14
14.66
15-23
15-85
16.53
50
I3-50
J 3-94
14.42
H-95
15-54
16.17
16.86
17-59
5i
14.23
14.72
15.26
iS-86
16.54
17.21
17.96
18.75
52
15-05
15.60
16.21
16.87
I7-58
18.35
19.16
20.04
53
15-95
16.58
17-25
17.99
18.77
19.60
20.50
21.46
54
16.97
17.66
18.41
19.22
20.07
20.99
21-97
23.01
55
18.10
18.87
19.69
20.57
21.51
22.52
23-59
24.71
56
19.36
20.20
21.10
22.07
23.10
24.20
25-35
26.56
57
20.75
21.67
22.67
23-73
24.85
26.04
27.28
28.59
58
22.28
23-3I
24-39
25-55
26.77
28.05
29-39
30.82
59
23-99
25.11
26.30
27.56
28.87
30.26
3i-73
33-26
60
25-87
27.10
28.40
29-75
3i-i8 ,
32.69
34-7
35-91
OF LIFE INSURANCE.
123
TABLE No. XLIV.
COST OF INSURANCE PER $1,000 OF A TEN-PAYMENT LIFE POLICY,
DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
S'.cond
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
7.64
7-52
7-39
7-25
7.09
6.92
6-75
6-57
21
7.70
7-56
7-43
7.28
7-12
6-95
6.78
6.58
22
7-74
7.60
7.46
7-31
7.16
6.99
6.80
6.61
23
7.78
7-65
7-50
7-35
7.19
7.02
6.83
6.64
24
7-83
7.69
7-55
7.40
7-23
7.06
6.87
6.66
25
7-88
7-74
7.60
7-44
7.27
7.09
6.90
6.69
26
7-94
7.80
7-65
7-49
7-32
7-i3
6.94
6-73
2 7
8.00
7-85
7.71
7-54
7-37
7.18
6.99
6.77
28
8.06
7.92
7.76
7.60
7.42
7.24
7-03
6.81
2 9
8.13
7-99
7-83
7.66
7.48
7-29
7.08
6.86
3
8.21
8.05
7.90
7-73
7-55
7-35
7-i5
6.92
3 1
8.28
8.13
7.98
7.81
7.62
7.42
7.21
6.99
3 2
8.37
8.23
8.06
7.88
7.70
7-50
7.29
7.06
33
8.47
8.32
8.15
7.98
7-79
7.60
7-37
7.14
34
8.57
8.41
8.26
8.08
7.90
7.69
7-47
7-23
35
8.68
8-53
8-37
8.20
8.01
7.81
7-57
7-33
36
8.81
8.65
8.50
8.32
8.14
7-92
7.69
7-44
37
8.94
8.80
8.63
8.47
8.27
8.06
7.82
7-57
38
9.10
8-95
8.80
8.61
8.42
8.20
7.98
7.71
39
9.27
9-i3
8.96
8.78
8-59
8.38
8.14
7.89
40
9.46
9-3i
9- T 5
8.97
8.78
8.57
8-35
8.09
4i
9.66
9-5 1
9-35
9.19
9.00
8.80
8-57
8.32
42
9.88
9-74
9.60
9-43
9.26
9.06
8.84
8-59
43
10.13
10.00
9.86
9.71
9-54
9-36
9-i5
8.91
44
10.42
10.29
10.17
10.03
9.88
9.71
9-5i
9.26
45
10.72
10.63
10.52
10.40
10.27
IO. 12
9.92
9-65
46
11.09
II. OO
10.92
10.83
10.70
10-57
10.37
10.09
47
11.50
"45
11.40
n-33
11.23
II.08
10.86
10.57
48
11.98
11.96
11.94
11.88
11.79
11.64
11.42
II. IO
49
I2 -53
12.52
12.54
12.51
12.42
12.27
12.03
11.68
5
13.16
13.21
13.22
13.20
I3-I3
12-97
12.71
12.32
51
I3-87
13-94
13.98
13.98
13.90
13-74
13.46
13.01
52
14.66
14-70
14.83
14.83
14.74
H-59
14.27
13-77
53
'5-5.5
15.68
15-77
15-79
I5-72
15-53
15- !7
14.61
54
16.54
16.70
16.82
16.85
16.77
16.56
16.16
15-5*
55
17.64
17.84
17.97
17.94
17.94
17.70
17.24
16.50
56
18.86
19.10
19.25
I9-3I
19.22
18.95
18.43
17-57
57
20.22
20.48
20.67
20.74
20.69
20.33
19.72
'8-73
58
21.71
22.03
22.24
22.32
22.20
21.83
21.13
2O.OI
59
23-38
23-73
23.92
24.06
23.92
23-49
22.70
21.40
60
25.22
25.62
25.90
25.07
25.81
25-33
24.41
22.91
124
PRINCIPLES AND PRACTICE
TABLE No. XLV.
COST OF INSURANCE PER $1,000 OF A TEN- YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
Ninth
year.
20
7.19
6-59
5-95
5.26
4-52
3-73
2.90
2.OO
1.03
21
7.24
6.6 3
5-99
5-29
4-55
3-76
2.92
2.OI
1.04
22
7.29
6.68
6.03
5-33
4-59
3.80
2-94
2.03
1.05
23
7-34
6.72
6.07
5-37
4-63
3-83
2.97
2.05
1. 06
24
7-38
6-77
6.12
5-42
4.67
3-87
3-00
2.07
1.08
2 5
7-43
6.82
6.17
5-46
4.71
3-90
3-03
2.IO
1.09
26
7-49
6.88
6.22
5-52
4.76
3-94
3-07
2.13
i. ii
27
7-56
6.94
6.28
5-57
4.81
3-99
3-"
2.15
1. 12
28
7.62
7.00
6-34
5-63
4.86
4.04
3-i5
2.18
I.I4
2 9
7.69
7.07
6.41
5-69
4-93
4.09
3-i9
2.22
1.16
30
7-77
7.14
6.48
5-77
4-99
4-15
3- 2 4
2.26
1.18
31
7-85
7-23
6.56
5-84
5.06
4.22
3-30
2.30
i. 20
32
7-93
7-32
6.65
5-92
5-H
4.28
3-36
2-34
1.23
33
8.04
7.41
6-74
6.01
5-22
4-37
3-42
2-39
1.26
34
8.14
7-5i
6.84
6.ii
5-32
4-45
3-50
2-45
1.29
35
8.25
7-63
6-95
6.23
5-42
4-55
3-58
2.51
1.32
36
8.38
7-75
7.09
6-35
5-54
4-65
3-67
2.58
1-36
37
8.51
7.90
7.22
6-49
5-66
4.76
3-76
2-65
1.41
38
8.68
8.05
7-38
6.63
5.81
4-89
3-88
2.74
1.46
39
8.84
8.23
7-54
6-79
5-96
5-4
4.00
2.84
I-5 1
40
9.04
8.41
7-73
6-97
6.14
5-i9
4.14
2-95
1.58
4i
9-23
8.61
7-93
7.18
6-33
5-38
4-3i
3.08
1.66
42
9-45
8.84
8.16
7.40
6.56
5-59
4-49
3-23
i-75
43
9.70
9.10
8.42
7.67
6.81
5-83
4.71
3-40
1.84
44
9.99
9-38
8.72
7.96
7.10
6.ii
4.96
3-59
1.96
45
10.30
9.72
9-5
8.30
7-44
6-43
5-24
3.80
2.08
46
10.66
10.09
9-44
8.70
7-83
6.80
5-55
4.04
2.22
47
11.07
10.52
9.89
9.16
8.27
7.20
5-9i
4-32
2. 3 8
48
"54
1 1. 02
10.41
9.67
8.76
7-65
6.29
4.62
2-55
49
12.09
n-59
10.99
10.24
9-3i
8.16
6-73
4-96
2-75
50
12.72
12.24
11.63
10.87
9-93
8-73
7-23
5-33
2.96
5i
13.42
1295
12.35
"59
10.61
9-36
7-77
5-75
3-20
52
14.20
13-75
I3-I7
12.39
11.38
10.07
8.38
6.22
3-48
53
15.08
14.66
14.07
13.28
12.23
io.S>
9.06
6-75
3-78
54
16.06
15-65
15.08
14.27
13.18
"73
9.82
7-33
4.12
55
I7-I5
16.77
16.19
15-36
14.23
12.70
10.66
7-99
4-50
56
18.37
18.00
17.42
16.59
15.40
I3-78
1 1. 60
8.71
4-92
57
19.72
19-37
18.80
17.94
16.71
14.99
12.64
9-52
5-40
58
21.20
20.89
20.33
19-45
18.16
16.32
13.80
10.43
5-93
59
22.86
22.58
22.03
21.12
19.76
17.80
15.11
11.44
6-53
60
24.69
2445
23.90
22-97
2 i-53
19.47
16.56
12.58
7.20
1
i
OF LIFE INSURANCE.
TABLE No. XLVI.
COST OF INSURANCE PER$I,OOO OF A FIFTEEN- YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7-45
7.12
6.77
6.40
5-99
5-56
5.10
4 .6l
21
7-50
7.17
6.82
6-44
6.03
5-61
5-15
4-65
22
7-55
7-22
6.86
6.48
6.08
5-65
5-^9
4.70
23
7.60
7.27
6.91
6-54
6.13
5-70
5-24
4-75
2 4
7-65
7-3'
6.97
6-59
6.19
5-76
S-29
4-79
25
7.70
7-37
7.02
6.65
6.2 5
5-8i
5-35
4-85
26
7.76
7-43
7.08
6.71
6-31
5-87
5-4i
4.91
27
7-83
7-50
7-i5
6.77
6-37
5-94
5-48
4.98
28
7.89
7-57
7.22
6.84
6.44
6.02
5-55
5-04
2 9
7-97
7.64
7.29
6.92
6-53
6.09
5-62
S-
3
8.05
7.72
7-38
7.01
6.61
6.17
5-71
5-21
3 1
8.13
7.81
7-47
7.10
6.70
6.27
5.81
5-3i
32
8.22
7.91
7-57
7.20
6.81
6.38
5-92
5-4i
33
8.32
8.01
7.67
7-3i
6.92
6.50
6-03
5-53
34
8-43
8.12
7-79
7-43
7-05
6.62
6.16
5-65
35
8-54
8.25
7.91
7-57
7.18
6.76
6.30
5-79
36
8.68
8.38
8.06
7.71
7-34
6.91
6-45
5-94
37
8.82
8-54
8.22
7.88
7-50
7.08
6.62
6** *
.12
33
8.98
8.70
8.40
8.05
7.68
7.27
6.82
6. 3 I
39
9-15
8.89
8.58
8.25
7.88
7-48
7-03
6-53
40
9-35
9.08
8.79
8.46
8.ii
7.71
7.28
6.78
4i
9-55
9-30
9.01
8.71
8.36
7-99
7-56
7-07
42
9-79
9-54
9.28
8.98
8.66
8.29
7.88
7.41
43
10.04
9.82
9-57
9-3
8-99
8.64
8.26
7.80
44
10.34
IO.I2
9.91
9- 6 5
9-37
9.06
8.68
8.23
45
10.66
10.48
10.28
10.06
9.82
9-53
9.17
8.71
46
11.04
10.88
10.72
10.54
10.35
10.05
9-70
9.26
47
"45
"34
11.23
11.08
10.89
10.64
10.30
9.87
48
11.94
11.88
ii. 81
11.69
"53
11.30
10.98
10.54
49
12.51
12.49
12.46
12.38
12.24
12.04
"73
11.30
50
I3-I5
13.18
13.18
I3-H
13.04
12.86
12.57
12.14
5i
13.88
13-95
13-99
13-99
x 3-93
I3-78
I3-50
13-07
52
14.68
14.81
14.90
14.94
14.92
14.79
14-53
14.11
53
I5-58
15-77
i5-9i
16.00
16.01
I5-9 1
,15.68
1^.26
54
16.60
16.83
17.04
17.17
17.22
17.17
16.95
16.54
55
17.72
18.02
18.28
18.47
iS-57
18.55
18.37
17.96
56
18.97
19-34
19.65
19.91
20.07
20.09
19-93
19-53
57
20.35
20.79
21. 18
21.50
21.72
21.79
21.66
21.26
58
21.88
22.40
22.88
23.27
23-55
23.67
23-57
23-3
59
23-58
24.19
24-75
25-23
25-57
25-74
25.70
25-35
60
25.46
26.17
26.82
27-37
27-79
28.05
28.05
27.72
126
PRINCIPLES AND PRACTICE
TABLE No. XLVII.
COST OF INSURANCE PER $ i, ooo OF A TWENTY- YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Affe.
First
year.
Second
year.
Third
year.
Fourth
)ear.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
7-58
7-38
7.17
6-95
6.70
6.44
6 17
5-88
21
7.62
7-43
7.22
6.99
6-75
6.50
6.22
5-93
22
7.67
7.48
7.27
7.04
6.80
6-55
6.27
5-98
23
7.72
7-53
7-32
7.IO
6.86
6.60
6-33
6.04
24
7-78
7-58
7-37
7-15
6.92
6.67
6.40
6. 10
25
7-83
7.64
7-44
7.21
6.98
6-73
6.46
6.17
26
7.89
7.70
7-50
7-28
7-05
6.80
6-53
6.25
27
7.96
7-77
7-57
7-36
7.12
6.88
6.62
6-33
28
8.02
7-84
7.64
7-43
7.20
6.96
6.70
6.42
29
8.10
7.92
7.72
7-5i
7.29
7-05
6.79
6.52
30
8.18
8.00
7.81
7.61
7-39
7-i5
6.90
6.62
31
8.26
8.09
7.91
7.71
7.48
7.26
7.01
6-75
32
8-35
8.19
8.01
7.8!
7.60
7-38
7.14
6.87
33
8.46
8.30
8.ii
7-93
7.72
7-5i
7.27
7-C2
34
8-57
8.40
8.24
8.06
7.87
7-65
7-43
7.17
35
8.68
8.1:4
8-37
8.21
8.02
7-82
7-59
7-35
36
8.82
8.67
8-53
8.36
8.19
7-99
7.78
7-54
37
8.96
8.84
8.69
8.c 4
8.37
8.18
7-97
7.76
38
9-*3
9.00
8.88
8.72
8.57
8-39
8.21
7-99
39
9-30
9.20
9.07
8.94
8.79
8.64
8.46
8.28
40
9-5
9-39
9-29
9.16
9.04
8.90
8-75
8.56
4i
9.71
9.62
9-52
9-43
9-32
9.21
9.08
8-94
42
9-94
9.87
9.80
9.72
9.64
9-55
9.46
9-36
43
10.20
10.16
10.10
10.06
IO.OO
9-95
9.90
9.84
44
10.50
10.47
10.46
10.42
10.42
10.42
10.41
10.38
45
IO.82
10.84
10.85
10.87
10.91
10.95
10.97
10.97
46
II. 21
11.24
11.30
11.38
11.46
"54
n. 60
11.64
47
11.63
11.72
11.83
11.96
12.09
12.21
12.31
12.39
48
12.12
12.27
12.44
12. 6l
12.78
12.94
13.10
13.21
49
12.69
12.90
13.11
13-34
13-55
13-77
13-97
14.14
50
13-34
13.60
I3-87
14.14
14.42
14.69
14.94
i;.i6
5i
14.08
H-39
14.71
15-05
15-38
i<c.7i
16.02
16.26
52
14.89
15.26
15.66
16.05
16.45
16.84
17.20
17-53
53
15.80
16.25
16.70
17.17
17.64
18.08
18.52
18.91
54
16.82
17-33
17.86
18.40
18.93
19.47
19.97
20.43
55
17-95
18.55
i9-'5
19.16
20.38
20.99
21.58
22.11
56
19.22
19.88
20.56
21.27
21.97
22.67
23-34
23-95
57
20.61
21.36
22.14
22.93
23-74
24-53
25.28
25.98
58
22.15
23.00
23.88
24.78
25.68
26.56
27.41
28.23
59
23.86
24.81
25.80
26.80
27.80
28.79
29.78
30.69
60
25-75
26.82
27.91
29.02
30.14
31.27
32-37
33-40
OF LIFE INSURANCE. I2 7
TABLE No. XLVIII.
COST OF INSURANCE PER $1,000 OF A TWENTY-FIVE YEAR ENDOWMENT
POLICY, DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
4r<.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
7.65
7-33
7.40
7.26
7.II
6-95
6.78
6.60
21
7.70
7-58
7-45
7-31
7.16
7.00
6.84
6.6 5
22
7-75
7-63
7-50
7-36
7-21
7.06
6.89
6.72
23
7.80
7.68
7-55
7.42
7.27
7.12
6.96
6.78
24
7-85
7-73
7.61
7.48
7-33
7.18
7.02
6.85
25
7.90
7-79
7.67
7-54
7.40
7-25
7.09
6.92
26
7.96
7-85
7-73
7.61
7-47
7-33
7.17
7-01
27
8.03
7.92
7.81
7.68
7-55
7.41
7.26
7-IO
28
8.10
7-99
7.88
7-76
7-63
7-50
7-3 6
7.19
29
8.17
8.07
7.96
7-85
7-73
7.60
7-45
7-31
3
8.25
8.15
8.05
7-94
7-83
7.69
7-57
7.42
31
8-34
8.24
8.15
8.05
7-93
7.81
7.68
7-56
32
8-43
8-35
8.26
8.15
S.os
7-94
7-83
7.70
33
8-54
8.46
8.36
8.28
8.18
S.oS
7-97
7-86
34
8.65
8.56
8-49
8.41
8-33
8.23
8.14
8.03
35
8.76
8.70
8.63
8.56
8.48
8.41
8.31
8.22
36
8.90
8.84
8.79
8.72
8.66
S.sS
8-51
8.42
37
9.04
9.00
8-95
8.90
8.84
8.79
8.72
8.66
33
9.21
9.17
9.14
9.09
9-05
9.01
8.96
8.92
39
9-38
9-36
9-33
9-3i
9.28
9.26
9.24
9-23
40
9-58
9-56
9-56
9-54
9-55
9-54
9-55
9-56
4 1
9-79
9-79
9.80
9.82
983
9-87
9-9
9-95
42
10.03
10.04
10.08
IO. II
10.17
10.23
10.30
10.41
43
10.28
iQ-33
10.38
10.46
10.54
10.64
10.78
10.92
44
10.58
10.65
10.74
10.84
10.97
11.13
11.31
11.50
45
10.91
11.02
11.14
11.29
11.48
11.69
11.91
12.14
46
11.29
"43
1 1. 60
ii.Si
12.05
12.31
12.58
12.89
47
11.72
11.91
12.14
12.40
12.69
13.00
I3-32
13.66
48
12.24
12.46
12.75
13.07
13.40
I3-76
14.18
14-54
49
12.78
I3-I3
13-44
13.80
14.20
14.62
15.09
15-53
50
13-44
13-80
14.20
14.63
15.09
15-57
16.09
16.61
5i
14.17
H-59
15-05
15-55
16.07
16.63
17.21
17.79
5 2
14.99
15-47
16.00
16.56
17.16
17.79
18.43
19.11
53
15.90
16.46
17.06
17.70
iS-37
19.06
19.80
20.55
54
16.92
17-55
18.23
18.94
19.69
20.48
21.30
22.14
55
18.05
18.77
19.52
20.30
21.15
22.03
22.95
23.89
56
19.32
20. ii
20.94
21.83
22.77
23-74
24-75
25-79
57
20.71
21-59
22.52
23-51
24-54
25.62
26.73
27.87
58
22.25
23-23
24.26
25-35
26.49
27.67
28.89
30.16
59
23.96
25-04
26.19
27.38
28.62
29.92
31.28
32.66
60
25-85
27.04
28.30
29.60
30.96
32.40
33-88
35-39
i
128
PRINCIPLES AND PRACTICE
TABLE No. XLIX.
COST OF INSURANCE PER $1,000 OF A THIRTY- YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
7.69
7.62
7-54
7.46
7-36
7.26
7.16
7-05
21
7-74
7.67
7-59
7-50
7.41
7-32
7.22
7-10
22
7-79
7.72
7.64
7-55
7-47
7-37
7.27
7.17
23
7.84
7-77
7-69
7.61
7-53
7-44
7-34
7.24
2 4
7.89
7-82
7-75
7.67
7-59
7*1
7.41
7-31
25
7-95
7.88
7.81
7-74
7.66
7.58
7.48
7-39
26
8.01
7-95
7.88
7.81
7-73
7-65
7-57
7-48
27
8.07
8.01
7-95
7.89
7-81
7-73
7.66
7-57
28
8.14
8.09
8.03
7-96
7.90
7-83
7.76
7.67
2 9
8.22
8.17
8.ii
8-05
7-99
7-93
7-85
7-79
30
8.30
8.25
8.20
8.15
8.09
8.02
7-97
7.91
31
8.38
8-34
8-30
8.25
8.20
8-15
8.09
8.05
32
8.48
8-44
8.40
8.36
8.32
8.27
8.24
8.19
33
8-58
8-55
8.51
8.48
8-45
8.42
8-39
8.36
34
8.69
8.66
8.64
8.62
8.60
8.58
8.56
8-53
35
8.81
&8o
8.78
8.77
8.76
8-75
8-74
8-73
36
8. 94
8-93
8-94
8-93
8-94
8-93
8-94
8-94
37
9.09
9.10
9.10
9.12
9.12
9.14
9-*5
9.19
38
9-25
9.27
9.29
9-3i
9-33
9-37
9.41
9-45
39
9-43
9.46
9-49
9-52
9-56
9.62
9.68
9-77
40
9-63
9.66
9.71
9.76
9-83
9.90
10.00
IO. II
4i
9.84
9.89
9-95
10.03
IO. II
10.23
10.36
10.51
42
10.07
10.14
10.23
10.33
10.46
1 0.60
10.77
10.98
43
10.33
10.43
!o-53
10.63
10.83
1 1. 02
11.25
11.51
44
10.63
10.74
10.90
ii. 06
11.26
11.51
"79
12.10
45
10.95
II. 12
11.29
11.51
11.77
12. IO
12.40
12-75
46
".-34
11.52
"75
12.03
12-35
12.69
13-07
I3. 4 8
47
11.76
12.00
12.29
12.62
12.99
13-39
13.82
14.29
48
12.25
12.56
12.90
13.29
i3-7i
14.16
14.66
5- l 9
49
12.83
I3-I9
13-59
14.03
14.50
15.02
I5-58
16.18
50
I3-48
13.90
M-35
14-85
J5-39
15.98
16.61
17.27
5i
14.21
14.68
15.20
15-77
'6-37
I7-03
17-73
18.46
53
15-03
I5-56
16.15
16.78
17-47
I8.I9
18.96
19.78
53
15-94
16.55
17.20
17.91
18.66
19.46
20.32
21.22
54
16.96
17.64
18-37
'9-J5
19.98
20.87
21. Si
22.81
55
18.09
18.85
19.66
20.51
21.44
22.42
23-45
24-54
"
OF LIFE INSURANCE.
129
TABLE No. L.
COST OF INSURANCE PER $1,000 OF AN ORDINARY LIFE POLICY, DURING
VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth *
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7-25
7.28
7-32
7-37
7.41
7.46
7-51
7.56
21
7-33
7-37
7.41
7.46
7-50
7-55
7.60
7-66
22
7.4i
7.46
7-51
7-55
7.60
7-65
7.71
7-77
23
7-5i
7-56
7.60
7-65
7.71
7-77
7-83
7-89
24
7.61
7.66
7.71
7.76
7.82
7.88
7-95
8.02
25
7.71
7.76
7 .82
7.88
7-94
8.01
8.08
8.15
26
7.82
7.88
7-94
8.00
8.07
8.14
8.21
8.29
27
7-94
8.00
8.06
8.13
8.20
8.28
8-35
8.42
28
8.07
8.13
8.20
8.27
8-35
8.42
8.49
8.57
29
8.20
8.27
8-34
8.42
8.49
8-57
8.65
8-73
3
8-35
8.41
8-49
8.57
8.64
8.72
8.80
8.88
3 1
8.50
8-57
8.65
8.73
8.81
8.89
8.96
9.04
32
8.66
8.74
8.81
8.89
8.97
9-05
9-13
9.21
33
8.83
8.90
8.98
9.07
9.14
9-23
9-3i
9-38
34
9.00
9.08
9.16
9.24
9-33
9.40
9.48
9-56
35
9.18
9.26
9-34
9-43
9-5i
9-58
9.67
9-77
36
9-37
9-45
9-54
9.62
9.70
9.78
9.88
10.04
37
9-56
9- 6 5
9-74
9.81
9.90
10.00
10. 16
10.38
38
9.78
9.86
9-94
10.03
10.13
10.29
10.51
10.78
39
9.99
10.07
10.16
10.27
10.43
10.65
10.92
11.27
40
IO.2I
10.30
19.41
'0-57
10.80
11.07
11.42
11.79
4 1
10-45
10.56
10.72
10.96
11.23
"59
11.97
12.37
42
10.72
10.89
11.13
11.41
11.77
12.15
12.56
12.99
43
11.07
11.30
n-59
11.96
12-34
12.76
13.20
13.66
44
11.50
11.79
12. 16
12.55
12.97
13.42
13.90
14.40
45
11.99
12.37
12.77
13.20
i3- 6 5
14.14
14.65
15.20
46
12.60
13.01
13-44
13.90
14.40
14.92
15.48
16.08
47
13.26
13 7<>
14.17
14.67
15.21
I5-78
16.38
17.00
48
13-97
H-45
14.96
15.51
16.09
16.71
17-33
18.01
49
14-75
15-27
15-83
16.42
i7-5
17.69
18.38
19.10
50
15-59
16.16
16.77
17.41
18.06
18.77
19.50
20.24
5'
16.52
17.14
17.80
18.46
19.18
*9-93
20.69
21.49
52
17-53
18.20
18.88
19.62
20.40
2I.1O
21.98
22.83
53
18.64
1933
20.09
20.87
21.66
22.50
23-38
24-34
54
19.81
20.60
21-39
22.19
23.06
23-95
24.94
25.-97
55
21. II
21.93
22.76
23-54
24.56
25-58
26.63
27-75
56
22.51
23-36
24.26
25.21
26.25
27-33
28.48
29.67
57
24.OO
24-93
25.90
26.97
28.08
29.26
30.48
31-75
58
25-64
26.63
27-73
28.88
30-09
31-34
32-65
34.02
59
27.42
28.55
29.72
30.99
32.26
33-6i
35-02
36.46
60
29.41
30.62
31.92
33- 2 4
34-63
36.08
37-57
39-"
61
3I-58
32-92
34.28
35-72
37-22
38.75
40-34
41.94
'62
33-98
35-39
36.88
38.42
40.00
41-65
43-40
44-95
63
36.58
38.11
30-71
41-34
43-04
44-75
46.46
48.21
6 4
39-43
41.08
42.76
44-52
46.29
48.06
49.87
51.69
65
42-53
44.28
46.10
47-93
49-76
51.64
53-52
55-42
130
PRINCIPLES AND PRACTICE
TABLE No. LI.
COST OF INSURANCE PER $1,000 OF A TEN- PAYMENT LIFE POLICY, DURING
VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Afft.
first
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
7.II
7.OO
6.88
6.76
6.62
6.47
6.31
6.14
21
7.19
7.08
6.96
6.83
6.69
6-54
6-37
6. 20
22
7.27
7.16
7.04
6.91
6-77
6.61
6-44
6.26
23
7-36
7-25
7.12
6.99
6.84
6.69
6.51
6-33
24
7.46
7-34
7.22
7.08
6.94
6-77
6-59
6.40
25
7-56
7-44
7-3i
7.17
7-02
6.86
6.67
6-47
26
7-66
7-54
7.42
7.27
7.12
6-95
6.76
6-55
27
7-77
7.66
7-52
7-38
7-22
7-5
6.85
663
28
7.90
7-77
7.64
7-49
7-33
7-i5
6-94
6.71
29
8.03
7.90
7.76
7.61
7-44
7-25
7-03
6-79
30
8.16
8.04
7.90
7-74
7-55
7-36
7-13
6.87
31
8.31
8.18
8.03
7.86
7.68
7-47
7-23
6.96
32
8. 4 6
8-33
8.17
8.00
7.80
7-58
7-33
7-05
33
8.62
8.48
8.32
8.14
7-93
7.70
7-43
7-i3
34
8.79
8.64
8.47
8.28
8.07
7-82
7-54
7-23
35
8.96
8.8j
8.63
8-43
8.20
7-94
7-65
7-34
36
9-'5
8.98
880
8.^9
8-34
8.07
7.78
7-49
37
9-38
9.17
8-97
874
8-49
8.22
7.96
7-69
3
9-54
9-36
9-i5
8.92
8.67
8-43
8.19
7-93
39
9-74
9-55
9-34
9.11
8.90
8.69
8.46
8.23
40
9-95
9.76
9-55
9-36
9.19
8.99
8.81
8-55
4i
10.19
IO.OO
9-83
9-68
9-53
9-38
9.17
8.89
42
10.45
10.30
10.19
10.06
9-95
9-79
9-56
9.26
43
10.78
10.69
10.60
10.52
10.41
10.23
9-99
9-6?
44
11.19
11.13
II. IO
11.03
10.90
10.72
10.45
10.10
45
11.67
11.68
11.65
"57
11.44
11.24
10.95
10.57
46
12.27
12.27
12.24
12. 16
1 2. 02
ii. 81
11.50
11.07
47
12.90
12.91
12.89
12. 8l
12.66
12.43
12.09
1 1. 60
4 8
13-59
13.61
13-59
13-51
13-36
13.10
12.71
12. IS
49
14-34
14.38
14-36
14.28
14.11
13.82
13-39
12.80
50
if.i6
15.21
15.20
15.12
14.91
14.60
14.12
!3-44
5i
16.05
16.12
16.12
16.01
15.80
15-44
14.89
4-l3
52
17.04
17.11
17.09
16.99
16.75
16.33
15-72
14.88
53
18.11
18.17
18.17
18.05
17.76
i7-3o
16.63
I5-72
54
19.25
19-34
19-33
19.17
18.86
18.35
17.64
16.61
55
20. 5 1
20. 6 1
20.56
20.40
20.05
19-53
18.73
17-59
56
21.87
21.95
21.92
21-73
21.40
20.81
19-93
18.64
57
23-32
23.42
23-39
23.24
22.86
22.22
21.22
19.79
58
24.91
25-03
25-05
24.87
24.47
23-75
22.U4
21. 02
59
26.65
26.83
26.85
26.68
26.22
25-42
24.17
22.34
60
28.60
28.80
28.84
28.64
28.14
27.24
25.84
23-79
OF LIFE INSURANCE. jj,
TABLE No. LII.
Cos/- OF INSURANCE PER $1,000 OF A TEN-YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
6.70
6.16
5-58
4-95
4.28
3-55
2.76
1*1
.21
6.78
6.24
5-65
5-02
4-34
3.60
2.8o
1.94
22
6.86
6.32
5-73
5-o8
4.40
3-66
2-85
1.98
23
6.96
6.40
5-8i
5-i6
4-47
3-72
2.90
2.O2
2 4
7-05
6.49
5-89
5-24
4-54
3-78
2.96
2.05
25
7.14
6-59
5-98
5-33
4.62
3-85
3-oi
2.09
26
7-25
6.69
6.08
5-42
4.71
3-92
3-o7
2.14
27
7-36
6.80
6.19
5-52
4-79
4.00
3-i3
2.18
28
7-49
6.92
6.30
5-62
4.89
4.08
3-i9
2.22
2 9
7.61
7.04
6.41
5-73
4-99
4.16
3.26
2.28
3
7-75
7.17
6-54
5-85
5-09
4-25
3-34
2-33
31
7.89
7-3i
6.67
5-97
5-20
4-35
3-4i
2.38
32
8.05
7.46
6.80
6.09
5-3i
4.40
3-49
2-44
33
8.21
7.60
6-95
6.22
5-42
4-54
3-57
2-49
34
8-37
7-77
7.10
6.36
5-55
4-65
3-65
2-55
35
8.55
7-93
7-25
6.51
5-68
4.76
3-74
2.63
36
8-73
8.10
7.42
6.65
5-8i
4.87
3-84
2.71
37
8.91
8.29
7-59
6.81
5-95
5-oo
3-96
2.82
38
9.12
8.48
7.76
6.97
6.ii
5-17
4-i3
2-95
39
9-32
8.67
7-95
7.16
6.31
5-38
4-3i
3.10
40
9-54
8.88
8.16
7.40
6.56
5.62
4-55
3-27
4i
9-77
9.12
8-43
7.69
6-85
5-9i
4-79
3-45
42
10.03
9-42
8-77
8.03
7.21
6.23
5-05
3-66
43
10.36
9-79
9-^5
8-45
7.60
6.58
5-34
3-88
44
10.77
10.22
9-63
8.90
8.02
6-95
5-67.
4.12
45
11.24
10-75
10.14
9.40
8.48
7-37
6.02
4-38
46
11.82
11.32
10.71
9-94
8-99
7-83
6.41
4.67
47
12.24
"95
11.32
10.52
9-54
8-33
6.83
4-99
48
i3-i3
12.63
11.98
11.17
10.15
8.88
7.28
5-33
49
13-87
13-37
12.71
11.88
10.81
9.46
7.80
5-7i
50
14.69
14.18
13-52
12.65
"53
IO.I2
8.36
6.12
5i
15-57
15-07
H-39
13.48
12.32
10.83
8.94
6-57
52
16.55
16.04
15-33
14.40
I3-I7
11.58
9-58
7.06
53
17.61
17.08
16.36
15-39
14.09
12.42
10.29
7.62
54
18.74
18.23
17.49
16.45
15.10
13-34
II. IO
8.27
55
19.99
19.47
18.69
17.62
16.20
H-37
11.98
8.92
56
21-34
20.80
20.00
18.90
17-45
i5-5i
12.97
9.67
57
22.79
22.25
21.44
20.34
18.88
16.76
14.04
10.50
58
24.38
23-84
23.06
21.92
20.32
18.14
15-23
11.42
59
26.10
25-63
24-83
23.66
21-97
19.66
16.55
12.42
60
28.15
27.58
26.79
2S-S6
23.80
21.34
17.99
'3-55
132
PRINCIPLES AND PRACTICE
TABLE No. LIII.
COST OF INSURANCE PER $i ,000 OF A FIFTEEN-YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
AS*.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
20
6.94
6.66
6-35
6.03
5-67
5-29
4.88
4-43
21
7-03
6-74
6.44
6.H
5-75
5-37
4-95
4-50
22
7.II
6.83
6.52
6.19
5-84
5-45
5-03
4-57
23
7.21
6.92
6.61
6.29
5-93
5-54
5-n
4.66
24
7-3
7.02
6.71
6.38
6.03
5-63
5-21
4-75
25
7.40
7.12
6.82
6.49
6.13
5-74
5-3i
4.84
26
7-5i
7-23
6-93
6.60
6.24
5-84
5-42
4-94
27
7-63
7-35
7-05
6.72
6-35
5-96
5-53
5-03
28
7-75
7.48
7.17
6.84
6.48
6.08
5-64
5-H
2 9
7.88
7.61
7-3i
6.98
6.61
6.20
5-75
5-27
30
8.03
7-75
7-45
7.12
6.74
6.33
5-88
5-38
31
8.17
7.90
7.60
7-25
6.89
6.47
5-99
5-50
3 2
8-33
8.06
7-75
7.41
7-3
6.61
6.14
5-63
33
8.50
8.22
7.91
7-57
7.19
6.76
6.29
5-76
34
8.67
8-39
8.08
7-73
7-35
6.92
6-43
5-9
35
8.85
8-57
8.26
7.91
7-52
7.08
6-59
6.06
36
9.04
8-75
8-44
8.09
7.69
7-25
6.76
6.25
37
9-23
8-95
8.64
8.27
7.87
7-44
6.98
6.51
33
9-44
9.16
8.83
8-47
8.08
7.68
7.26
6.80
39
9-65
9-36
9.04
8.70
8-35
7-99
7-58
7.14
40
9.87
9-59
9.28
8.98
8.68
8-34
7-97
7-52
4i
IO. II
9.82
9-59
9-34
9.06
8-77
8.40
7-94
42
10.38
10. 16
9.96
9-75
9-52
9-23
8.87
8-39
43
10.72
10.57
10.40
10.25
10.03
9-45
9-37
8.89
44
11.15
11.03
10.94
10.79
10.59
10.30
9.92
9-44
45
11.63
n. 60
11.52
"39
11.19
10.91
10.53
10.04
46
12.23
12.21
12.15
12.03
11.85
11.58
11.20
10.70
47
12.88
12.89
12.84
12.74
12.57
12.30
"93
11.40
43
13-59
I3.6l
13-59
i3-5i
I3-36
13.10
12.71
12.18
49
H-35
14.41
14.41
14.36
14.22
13.96
13-57
13-03
50
!5-i9
15.28
I5-3I
15.28
I5-H
14.90
H-Si
13-94
5i
16.10
16.23
16.30
16.27
16.16
15-93
I5-5I
14.92
52
17.11
17.27
17-35
I7-36
17.27
17.02
16.61
16.00
53
18.20
lS-37
18.51
18.54
18.44
18.22
17.82
17-23
54
19.36
19.60
19.76
19.80
19-74
19-53
19.18
18.58
55
20.65
20-93
21 10
21. 18
21.15
2I.OO
20.64
20.05
56
22.05
22-34
22.56
22.69
22.73
22 6l
22.28
21.67
57
23-53
23.88
24.16
24-38
24.46
24.38
24.06
23.46
58
25-15
25-57
25-95
26.23
26.37
26.31
26.02
25.42
59
26.93
27.46
27.89
28.26
28.45
28.44
28.18
27-55
f
60
28.99
29-53
30.07
30.48
30-73
30.78
30-52
29.91
OF LIFE INSURANCE.
'33
TABLE No. LIV.
COST OF INSURANCE PER $I,OOOOF A TWENTY- YEAR ENDOWMENT POLICY,
DURING VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Agt.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7.06
6.90
6-73
6-55
6-35
6.13
5-80
5-65
21
7.14
6.98
6.82
6.64
6-43
6.22
5-99
5-74
22
7-23
7.08
6.91
6-73
6-53
6.32
6.09
5-84
23
7-33
7.17
7.00
6.83
6.63
6.42
6.19
5-95
2 4
7-43
7.27
7.11
6-93
6.74
6-53
6.31
6.05
25
7-53
7-38
7.22
7-5
6.86
6.65
6.42
6.17
26
7.64
7-49
7-34
7.17
6.98
6.77
6-55
6.29
27
7-75
7.62
7.46
7-30
7.11
6.91
6.68
6.42
28
7.88
7-74
7.60
7-43
7-25
7.04
6.81
6.56
2 9
8.02
7.89
7-74
7-57
7-39
7.18
6.96
6.70
30
8.16
8.03
7.89
7-73
7-54
7-34
7.11
6.84
31
8.31
8.19
8.04
7.88
7.70
7-49
7.26
7.00
32
8.47
8-35
8.20
8.05
7-S6
7-65
7.42
7.16
33
8.64
8.51
8.38
8.22
8.03
7-83
7-59
7-32
34
8.81
8.69
8-55
8-39
8.21
8.00
7-77
7-50
35
9.00
8.88
8-73
8.58
8.40
8.18
7-94
7.69
36
9.19
9.06
S-93
8.77
8.58
8.38
8.18
7-92
37
9-38
9.27
9-i3
8.97
8-79
8.60
8.42
8.25
38
9-59
9.48
9-34
9.18
9.02
8.87
8-75
8.61
39
9.81
9.69
9-56
9.42
9-3i
9.22
9.12
9.04
40
10.03
9.92
9.81
9.72
9.67
9.62
9.60
9-52
4i
10.27
10. 18
10.13
10. IO
10.09
IO.II
10.08
10.04
42
10.54
10.51
10.52
10.54
10.60
10.64
10.64
1 0.60
43
10.89-
10.93
10.98
11.08
n. 16
11.22
11.23
11.22
44
11.32
11.40
10.54
11.66
11.77
11.85
11.89
Il.Sg
45
n. Si
11.99
12.15
12.30
12.43
12.54
12. 6l
12.64
46
12.42
12.62
12. 8l
12.99
I3-I5
13.29
13-39
13-45
47
13-07
i3-3i
13-53
13-74
13-94
14.11
14.24
H-3I
48
13-79
14.05
14-32
H-57
14.80
15.01
15-15
15-36
49
14.56
14.87
15-17
15-47
15-74
15-97
16.16
l6.30
50
15-41
15-76
16.11
16.45
16.74
17.02
17.24
17-39
5i
16.34
>
16.74
17-13
17.49
I7-85
18.16
18.40
18.59
52
17-35
17.80
18.22
18.65
19.04
19,38
19.67
19.90
53
18.45
18.93
19.42
19.90
20.31
20.70
21.04
21.36
54
19.63
20.18
20.72
21.22
21.70
22.15
22.59
22.96
55
20.93
21-53
22.10
22.67
23.21
23-77
24.27
24.71
56
57
22.33
23-83
22.97
24-54
23.61
25.26
24.25
26.01
24.90
26.75
25-53
27.46
26.12
28.11
26.6l
28.70
58
25.46
26.26
27.10
27.94
28.77
29.56
30-31
30-97
59
27-25
28.18
29.11
30-05
30-97
31.86
32.69
33-43
60
29-25
30.27
3I-32
32-34
33-37
34-36
35-28
36-13
134 PRINCIPLES AND PRACTICE
TABLE No. LV.
COST OF INSURANCE PER $1,000 OF A TWENTY-FIVE YEAR ENDOWME-XT
POLICY, DURING VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7-13
7.04
6.94
6.85
6.74
6.61
6.49
6-34
21
7.21
7-13
7.04
6.94
6-83
6.71
6-59
6-45
22
7-3
7-22
7-13
7-03
6-93
6.81
6.69
6-55
23
7.40
7-32
7-23
7.14
7.04
6-93
6.8i
6.68
24
7-50
7.42
7-34
7-25
7-i5
7.04
6-93
6.80
25
7.60
7-53
7-45
7-37
7.27
7.17
7.06
6.94
26
7.71
7.64
7-57
7-49
7.40
7-30
7.19
7.07
27
7-83
7-77
7.70
7.62
7-54
7-44
7-34
7.21
28
7.96
7-9
7.84
7.76
7.68
7-59
7.48
7-36
2 9
8.08
8.04
7.98
7.91
7.84
7-74
7.64
7-52
30
8.24
8.19
8.14
8.07
7-99
7.90
7.80
7.67
31
8.39
8-35
8.30
8.23
8.16
8.07
7.96
7-85
32
8.55
8.51
8.46
8.40
8-33
8.24
8.14
8.02
33
8.72
8.68
8-63
8-58
8.50
8.42
8.32
8.20
34
8.89
8.86
8.82
8.76
8.69
8.61
8.50
8.38
35
9.08
9-5
9.00
8-95
8.88
8.80
8.69
8-59
36
9.27
9-24
9.20
9->S
9.08
9.00
8.92
8.87
37
9-47
9-44
9.40
9-35
9.29
9-23
9.20
9.21
33
9.68
9-65
9.61
9-57
9-53
9-52
9-56
9.60
39
9.90
9.87
9.84
9.82
9-83
9.89
9.96
10.08
40
10.12
IO.IO
10-09
10.13
IO.2I
10.31
10.47
10.60
4i
10.36
10.37
10.42
10.52
10.64
10.83
10.99
11.17
42
10.63
10.70
10.82
10.97
II.I8
11.38
11.48
11.78
43
10.98
II. 12
11.29
11.52
11.76
12. OO
12,22
13.45
44
11.41
1 1. 60
11.86
12.12
12-39
12.66
12-93
13.18
45
Il.gi
12.19
12.48
12-77
13.07
13-38
13.68
13.09
46
12.51
12.83
i3-'5
I3-48
13-82
14.17
H-5 1
14.86
47
I3-I7
13-53
13.88
14.25
14.63
15.02
15.42
I5-78
4 8
I 3 .S9
14.28
14.68
I5.IO
I5-52
15.96
16.37
16.80
49
14.67
15.10
i5 : 55
16.01
16.49
16.95
17-43
17.90
50
I5-52
16.00
16.50
17.01
I7-52
18.05
18.57
19.06
5 1
16.45
16.98
i7-5i
18.08
18.65
19.23
19.77
20-33
52
17.46
18.05
18.63
19.25
I 9 .S7
20.47
21.09
21. 7O
53
18-57
19.19
19.84
20.:; i
21. l6
21.84
22.51
23.24
54
19.74
20.44
21.15
21.85
.22.57
23-31
24.11
24.90
55
21.05
21.80
22.54
23-3I
24.11
24.97
25-83
26.73
56
22-45
23.24
24.06
24.90
2v82
26.75
27.72
28.69
57
23-95
24.81
25.70
26.68
27-68
28.72
29.76
30.83
53
25-59
26.53
27-55
28.61
29.72
30.84
3^99
33- * 5
59
27-37
28.45
29.56
30-73
31.92
33-15
34-40
35-66
60
29-37 30-54
3i-77
33-02
34-33
35-66
37-oi
38-38
OF LIFE INSURANCE.
'35
TABLE No. LVI.
COST OF INSURANCE PER $1,000 OF A THIRTY- YF.AR ENDOWMENT POLICY,
DURING VARIOUS YEARS, COMBINED EXPERIENCE, 4 PER CENT.
Age.
First
year.
Second
year.
Third
year.
Fourth
year.
Fifth
year.
Sixth
year.
Seventh
year.
Eighth
year.
2O
7.17
7-13
7.08
7-03
6.98
6.92
6.8 5
6.80
_ i
7.26
7.21
7.17
7-13
7-07
7-O2
6-95
6.89
22
7-34
7-31
7.27
7-22
7.18
7-13
7.07
7-01
23
7-44
7.41
7-37
7-33
7.29
7.24
7.19
7-13
24
7-54
7-51
7-47
7-44
7.41
7-36
7-3i
7.26
25
7.64
7.62
7-59
7-56
7-53
7-49
7-45
7.40
26
7.76
7-73
7-72
7.69
7.66
7-63
7-59
7-54
27
7.87
7.86
7.84
7-83
7.80
7-78
7-73
7.69
28
S.oo
7-99
7.98
7-97
7-95
7-93
7-89
7-85
2 9
8.14
8.14
8., 3
8.12
S.ii
8.08
8.05
8.01
30
8.28
8.28
8.29
8.28
S.2 r )
8.25
8.22
8.18
31
8-43
8.44
8-45
8-44
8-43
8.42
8. 3 S
8-35
32
8.60
8.61
8.61
8.61
8.61
8-59
8-57
8-54
33
8.77
8.78
8.79
8-79
8.78
8.78
8.7 ,
8.71
34
8.94
8.96
8.97
8-97
8-97
8.97
8-94
8.91
35
9.12
9-15
9.16
9.17
9.17
9.16
9^5
9- J 3
36
9-32
9-34
9-36
9.37
9-37
9-37
9-37
9.42
37
9-5i
9-54
9-56
957
9-.SS
9.60
9.66
9-77
38
9-73
9-75
9-77
9-79
9.82
9-9
IO.O2
10. 18
39
9-94
9-97
10.00
10.04
10.13
10.27
10.44
10.67
40
10.17
IO.2O
10.25
10.35
10.51
10.70
10.95
II. 21
4i
10.41
10-47
10.58
10.75
10.95
11.23
11.48
II.80
42
10.68
I O.8O
10.98
1 1. 20
11.49
11.79
12. II
12.43
43
1 1. 02
11.22
"45
11.76
12.08
12.42
12.76
13.12
44
11.46
II.7O
12.03
I--36
12.72
13.08
13-47
I3-87
45
11.96
12.30
12.615
13.01
I3-4I
13.82
14.24
14.69
46
12.57
12.93
J 3-33
13-73
14.16
14.61
15.09
I5-58
47
13.22
12.63
14.06
i4-5i
14.98
15.48
16.00
16.52
4 8
J 3-94
H-39
14.86
15-35
15.88
16.42
16.97
17-55
49
14.72
15.21
15-73
16.27
16.85
17.42
18.04
18.66
50
15-57
16. ii
16.68
17.27
17.87
18.52
19.18
I 9 .8 3
5 1
16.50
17.09
17.71
18.34
19.01
19.70
20.39
21. II
52
i7-5i
18.16
18.81
19-Si
20.23
20.95
21.70
22.49
53
18.02
19.29
20.02
20.77
21.52
22.^1
23- '3
24.02
54
19.79
20.54
21.32
22. IO
22.92
23.78
24.72
25.68
55
21.09
21.90
22.70
23-56
24-45
25.42
26.43
27.50
136
PRINCIPLES AND PRACTICE
TABLE No. LVII.
NET SINGLE PREMIUMS PER $1,000 FOR A TEMPORARY INSURANCE FROM
ONE TO FIFTEEN YEARS (MASSACHUSETTS NoN-FoRFEITURE LAW,)
COMBINED EXPERIENCE, 4 PER CENT.
Ages.
20
22
22
23
24
25
2G
27
Tears.
I
7-01
7.09
7.17
7.27
7-37
7-47
7-58
7.70
2
I3-73
13-94
14.12
H-3I
H-50
14.71
M-93
15.16
3
20.32
20.57
20.83
21. II
21.40
21.72
22.05
22.40
4
26.64
26.98
27.32
27.70
28.09
28.51
28.95
29-43
5
32.76
33-17
33-61
34.08
34-57
58.10
35-66
36-25
6
3 8.6 7
39- i 7
39-70
40.26
40.86
41.49
42.17
42.88
7
44.40
44.98
45.60
46.26
46.96
47.70
48.49
49-33
8
49-95
50.62
5'.33
52.08
52.88
53-74
54-64
55-59
9
55-33
56.08
56.88
57-74
58.64
59.60
60. 6 1
61.68
10
60. ?4
61.39
62.28
63-23
64.24
65-30
66.43
67.61
n
65.61
66.54
67.52
68-57
69.68
70.85
72.08
73-38
12
70.52
7i-54
72.62
73-76
74-97
76.25
77-58
78.99
13
75-30
76.41
77-57
78.81
80.12
81.49
82.94
84.46
H
7994
81.14
82.29
83-73
85-I3
86.60
88.16
89.79
15
84.46
85-74
87.08
86.50
90.00
91.58
93-23
94.98
Ages.
28
29
so
31
32
33
34
35
Years.
I
7-83
7.96
8.10
8.25
8.41
8.58
8-75
8-93
2
I5-4I
15.68
15-97
16.27
16.58
16.91
17.26
17.62
3
22.78
23.18
23.61
24.06
24-53
25.02
25-53
26.06
4
29-93
3-47
31.04
3I-63
32.26
32.91
35-59
34-30
5
36.89
37-55
38.26
39.00
39-78
40.58
4i-43
42-31
6
43-64
44-44
45-28
46.17
47.09
48.05
49.06
50.11
7
50.21
5i-H
52.12
53-H
54-21
55-33
56-49
57-7i
8
^6.60
57.66
58.76
59-93
61.14
62.41
63-73
65.14
9
62.81
63-99
05.24
66.54
67.89
69.31
70.81
72-43
10
68.86
7o-i7
7i-54
- 72.97
74-47
76.05
77-75
79-63
ii
74-74
76.18
77.67
79.24
80.90
82.67
84.62
86.78
12
8048
82.03
83-65
85-37
87.21
89.22
9*-43
93-92
13
86.06
87-73
89.49
91-38
93-44
95-7i
98.24
101.06
H
91.49
93-30
95-23
97-33
99-63
102.19
105.03
108.20
15
96.79
98.76
100.90
103.23
105.81
108.67
111.84
"S-34
4r-
3d
37
38
39
40
41
42
43
Years.
I
9.12
9-31
9-53
9-74
9.96
10.24
10.48
10.82
2
17.99
18.38
18.80
19.22
19.67
20.17
20.77
21.51
3
2 ! '.63
27.22
27-83
28.47
2 9 .l6
29.96
30.94
32.12
4
35-04
35-82
36-63
37-49
38.47
39-63
41.03
42.69
5
43-23
44-20
45-22
46.36
47.68
4>23
51.10
53-27
6
51.21
52-38
53-66
55-12
56.81
58.82
61.17
63-87
7
59.00
60.42
61.99
63-81
65-93 .
68.39
71.24
74-47
8
66.66
68.36
70.27
72.50
75-05
77.98
81-33
85.10
9
74.22
76.25
78.. S3
81.17
84-17
87-57
91.44
95-72
10
Si-73
84.12
86.79
89-85
93-30
97.19
101.58
106.43
ii
89.22
91.98
95-05
98-54
102.45
106.84
111.76,
117.18
12
96.71
99-85
103.33
107.25
111.63
116.52
121.99
127.97
13
104.21
107.74
111.63
"5-99
120.84
126,25
132-25
138.81
14
111.71
"5- 6 3
"9-95
124.76
I3O.IO
136.01
142.56
149.70
15
119.23
123-55
128.30
133-57
139-39
145.82
152.91
160.61
OF LIFE
137
TABLE No. LVII (CONTINUED.)
NET SINGLE PREMIUMS, PER $1,000, FOR A TEMPORARY INSURANCE FROM
ONE TO FIFTEEN YEARS (MASSACHUSETTS NoN- FORFEITURE LAW)
COMBINED EXPERIENCE, 4 PER CENT.
Ages.
44
45
46
47
48
49
50
51
Tears.
I
11.25
11.74
12-35
13.00
I3-7I
14.48
15-33
16.25
2
22.41
23-47
24.68
26.00
27.44
29.00
30.70
32.56
3
33-55
35-18
37-03
39-02
41.19
43-56
46.14
48.95
4
44.68
46.91
49-38
52.07
55-00
58.17
61 64
65-39
4
55-83
58.65
61.77
65.16
68.85
72.86
77-2i
81.91
6
66.98
70.41
74.20
78.3'
82.77
87-59
92-83
98.50
7
78.16
82.21
86.67
96.74
102.40
108.53
115.13
8
8937
94.06
99.20
104.76
110.77
117.26
124.27
131.80
9
100.63
105.94
111.78
118.07
124.86
132.17
140.04
148.51
10
111.94
117.88
124.41
131.43
138.98
147.11
I55-85
165.28
ii
123.29
129.88
137.10
144.83
I53-I5
162.08
171.72
182.09
12
HI-93
149.82
158.26
167-34
177.11
187.62
198.93
13
146.15
154.01
162.57
I 7 I -73
181.58
192.17
203.56
215.76
14
157-63
166. 12
175-34
185.24
195.86
207.26
219.48
232-55
15
169.13
178.25
188.17
198.78
210.16 | 222.34
235-37
249.28
Ages.
53
53
54
55
56
57
58
59
Tears.
I
17.26
18.36
19-53
20.83
22.24
23-73
25-37
27.16
2
34.60
36.78
39.16
41-75
44-53
47-52
50.80
54-42
3
51-99
55-29
58.86
62.72
66.88
71-37
76.31
81-73
4
69.47
73-87
78.61
83-74
89.27
95-30
101.89
109.10
5
87.02
92.50
98.42
104,81
111.75
119.28
127.51
136.45
6
104.61
111.18
118.26
12595
134.28
I43-3I
163.76
7
122.25
129.90
138.18
U7-I.5
156-85
167.32
178^68
190.95
8
139-93
148.69
158.14
168.38
179.40
191.29
204.13
217.94
9
I57-67
167.52
178.14
189.60
210.92
215.17
229.40
244.67
10
175-45
186.38
198.13
210.78
224.34
238.87
254.42
271.01
ii
193.26
205.23
218.09
231.87
246.61
26^.33
279.08
296.85
12
211.06
224.05
237.96
252.81
268.64
285.46
303-27
322.08
13
228.83
242.79
257.68
273-55
290-37
308.14
326.89
346.59
H
246.53
261.40
277.21
293.98
311.67
330-29
349-84
370.27
15
264.10
279.82
296.46
314.02
332-48
372.01
393-01
4f-
6O
61
62
63
64
65
66
67
i
29.17
3I-36
33-77
36.38
39-25
42-39
45-78
49-49
2
58.41
62-77
67-53
72.70
78-35
84.47
91.10
98.28
3
87.69
94.17
101.22
108.87
117.16
126.13
I35-78
146.13
4
116.97
I25-5 1
134-77
144-77
I55-58
167.19
179.60
192.86
5
146.19
156.72
168.09
180.32
'93-45
207.47
222.40
238.26
6
I75-29
187.71
2OI.O7
2I5-36
230.60
246.80
263.97
282.12
7
204.18
218.39
233-57
249.72
266.88
285.01
304-I3
324.21
8
232.79
248.63
283.26
302.12
321-93
342.68
9
260.98
278.28
296.59
3I5-89
336.16
357-36
379-45
402.38
10
288.63
307-24
326.84
347-31
368.84
391.16
414.26
438.08
ii
3I5-63.
335-38
356.07
377-55
400.01
423.16
446.95
471.33
12
34I-87
362.56
384.12
406.39
429.52
453-20
477.40
502.03
13
367. 21
388.66
410.87
433-69
457-23
481.19
505-5I
530.06
H
391-54
41.3-54
436.20
459-32
483.05
507-03
53I-I9
555-38
15 ! 4H-74
459.98
483.21
506.88
530-63
554-37
577-95
PRINCIPLES AND PRACTICE
TABLE No. LVIII.
SHOWING INSURANCE DUE ON WHOLE LIFE POLICIES, ACCORDING TO
THE MASSACHUSETTS NON- FORFEITURE LAW.
No. of
Prttn iu tns
Age 2O.
Age 21.
Age 22.
Age 23.
Age 24.
paid.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
I
- 2 5 6
263
.. 271
.. 2 7 8
.. 285
2
I I5S
I 169
I 184
I I 99
I 213
3
2 6l
2 83
2 IO5
2 127
2 H9
4
2 341
3 4
3 33
3 62
3 9
5
3 264
3 299
3 334
4 3
4 38
6
4 194
4 235
4 275
4 3i6
4 355
7
5 128
5 175
5 222
5 268
' 5 3H
8
6 68
6 121
6 172
6 224
6 276
9
7 ii
7 69
7 127
7 185
7 243
10
7 324
8 22
8 85
8 149
8 211
ii
8 276
8 344
9 47
9 "3
9 175
12
9 231
9 303
10 6
10 68
10 120
13
10 iS^;
10 254
10 3i5
10 364
ii 37
H
ii 128
ii 186
ii 233
ii 267
ii 291
15
12 47
12 91
1.2 121
12 142
12 149
No. of
Age 25.
Age 26.
Age 27.
Age 28.
Age 29.
Prem 111 ins
paid.
Years. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
I
293
300
307
315
322
2
I 228
I 242
I 257
I 271
I 286
3
2 170
2 192
2 213
2 234
2 255
4
3 "9
3 146
3 174
3 202
3 230
5
4 72
4 107
4 HI
4 176
4 211
6
5 3i
5 72
5 "3
5 i54
5 196
7
5 36o
6 42
6 89
6 137
6 184
8
6 328
7 iS
7 69
7 121
7 168
9
7 3oo
7 357
8 46
8 94
8 134
10
8 272
8 326
9 7
9 44
9 7i
n
9 229
9 2 73
9 307
9 3 2 9
9 34i
12
10 161
10 191
IO 2IO
10 218
10 216
13
ii 64
ii 79
II 84
ii 77
ii 60
H
ii 302
ii 302
II 292
ii 270
ii 242
i5
12 145
12 130
12 105
12 72
12 26
No. of
Age 3O.
Age 31.
Age 32.
Age 33.
Age 34.
paid.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
I
329
337
344
352
.. 362
2
I 300
i 3i5
i 330
i 345
I 360
3
2 277
2 2 99
2 321
2 343
3 2
4
3 259
3 288
3 3i7
3 347
4 14
5
4 246
4 282
4 3i8
4 356
5 26
6
5 238
5 279
5 320
5 356
6 20
7
6 229
6 272
6 307
6 334
6 35i
8
7 210
7 243
7 266
7 280
7 284
9
8 164
8 183
8 193
8 193
8 186
10
9 87
9 9 2
9 88
9 78
9 53
ir
9 343
9 335
9 319
9 291
9 257
12
10 203
10 183
10 150
IO 112
10 72
13
ii 36
10 363
10 321
10 270
10 214
H
II 200
" 153
ii 98
II 38
10 338
15
II 341
ii 282
ii 218
II 148
ii 74
OF LIFE INSURANCE.
TABLE No. LVIII. (CONTINUED.)
SHOWING INSURANCE DUE ON WHOLE LIFE POLICIES, ACCORDING TO
THE MASSACHUSETTS NON-FORFEITURE LAW.
No. of
Age 35.
Age 36.
^Ifire 37.
Age 38.
^Ifire 39.
paid.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
1
i 3
I II
I 20
I 2 9
i 39
2
2 12
2 29
2 47
2 6 5
2 82
3
3 27
3 52
3 69
3 99
3 "5
4
4 46
4 74
4 98
4 114
4 123
5
5 56
5 78
5 93
5 99
5 96
6
6 41
6 52
6 56
6 49
6 36
7
6 359
6 359
6 349
6 332
6 307
8
7 280
7 266
7 245
7 216
7 181
9
8 167
8 142
8 109
8 69
8 24
10
9 24
8 35i
8 308
8 258
8 202
ii
9 215
9 167
9 "3
9 59
8 354
12
10 14
9 32i
9 258
9 193
9 116
13
10 152
10 85
10 13
9 3i
9 219
H
10 267
10 191
10 114
10 24
9 299
15
10 359
10 274
10 184
10 91
9 359
No. of
Age 4O.
Age 41.
Age 42.
Age 43.
^lf/e 44.
Pretn ititns
paid.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
I
I 49
i 57
I 64
i 66
I 6 5
2
2 96
2 106
2 IO9
2 106
2 98
3
3 "5
3 128
3 123
3 "i
3 95
4
4 123
4 116
4 102
4 81
4 56
5
5 86
5 69
5 45
5 i5
4 344
6
6 16
5 353
5 3i8
5 279
5 234
7
6 276
6 238
6 194
6 144
6 88
8
7 139
7 9i
7 38
6 344
6 282
9
7 337
7 280
7 217
7 I5 1
7 81
10
8 141
8 76
8 5
7 295
7 217
ii
8 285
8 210
8 132
8 49
7 327
12
9 38
8 320
8 234
8 H3
8 50
13
9 J 33
9 42
8 3^3
8 216
8 117
H
9 205
9 108
9 7
8 269
8 164
15
9 258
9 J 54
9 48
8 304
8 194
JV0. o/
-f !7<- 45.
Age 46.
^.fire 47.
Age 48.
Age 49.
paid.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
Tears. Days.
I
i 61
i 55
I 48
I 40
I 3 2
2
2 86
2 72
2 57
2 41
2 24
3
3 75
3 52
3 28
3 16
2 340
4
4 26
3 359
3 325
3 289
3 253
5
4 306
4 262
4 220
4 176
4 131
6
5 184
5 135
5 80
5 3
4 342
7
6 34
6 14
5 280
5 218
5 156
8
6 217
6 150
6 82
6 12
5 306
9
7 75
6 333
6 221
6 143
6 65
10
7 136
7 53
6 334
6 249
6 164
ii
7 239
7 H9
7 59
6 332
6 241
12
7 320
7 224
7 127
7 3o
6 299
13
8 15
7 279
7 T -77
7 75
6 339
H
8 58
7 3i6
7 210
7 *4
6 364
IS
8 83
7 338
7 228
7 120
7 n
140
PRINCIPLES AND PRACTICE
TABLE No. LIX
DECIMAL PART OF A YEAR FROM ANY DATE TO JANUARY i, FOLLOWING.
Day.
^aw.
Feb.
March.
April.
May.
June.
I
.0000
9*51
.8384
7534
.6712
5863
2
9973
.9123
8356
7507
66S 5
5836
3
9945
.9096
.8329
7479
.6658
.5808
4
.9918
.9068
.8301
7452
.6630
578l
5
.9890
.9041
.8274
7425
.6603
5753
6
.9863
.9014
.8247
7397
6575
.5726
7
.9836
.8986
.8219
.7370
.6548
5699
8
.9808
8959
.8192
7342
.65,1
5671
9
.9781
.8932
.8164
7315
6493
5644
10
9753
.8905
Si37
.7288
.6466
.5616
ii
.9726
.8877
.8110
.7260
6438
5589
12
.9699
.8849
.8082
7233
.6411
5562
13
.9671
.8822
8055
7205
6384
5534
H
.9644
8795
.8027
.7178
6356
5507
15
.9616
.8767
.8000
7i5i
.6329
5479
16
9589
.8740
7973
7123
.6301
5452
17
.9562
.8712
7945
.7096
.6274
5425
18
9534
.8685
.7918
.7068
.6247
5397
19
9507
.Sf- 5 8
.7890
.7041
.6219
5370
20
9479
.8630
.7863
.7014
.6192
5342
21
9452
.8603
.7836
.6986
.6164
53i5
22
9425
8575
.7808
6959
6i37
.5288
23
9397
.8548
.7781
.6932
.6110
.5260
2 4
9370
.8521
7753
.6904
.6082
5233
25
9342
8493
7726
.6877
6055
5205
26
93i5
.8466
.7699
.6849
.6027
5178
27
.9288
.8438
.7671
.6822
.6000
5i5i
28
.9260
.8411
.7644
6795
5973
5123
2 9
9 2 33
.8411
.7616
.6767
5945
.5096
30
.9205
75S9
.6740
.5918
.5068
31
.9178
.7562
5890
ist Mo.
ad Mo.
jd Mo.
4th Mo.
Jth Mo.
6th Mo.
OF LIFE INSURANCE.
141
TABLE No. LIX (CONTINUED.)
DECIMAL PART OF A YEAR FROM ANY DATE TO JANUARY i, FOLLOWING.
July.
Aug.
Sept.
Oct.
Nov.
Dec.
Day.
.5041
.4192
3342
.2521
.1671
.0849
I
.5014
.4164
3315
2493
.1644
.0822
2
.4986
4137
.3288
.2466
.1616
0795
3
4959
.4110
.3260
2438
.1589
.0767
4
4932
.4082
3233
.2411
.1562
.0740
5
.4904
4055
3205
.2384
1534
.0712
6
.4877
.4027
3178
2356
1507
.068?
7
.4849
.4000
3151
2329
.1479
.0658
8
.4822
3973
3 r 23
.2301
.1452
.0630
9
4795
3945
.3096
.2274
.1425
.0603
10
.4767
.3918
.3068
2247
1397
0575
ii
.4740
3890
3041
.2219
1370
0548
12
.4712
3863
.3014
.2192
.1342
.0521
13
.4685
3836
.2986
.2164
1315
0493
H
4658
.3808
2959
2137
.1288
.0466
15
.4630
378i
.2932
.2ITO
.1260
.0438
16
.4603
3753
.2904
.2082
1233
.0411
i7
4575
.3726
.2877
2055
.1205
.0384
18
4543
3699
.2849
.2O27
.1178
0356
19
.4521
.3671
.2822
.2OOO
.1151
.0329
20
4493
3644
2795
1973
.1123
.0301
21
.4466
.3616
.2767
1945
.1096
.0274
22
4438
3589
.2740
.1918
.1068
.0247
23
.4411
3562
.2712
.1890
.1041
.0219
2 4
4384
3534
.2685
.1863
.1014
.0192
25
4356
3507
.2658
.1836
.0986
.0164
26
4329
3479
.2630
.1808
0959
0137
27
.4301
3452
.2603
.1781
.0932
.OIIO
28
4274
3425
2575
1753
.0904
.0082
2 9
.4247
3397
2547
.1726
.0877
0055
30
.4219
3370
.1699
.0027
31
7th Mo.
8th Mo.
9th Mo.
loth Mo.
nth Mo.
1 2th Mo.
LIFE INSURANCE FORMULAE.*
In the American Table of Mortality we have at the age 10
100,000 persons living at the beginning of the year, and during
that year 749 die before the survivors reach the age n. In the
application of algebraic notation to life insurance, we designate
the living at any age in the table of mortality by /, or by /
with the number denoting the age, as / 10 , /, etc. If we make
#=10, the number living at the age n is denoted by 4+ and
at 12 by 4+z> and hence we have a series of living at all ages,
/ 10 + / n+ / 12 .... / 95= 4+4+i+4+s / the oldest age in the
mortality table expressed by lo. The same formula will apply
if we make any other number in the table =#, as 4>+4i+4i
etc. =/ a +4 + i+4+2j etc. But since 4 is the number living at the
beginning of the year, and 4+i the number living at the end,
the probability of a person aged x surviving during the year is
2*~- , and at the end of each of two years is -y^-H y^-, and con-
^x ^x LX
sequently the probability of his surviving each year till he reaches
the age 95 is expressed by the formula, * + ' + -y^- + *,* " -7*
4c 'x l x ''x
If each person in the number/ should pay $i at the beginning of
each year during life into a common fund, the total amount paid
would be 4+4+1+4+2 ' lu dollars, and the average amount
which each person living at the age x would pay would be
-f--\ ^p- + -^p-.... j-. But payment! to be made in the future
l x l x f x l x
have a present value depending upon the rate of discount assumed,
as well as the probability of living ; and, if we discount each term
in the series after the first by 4 1-2 per cent, or multiply each term
after the first by , ( ) , ( ) , etc., and make =v y
J 1.045' Vi.045/ ' Vi.045/ ' 1.045
* In these formulae the life insurance symbols of Dr. William Farr, as
published in Circular No. 39 of the New York Insurance Department,
have been adopted.
OF LIFE INSURANCE. 143
. /_ v. /,+! v^L+t v s . 1..+3 w-j*. lu , P
we have the series ~+ f 2 + f^-+ r^ ---- 7 If we
l x tx lx . lx lx
multiply the numerators and denominators of this series by -v
raised to the #th power, which does not alter the value of the
f .. V". l x . ,+ ,
fractions, we have -~+ - -= f + . ...
v*. l x v*. l x v*. 4 v*. l x
v u . lu _ _ . D, D +1 D.,+a
-jrT' Making v*.l x =u m , we have the series ~+ * + '
*x *-*x *^x ^x
; .D ?= p.+D,H..+D. +i +D,H.. > etc>; and? substituting N> for a]i
the terms in the numerator up to and including the oldest age in
N
the mortality table, we have the last fraction =j^ a formula which
is applied to a life annuity, the first payment to be made at the
beginning of the year at age *, and which is also represented by
A*
Since A x = ^ + Jl +1 H j|" *i etc v tne temporary annuity of
$i for one year is =f = x ~ x ~ 1 = A z , = I, and for two
years is g*.+ ^1 = N ^- N +a = A ^ and for n years is
N a -N z+n _*
D z A *'
The present value of an annuity deferred for three years is
N a Dg+Dg+i+Ds+a D.+, + D,+4 + D,+5.etc., _ N Z J and in
D X ' -IDT ~^T ~ i>, '
general, the expression for a deferred life annuity is +B =A,| n .
The formula for a deferred temporary annuity to commence
after n years and to continue m years, is
X
The number of deaths at any given age x is expressed by d,.
At age 10 the number dying during the year is, by the American
Table of Mortality, 749, and hence the probability that a person
aged 10 years will die during the year is ~^'^ = ~~f- The
probability of dying during each of the first' two years is
yH ^-, and we have the following series representing the
'x x
J J J
probability of a life aged x dying each year : y 5 -I- ' +1 + ^ +
^p*, etc. Since ~ is the probability of dying during the first
144 PRINCIPLES AND PRACTICE
year, it is the undiscounted sum required to insure the life x for
$i one year, or payable at the end of the year. The premium
required payable at the beginning of the year is -f- multiplied
, '*
by the present worth of $i, or ^-^and for two years is $i mul-
, 2 l *
tiplied by -^ - + - ' x+1 , and, generally, the single premium to
T/. i . v. d v z <_+i ,+ t
insure a life aged x is y* + f -- 1 -- -r > e * c<
. . . . etc.
"x
Multiplying both numerator and denominator by z'*, we have
<4xtr+ 2 . d x+1 xv*+ s . d x +,, etc. -D ... ,,1 , ~
- ^- - z - . Putting #+*. ? = C., we
, ,, i C,.+ C,.+ i + Cx+a> etc. , . .
have the single premium = - - ^ - : - , and, making
the numerator or the sum of all the C's = M,, we have the
M
single premium = ~, which we represent by !!.
If rr x represents the annual premium on a life aged AT, it is
evident 11,., the single premium, is the present value of the
annuity ff x, or the annual premiums during life. Hence, ir x . A x = Uj.,
n, . M, , . N z H x M x N x MX
and7r *= A? Since n s = ^-, and A z =^, _ = --,^ = -,
the net annual premium.
The annual premium on a limited payment life policy is found
by dividing the single life premium by the temporary annuity for
the number of years in which the payments are made:
Ji, M, _ Nx-N x+n _ M g
*" - A. S ' D. * D x : N^N^T n -
Term Insurance. We have seen that the cost of insuring a
r . v l . d x Cx M x M x +i jf
person for a single year is - = =r- = -- = ^ , and for two
*V t>x L'x -^^a;
years is ~ + -~- = x x+2 , and therefore the single pre-
\Jx *-*x J-'aj
mium to insure a life for n years is * _ X+TO . To find the annual
premium, we divide this by the temporary annuity for n years,
MX-MX+,, N g -N z+n _ M a; -M a .+ n
D z . Dx N x -N x+n '
Endowment. The single premium required to purchase the
simple endowment of $i payable n years hence, if the insured
lives, is the discounted number of the living at the age x + n
OF LIFE INSURANCE. 145
V*+ n . I +
divided by the discounted number of living at age x, ^T"/~
~ , and the annual premium is found by dividing the single pre-
mium by the temporary annuity for n yer.rs, ^~ -. ~f>~^~ Ji=
Endowment insurance. This is a combination of term in-
surance and simple endowment. The single premium on an en-
dowment assurance policy payable in n years or at death, if prior,
is the sum of the single premiums of a term and a simple endow-
r M,-M T+n D, +n M J -M J+K + D x+n
ment policy for n years = ~- - + ) = - -j^
and, dividing by the temporary annuity x J+n , to obtain the
i ^1 c i M, M_+ n + P,+_
annual premium, we have the formula ^x = f . . * " .
N*-N I+n
For an endowment insurance payable in n years or at death, if
prior, the premiums being paid annually during m years, ;;/ bejng
less than n, we divide the single premium given above by the
temporary annuity of $i for /;/ years, ir n = ^ ^-i-
N g -N J+Bt _ M.-M, + n -D J+n
D, N z -N^ m
Annual premium during n years to insure a life annuity of a
dollars at age xn. a. A x + n = present value of the annuity a at
age x + n. This is the quantity to be insured on a simple endow-
D,+_ IX+- <* N,+_ a. N,+_
ment, or^-; ~ x a. A a .+ B = ^ ^r x * " = ^ '
N x -N I+n N a -N x+n D J+n N,-N X +.
Annual premium to insure b dollars to the age x + n, if death
occurs within n years, and to insure a life annuity of a dollars
during life from age x+n. Add the term insurance on b dollars
, , , . f , a. N.,+ n + (M, M,+_)
to the last formula, ^" :..-* ^.
N I -N x+n
It is often convenient, especially in computing joint-life pre-
miums, to be able to use only the D and N columns, and a
few formulas are given explaining the method.
Since n,= ^ + *^L + -*L, etc., and rf.-/.-/. +1>
'* '* '
and d.4 , =- /. +1 _ /, +J , etc., we have n, _ t/(/ '~/ J+l) +
*
fV. -t. .-/.*.) + ^O1ZAI/, etc . Separating this formula into
' l
146 PRINCIPLES AND PRACTICE
two parts, we have
_ r.r./r+it, etc.) v(Z x +i+v.l x +-i+v.Z x +s, etc.)
' I, /.
x - A,+ , = w.A, - (A, _ ,) = i-Qi f)A x , and TT X =
Single premium^ life. Making z" the rate per cent,
-. A
.
Annual premium Jifc.- t = = (1-7^7 x ^-) ^ =
D, / i /
Whole life insurance by n annual premiums.
, x-(i-w)A, r y N N, -| D z
= - *-J - - = I (i f) TT X XT . XT -- =
A iB L ' D r J N x N x+n
- i+n ,- a;+n x - z+n N -N +
Endowment insurance. The single premium for a tem-
porary insurance of n years is
rr - ( l x +v - l *+ t+yl>l *+* +v *Ix+ s ' pn 4+n)
* ~" v.l,
P .( N -~ D N - + ") - *( Nr+1 ""j^'*""")* divided by the tem p rar y
annuity, ^T-^i, v - ( Nj+ '~^'"' M ) = annual premium
for temporary insurance. Adding the single premium of sim-
ple endowment, J^ 2 - to the single premium for temporary
insurance, and, since N x+n+ , + D I+n N a + n , we have the single
premium endowment = v ( ' *~ D - J ^- 5 - ) ( X+ ' D ^^ ) and
jj _ N +
dividing by the term annuity, i ~f)~ j!L ~ i we have, annual pre-
mium = v \-~^*_ I+n ) Net annual premium for n years,
payable in m payments, v ( ^r + l_ N '-").
Joint lives. We have seen that the general formula for an
annuity on a life x is A, = ^.7,+. +./.+.+*./,+. >etc>
OF LIFE INSURANCE. 147
if there are two lives, x and y, the result of a combination of them
will be their product, and
A l x- l + v - '*+! ',, + i+f 5 - /!+* l a +i + v s l x +3- L + s, etc. , .
A, y - s - - -H- - 2 - , and mul-
' 'y
tiplying by T>% we have
. If l x . ly
f
, etc., _
>*.,
Ill preparing the column D x . y , if .* 15 and ^/ 10 years ot
age, then we add the logarithm of D x u to the logarithm of y w
or /', the number of living at the age 10, which gives the
logarithm of D,. y , and the log. D 16 + log. y n = log. D x +,. y+1 ,
and so on throughout the column D,. The numbers corre-
sponding to these logarithms will be the column D z . y . The
column N, , is found b/ the summation of the column D,
J *. y
With the D,.. y and N,. ,, columns of any combination of ages,
the operations in joint lives are performed in the same manner as
those of single lives.
Rcttirn premium plan. This plan of insurance provides
for the return of all the premiums paid when policy becomes a
claim. In this kind of policy there are two parts to be consid-
ered, the specified sum insured and the part constantly increas-
ing by K X each year. The first has - - for the annual pre-
mium, and the latter has ^ x (~- + -\> + vr~ &c -' ) = "T3?
Putting these together, we have -r^ + K X . - = * Clearing of
fractions M, + TT X R, = w. N 2 , and IT, = , M * .
Loaded annual premium. Let TT, = net annual premium
and ($1 + loading) = g. Multiplying -^ + ir x ^/ = ir a by g^
Nx N a
we have g -^- + K S g. -^- = g . TT X , therefore,
i\ a IN^
M.
{?. MX
ff. 7T X = ~~ p- =1
A' x
r ct annual premium for the return of gross premiums.
M.
i
itS PRINCIPLES AND PRACTICE
Limited-payment annual return premium.
* m ** N X -N X+W + *" ( N.-N.+. + N.-N.+, + N Z - Z N X+B '
r + n~" * I _^_ * J. 7T | _ x ^ . *__1^_ \
N - N x + n ' N *- N z + * V N x -N x + n >/
Clearing of fractions, M x - (R, - R x+n ) = - x (N x - N s+n ),
With loading, f . ff .
^ (N x -N z+n ) (R x -R x+n )
T-, , . M, M,+.,4-D,+
Endowment, , - --
IJT.,, , ,.
with loadmg, g . ,.
(N _ N+J . (RjRn)
M + + D +
j (N x -N x+n ) - (R x -R x+n )
Single return premium. Let U, = single return premium,
M a M.
Uien n x - -^ + n x . 1 ^-
n x . D, = X M, + n x . IVT.
M x
". - D^NiT_
Net single premium for the return of grcss premium.
Let (i+/) ="= $i + loading; then
n = l + ^l>7 n *' whencc n - D X - M ;M.
Loaded single return premium.
n -
VALUATION OF POLICIES.
Let TT X be the annual premium payable on a life policy, it is
evident that if the policy were not subject to the future payment
of this annual premium, the value of it would be the single pre-
mium of a policy of assurance on a life aged * + = n x + n . But
in consequence of the charge of an annual premium on the
policy, the value will be reduced by a sum equal to the value of
all the future premiums, or the present value of an annuity of n m
on a life equal to +, the first payment of which will be made
OF LIFE INSURANCE. 149
immediately, and the formula will be H.,.+ n = n +n ir x x A^+^SB
("-.+. ~ **) Ax+- But ff x+ = T- 1 (i-*0 and TT X . i _
Additional formulae for the value of whole life policies :
TT l ~^x + n TT 7T x + n~ 7r x
Value of a life policy paid up by m premiums is at the end ot
N + N +
n years, II x + n = n x+B TT, ~rT~
Value of an endowment policy payable in m years or at pre-
vious death,
H 4- =1 I ^ ^ 2L -3- * ^ * + n -[ =3: i *+n ro
V J-^z+n *}* ' A^
Also, H x+n = D I+n - TT, 5Zl_i_
Here n z+n = the net single premium of a policy issued at the
age x + n and payable at the age x+m.
Value of an endowment policy payable at previous death or in
m years by m number of payments.
H x+ n = n I+n - TT X . NT+ D~ + ^ +OT> '
Value of a term policy to expire at age x+m.
The explanation of these three last formula? is found on
page 46.
Value of a simple endowment policy. In this form of policy
the company does not assume any risk, and the reserve at the
end of any given year is the reserve of the previous year in-
creased by the co-efficient of accumulation.
HX+ = (H x + m -i + **) x+-- Also, U f+n =n sfB - TT B .
j^- }^
-- in which U x+n = single premium at age x+n to
insure policy payable at x+m,
- D *+m _3-Jfi_ N,+ M -N,+,
"+ = Di+n N X -N Z+M D x+lt
*5 PRINCIPLES AND PRACTICE
Wright's Accumulation Formula, Let H i+1 = the value of
a policy at the end of the first year, c t =. v -, the risk of $i at
*x
the age #, and TT X = the net premium paid, then we shall have
I : c x : : I H I+ , : c x . H, +1 == the value of the actual risk run by
the company on $i insured. Subtracting this value from the net
premium, and accumulating the remainder at the assumed ratio
of interest = r, we have
v
H I+1 = r (n- x c ie +c x . H a+ j), which reduces to
Buti-r.c.= (i-
Representing this last fraction by u z , we have the formula,
H.,, + i = u x (K X C^ = the value of a policy at the end of the first
year. The value at the end of the second year is
H^+2 = u x+1 (H I+ i + ?r x 0,+,), and generally
H Z+B = +_! (H, +n _i + TT X c I+n _,).
Fackler's Formula. H I+n+1 = (H 4+0 + ^ u, +n /+, in
which k x+n = -=- x - 2 -.
D x+n+l
Me ClintocK's Formttla. The following formula gives a some-
what shorter process than the two preceding ones.
Let us suppose a group of /*+-! policyholders assured $1
each, and having a reserve for each one of !!,+_,, making a
total present reserve for the group amount to 4+ n _i (!!,.+_,).
A year from the present time, after adding premiums of ri x each
now due, and increasing the sum of these reserves and premiums
by interest at the rate of i + r, the fund will have amounted to
(i + r) (H.,. +B i +ir x ) /.,+_!. There will have died several of
the group, reducing the number of living to /+, to whose heirs
at $i each the sum of l x+n -\ 4+ dollars are paid. The fund
is then reduced to i+ r (H. jefH - l + -re,) /*+-! + (l x + n -\ 4+)
= 4 +1 .-4+-i [i-(i+r) (H I+n _, + )]. Dividing the amount
of this reserve by / x+n , the number of policyholders, and putting
,+-iC^ tj. _ u x+n - l andg-=v ?r x , the reserve on each policy
is found to be H z+n !-,+_, (^-H s+w _,).
The column c x or k x is dispensed with, leaving but one column
u x to be kept on hand and referred to.
OF LIFE INSURANCE. 15*
Rule. Subtract the net premium paid on each $i (and last
year's reserve on each $i assured, if any) from the present value
of $i due one year hence. Multiply the remainder by the value
of u, corresponding to the party's age at the beginning of the
year, and subtract the product from unity.
ffomans's Contribution Formula. Let r = the actual rate
of interest received, e= the expenses, and * +n (i H x + n +j)
the actual cost of insurance, then
rf 'x + n
x+n i' x + n x + n + i
contribution to surplus.
Formulae for verifying Commutation Columns.
C x = v. D x Dx+i MX = v. Nx_! NX = Dx v. N x
R x = v . Sx-, - Sx M x+n = v. N x+n -, - N I+n =
R x+n = f. S x+n - t -S I + n .
Equation of Life. Let l x = the number of living at age #,
the number of living at the age of equation, 4 +B the number
2
of living at the beginning of the year in which the equation takes
place, /, +H +i the number living at the end of the year,y= the
fraction of a year, which, added to x+n, will make the equation
then = /,++/ and we have
2
f __ j=+n x+n+/ substitutinjr for L,^ t
7 + -^
** + n 2
C + .~ 4 + n+l
Expectation of Life.
WRIGHT'S FORMULA FOR INSURANCE VALUES.
Representing the insurance value at the age x+n by X + B L,
we have the general formula,
N d " N **'* '
, + ! = ^-r- X
If we assume x = 10, and perform all the multiplications of
j /i i .
into N n , and -j into N 12 , &c., as indicated by tlie numera-
/u n
152 PRINCIPLES AND PRACTICE
tor three lines above, the summation of the products, after the
manner in which the N column is produced from the D, will
produce a column of numerators which we will call A, and this
will give us x+n 1*=-^- x ^L, and x+n l x+t = -5^_ x
x + n **x **m +*"
x+ " x+t when the policy has completed /years and the (/+ i)th
premium is just paid.
The formula for the insurance value on a paid-up policy is
r+
The formula for any policy payable at age x + n, or previous
death, including the ordinary whole life policy, is thus modified
by Mr. McClintock. Let K X be the annual premium to be paid
q times and when the first premium is just paid, we have
j T x + n 'V * + y A.X
and when the (/+i)th premium has just been paid,
T ! ,7 * + n A * + < . + ,** + ,
.+ i.t, | i - D ^- T, x+t
PROF. BARTLETT'S FORMULA FOR SURRENDER
VALUES.
Prof. Bartlctt, actuary of the Mutual Life Insurance Company
of New York, has pi'oposed the following formulae for finding
the surrender value of a policy, which is based upon the fol-
lowing assumptions :
A reserve of an individual member of a company is what the
company should have to the member's credit at a given epoch
after subducting from the amonnt paid by him, augmented by
his interest earnings, his proportion of the death claims that
have matured up to the same epoch. A surrender value is the
amount the company should pay to abrogate a contract between
itself and one of its members.
By the terms of this contract the company promises to pay to>
the heirs of the assured at his death, whenever that may hap-
pen, a certain specified sum of money. And the assured pays r
in consideration, another sum down, called, let us suppose, a
single net premium, which is the present net value of the assur-
ance. This premium must be such as to amount at compound
interest to the sum assured, should the assured live to the great-
OF LIFE INSURANCE. r$3
est age of the tables, and, besides, it must contribute its share to
the payment of the death claims, from year to year, of other
members who die before attaining to this age ; and this obliga.
tion to pay death claims must last during the life of the assured,
which life is assured in the original agi'eement to extend to the
oldest limit of the tables of mortality employed in computing the
premium.
The company and the assured have, therefore, joint interest in
the policy of the latter. The present money values of these in-
terests being found at the time of the surrender, their difference
will obviously be the surrender value.
The company's interest in any particular policy is the present
value of the sums the policy would, if continued in the company
in its present condition, contribute from year to year to pay death
claims on other policies.
The interest of the assured, or of his heirs, in his policy is the
present value of the reversion or sum the latter would receive at
the death of the owner, provided he pay nothing more than he
has already paid. This interest is the present reserve.
Make
11^= Single net premium at age x to insure one dollar at death.
R, = Net reserve on policy at age x when surrender is made.
m Number of years the policy has to run to maturity.
*z = Difference between the oldest age of tables and that of
policyholder at time of surrender.
V z = Present value of one dollar due in x years.
tf= Sum assured or amount of policy.
Life Single Premium. Take the life single premium as a
standard, we have R, = TT,. and /;/ = n.
Denoting the surrender value by Q_, the surrender value of tf
is found by the formula :
x- _ C.,. Rj + i + C r +\- Rz+a . . . . + C x + n R^+,, + 1
Tabulate the numei'ator of the second member under the head
T, after the manner of the commutation columns N, M, S, &c.
Then will Q*. = a -2f- ( z )
Life Annual Payments. In this case
T> rr>
154 PRINCIPLES AND PRACTICE
Life, Limited Payments.
R T
^-"-nT-lt ...... (3)
this differing from the last case only in the value of R,.
Temporary Single Premiums. Here the formula becomes :
Q _ Cj. RI+I 4- Ci+i R T + 2 .... Qr+pt i. R g + OT i
^^
C x . Rx-H, *
~~
Temporary Anmial Premium.
o -- a -^r- C *- R *+" '"- 1 / C N
u '. ~~D~
IT a being the single premium to purchase temporary insurance
of $i at the age of surrender.
Simple Endowments Si):gle Premium. The company has
no interest in the longevity of the holder of this kind of policy.
On the contrary, by the principle of the Tontine, its interest is in
his early death, at least death before the policy matures.
The reserve being R, there are l x chances for and against the
company. Of these d x , d x+l , etc., to t/ 1>+OT _ 1 , favor lapse by death,
and the surrender value is
**'*'+--')
- (6)
Simple Endowments Annual Premiums.
Q_=..R, *-a (7)
Endowment Assurances Single Payment. This being a
combination of the simple endowment and temporary insurance,
the surrender value is found by taking the sum of equations (4)
and (6).
- (S)
Endowment Assurances Annual Payment. Here take the
sum of equations (5) and (7), or
. ..
The reserves R z and R, must be : the first for the assurance
part of the policy, the second for the endowment.
OF LIFE INSURANCE.
'55
TABLE No. LX
SURRENDER VALUES. LIFE POLICY FOR $1.000, ENTERED AT AGE 35,
PAYABLE AT AGE 100, OK PREVIOUS DEATH.
BY MR. WHIGHT'S METIIOH: Sun <ENDEK CHAKGK, 8 PER
PROF. RANTLKTT'S
CCNT OF INSUKANCK VALUK.
MbTIIOD.
Combined E.tpei tence,
Combined Experience,
American Experience,
4 pfr cent.
Actual Prrm.. $26.38.
6 per cent.
Actual Prem., $20.45.
* fer cent.
Actual Prem . $26.38.
Age.
Net Prem . $1987
Net Prnn.. $16.49.
Net. Prem., $18.84.
Surrender
Surrender
Surrender
Surrender
Surrender
Surrender
Value.
Charge.
Value.
Charge.
Value.
Charge.
36
O.OO
17-33
0.00
13.26
6.38
437
37
5-S9
17-45
3-44
13-45
13-14
8.74
38
18.02
17-57
12.31
13-64
20.29
13-H
39
30-56
17.69
21. 6l
13-S4
27.84
17-54
40
43-52
I/.82
3'-45
14.05
35-81
21-95
4i
56.91
17-95
4 I -5 I
14.27
44-20
26.36
42
70-75
18.09
52.24
14.50
53-03
30.78
43
85.07
lS.22
63-39
14-74
62.30
35-20
44
99-79
18-37
75-H
14.98
72.04
39.62
45
114.90
iS.si
87.27
l.S-23
82.23
44-03
46
130-37
iS.6s
99.80
15.48
92.90
48.42
47
146.14
18.78
112.77
15-73
104.03
52-79
48
162.21
18.90
126.12
15.98
115.64
57- 1 2
49
i/S-55
19.01
I39-83
l6. 21
127.72
61.40
5
I95-I9
19.11
1^4.01
16.45
140.25
65.62
5 1
212.07
19.21
168.50
16.68
153-23
69.76
52
229.22
19.28
183-31
16.89
166.66
73.80
53
246.57
19-35
198.50
17.10
180.54
77.72
54
264.14
19.40
214.13
17-30
194.84
Si-53
55
281.92
J 9-43
230.01
17-49
209.57
85.18
56
299.87
19-45
246.23
17-67
224.71
88.68
57
3 '7-98
19-45
262.68
17.82
240.24
92.00
58
33^-25
19.44
279-53
17.97
256.16
95-13
59
354-65
19.41
296.75
18.10
272.46
98.03
60
373-iS
19-35
3 14-11
lS.2I
289.10
100.73
61
39- /3
19.29
33I-65
18.30
306.07
103.18
62
4 '0-33
19.19
3-19-43
lS-37
323-34
105-37
63
428.90
19.08
367-38
18.42
340.89
107.30
64
447-42
18.94
3S4-5I
18.44
358.71
108.93
65
465-85
18.79
403-56
18.44
3/6-74
110.29
66
484.17
18.60
421-59
18.41
394.96
m-3
67
50^.32
18.40
439- M
18.36
4I3.34
112.06
68
520.29
18.16
457-93
lS.27
43' -84
112.46
69
538-04
17.91
4/5-84
18.16
450.42
112.52
ENDOWMENT POL. OF $1.000, ENTERED AT 35. PAYABLE AT 45 OR PREVIOUS DEATH.
Actual Prem., $105.58
Actual Prnn.. $89.25
Actual Prem., $io<; .53.
Net Prem., $85.03.
Net Prem., $76.71.
Net Prem.. $84.80.
36
77.19
2.72
70.05
2.65
72.49
7-47
37
161.38
-2.22
148.13
2.18
149.92
13.82
38
249-57
1.74
23I-47
i-74
232.67
18.90
39
342.00
1-30
320.47
1.32
32'-I3
22.51
40
438.77
.92
4I5-57
93
4I5-74
24.47
4i
540.48
.58
517-24
58
5I6.97
24-5*
42
647.10
30
625.92
32
625-38
22.46
43
758.99
.11
742.21
.11
741-55
17.92
44
876.51
.00
866.68
.00
866.17
io-55
45
1,000.00
.00
1,000.00
.00
I.OOO.OO
0000
156 OF LIFE INSURANCE.
VALUATION OF JOINT-LIFE POLICIES.
BY SETH C. CHANDLER, JR.,
Actuary of the Continental Life Insurance Company, of N. T.
The following simple modification of the "accumulation"
formula offers peculiar facilities for the valuation of all kinds of
joint-life and joint-endowment policies, though its application is
by no means limited to this class of insurances, but is universal.
By substituting the values of u and k,
r
in the " accumulation" formula,
n + ! 71
H xy = xy + n ( H xy + **) ~
we obtain the expression,
where p x y+n is the probability of two lives x+n and y+n or
the product of the probabilities of each life living one year.
This formula dispenses with the necessity for the preparation
of the auxiliary quantities u and k for different combinations of
ages, and requires simply a table of the arithmetical complements
of the logarithms of the probability of living one year.
The values of this element, according to the Actuaries'
table of mortality, are here inserted, and also an example of the
method of computation by the formula.
Example. Required, the net values by the " actuaries' " table
4 per cent interest at the end of the first and second years, of an
ordinary joint-life policy issued at ages 46 and 38.
TT 46-38 =----------- .041036
TT 46-38 xi. 04 =--------- .042677
^(TT 46-38 xi. 04) = ......... -957323
i-(7r 4 6-3Sxi.o 4 ) x-^-x ^- = ..... -979477
H'46-38 ..... ...... .020523
Second year.
1^46-38 + ^46-38 =---., ..... -061559
x 1.04 =----------- .064021
i (H '46-38 + ^46-38) i. 04 = ....... -935979
xx ?k" ......... - 958514
.......... .041486
PRINCIPLES AND PRACTICE
'57
TABLE No LXI
VALUATION OF JOINT-LIFE POLICIES, CHANDLER'S FORMULA, COM-
BINED EXPERIENCE, 4 PER CENT.
Age.
^og.~
I
7
Age.
Log.-
i
P
10
002.9458
i. 0068 i
48
006.2374
.01447
II
002.9571
1.00683
49
006.5907
.01529
12
002.9685
1.00686
50
006.9798
.01620
13
002.9845
1.00690
51
007.4015
.01719
4
003.0052
1.00694
52
007.8652
.01828
IS
003.0260
1.00699
53
008.3720
.01946
16
003.0519
1.00705
54
008 9128
.02073
17
003.0781
1.00711
55
009.5121
.02215
18
003. 1092
1.00718
56
010.1615
.02367
19
003.1410
1.00726
57
010.8526
02530
20
003.1780
1-00735
53
011.6130
.02710
21
003.2156
1.03743
59
012.4439
.02907
22
003.2538
1.00752
60
013.3788
.0^128
2.3
003 2976
1.00762
61
014.3991
* -0337 i
24
0033421
1.00773
62
015.5269
1.03640
25
003.3876
1.00783
63
016.7526
1-03943
26
0034387
1.00795
64
018.1024
1.04256
27
003.4910
1.00807
65
019-5793
1.04611
28
003.5491
1.00821
66
021.1869
1.04999
2 9
003.6087
1.00834
67
022.9508
1.05427
3
003.6743
1.008^9
68
024.8578
.05891
31
003.7416
1.00865
69
026.9124
06393
3^
003.8154
1.00882
70
029.1572
06944
33
003.8909
1.00900
7i
03 i- 599
07545
34
003.9682
1.00918
72
034-2363
.08202
35
004.0525
1.00937
73
037.1022
.08919
36
004.1389
1.00957
74
040.2280
.09700
37
004.2274
1.00978
75
043.6203
.10566
33
004.3237
I.OIOOI
76
047.2944
"505
39
004.4223
1.01024
77
051-3275
12545
40
004.5236
1.01047
78
055-7367
.13694
4i
004.6333
.01073
79
060.5131
M95*
42
004.7573
.01101
So
065.7068
16334
43
004.9139
.01136
Si
071.3152
.17846
44
005.1100
.01186
82
077-375I
.19502
45
005.3363
.01234
83
084.0265
.21346
46
005.6120
.01301
84
091.3426
.23408
47
005.9098
.01370
85
099.6848
.25801
158 PRINCIPLES. AND PRACTICE
A NEW METHOD OF VALUING POLICIES.
BY EMORY MCCLINTOCK,
Actuary of the Northwestern Mutual Life Insurance Company, Wis.
The following formula; for valuing whole life policies and
endowment policies premiums payable to a certain age, is now
published for the first time, and for one who has not the valua-
tion tables at hand, is the easiest method of finding the reserve
on a policy at the end of the year.
Having graded the column of " differences" according to the
space given for the table, the "values" are found by the follow-
ing formula.
Let d = the difference.
"Value" = looo [i log- 1 (o oooi x d) ]
Example. Let d = 500, required the " value."
1,000 [i log- 1 (o ooo i x 500)] = i, ooo [i log- 1 (0005)]==
1,000 [i log" 1 (9,9950000)] = i,ooox (i 9SS55) = n.45.
.98855 is the nearest number corresponding to log. 9,9950000.
Let d = 4000, required the " value."
1,000 [ i log" 1 (0,0000 1 x 40oo)] = icoo [i log" 1 (0.04)] =
1,000 x i log" 1 (9,960 0000) = i ooo x (i .91201)= 87. 99.
This table, which is simply one of the complements of loga-
rithms, and the complements of numbers corresponding to these
complements, applies to all the intermediate values of d, and to
any table of mortality and rate of interest.
The " age numbers" in this table for whole life policies, were
obtained by the formula, 100,000 (log. A 15 log. A 15+ /),
and the general formula is 100,000 [log. A x log. A x+m ), m
denoting the year of the policy in which the value is required.
The formula for " age numbers " on endowments issued at
age *, and payable at age x + n, is
100,000 Hog- *~ x+n log. ~ m *\
x ' "*" m '
Examples of finding the value of a policy by this method.
Required the value of a whole life policy, age 30, at the end
of the 3d year. American Experience 4^ per cent.
Under the column of " age numbers" of whole life policies
opposite age 30, is the age number 3,476 ; opposite 33, the age
at valuation, it is 4,531, and the difference of these " age num-
bers" is 1,055.- By inspecting the column of " differences," we
OF LIFE INSURANCE.
159
find the value opposite to 1,000 to be 22.76, and the difference
between 1,055 ant ^ !jOOO multiplied by the " multiple of differ-
ence" 2.25, gives 55 x 2.25 = 1.23, which added to 22,76, gives
22.76 + 1.23 = 23.09, the value required.
Required the value of the same policy at the end of the loth
year.
The age number at 40 is 7,700, and at 36 is 3,376, difference
of age number 4,224 ; value opposite, 4,200 = 92.18, corrections
4,2244,200 = 24 x 2.09 =50, therefore 92.18 + 50 = 92,88, the
value.
Required the value of an endowment policy, age 20, 3d year,
payable at death or 40. American Experience, 4* per cent.
The difference in the age numbers in the column " Death, or
40, is 9,4265,188 = 4,238 ; value opposite 4,200 = 92.18, cor-
rection (4,2384,200) 2.09 = So ; therefore 92.18 + So = 92,98,
the value.
This method of valuation applies only to the terminal values
of whole life policies and to continued premium endowments
maturing at certain ages, but the values of nearly all continued
premium endowments can be found by this table in the suffi-
cient exactness for all practical purposes. Thus the reserve on
a ten year endowment, age 43, payable at death, or 53, differs
but very little from the reserve on an endowment issued at 45
and payable at 55.
With a little practice, the terminal value of any policy given
in these tables can be found to the nearest dollar by inspection.
i6o
PRINCIPLES AND PRACTICE
TABLE NO. LXII.
VALUES AND DIFFERENCES FOR MCCLINTOCK'S METHOD OF VALUING
POLICIES, ADOPTED TO ANY TAIILE OF MORTALITY AND RATE OF
INTEREST.
Difference.
Value.
Multiple of
Difference.
Difference.
Value.
Multiple of
Difference.
.IOO
$2.30
2.29
5.100
$110.80
2.04
.2OO
4-59
2.29
5-200
112.84
2.04
.303
6.SS
2.29
5-300
11488
2.04
.400
9.17
2.28
5.400
116 92
2.03
./JOO
"45
2.27
5-50
11895
2.03
.Coo
13.72
2.27
5.600
20-98
2.02
.700
15-99
2.26
5.700
23.00
2. 02
.800
18.25
2.l6
5.800
25.02
2.OI
.900
20.51
2-25
5.900
27.03
2.01
I.OOO
22.76
2.25
6.000
29.04
2.OO
.100
25.01
2.24
6.2CO
33-4
99
.200
27-25
2.24
6.400
137.02
.98
.300
29.49
2-23
6.600
140.99
97
.400
3i-72
2.23
6.800
M4-93
97
.500
33-95
2.22
7 ooo
148.86
.96
.600
36.17
2.22
7.200
i5 2 -77
95
.700
3S-39
2.21
7.400
156.67
1.94
i.Soo
40 60
2.21
7.600
160.54
1-93
1.900
42.81
2.20
7.800
164 4O
1.92
2.OOO
45.01
2.19
8. ooo
I6S.24
1.91
2. IOO
47.20
2.19
8.200
I72.0(j
1.90
2.200
49.40
2.18
8.400
175.86
1.89
2-300
5i-5S
2.18
8600
I79- 6 5
1.88
2.400
53-76
2.18
8.800
183.^2
1.87
2.SOO
55-94
2.17
9.000
l8 7 .I7
i. 86
2.600
58.11
C.17
9.200
I9O.9O
i. 86
2.7OO
60.28
2-l6
9400
I9J.62
1-85
.Soo
62.44
2-15
9.600
19^-32
1.84
2.900
64-59
2-15
9.800
202. OI
1-83
3.000
6675
2.14
10.000
205.67
1.82
3.100
68.89
2.14
IO.2OO
209.32
i.Si
3.200
7i-c>3
2.14
10 400
21295
i.Si
3-300
73-'7
2-13
10.600
216.57
i.So
3.400
75-30
2.12
10 Soo
220.17
1.79
3.500
77-43
2.12
11. OOO
223-75
1.78
3.600
79- '5
2. 1 1
II.2OO
227.32
i-77
3.700
81.67
2.11
11.400
230.87
1.76
3 ^0
83.78
2.11
1 1 .600
234-40
1.76
39~o
85.89
2.IO
11.800
237-92
i-75
4.003
87.99
2.IO
12.000
241.42
1.74
4.100
90.09
2.O9
12.200
244.91
1-73
4 200
92.18
2.09
12 400
248.38
1.72
4.300
94.27
2.o8
I2.6OO
25I-3
1.72
4.400
90-35
2.08
12.800
255-27
1.71
4.500
98-43
2.07
13 ooo
258 69
1.70
4.600
100.50
2.O7
13.200
262.10
1.69
4.700
102.57
2.06
13.400
261 49
1.68
4.800
104.63
2. (.6
13 600
268.86
i. 68
4.900
106.69
2.06
13-SoO
272.22
1.67
5.000
10875
2.05
14.000
275-56
1.66
OF LIFE INSURANCE.
161
TABLE No. LXII. (CONTINUED.)
VALUES AND DIFFERENCES FOR MCCLINTOCK'S METHOD OF VALUING
POLICIES, ADOPTED TO ANY TABLE OF MORTALITY AND RATE OF
INTEREST.
Difference.
Value.
Multiple of
Difference.
Difference.
Value.
Multiple of
Difference.
14.200
278.89
1.66
25-a50
440.89
1.28
14.400
282.21
1.65
25-500
444.10
1.27
14.600
285.50
1.64
25-750
447-29
1.27
14.800
288.79
1-63
26.000
450.46
1.26
15.000
292.06
1.62
26.250
453-61
1.26
15.200
29.v3I
1.61
26.500
456.75
1.25
15400
298.54
1.61
26.750
459-87
1.24
15.600
301.77
i. 60
27.000
462.97
1.23
15.800
304.98
1-59
27.250
466.05
1.22
l6.OOO
308.17
1-58
27.500
469.12
1. 21
I6.2OO
3"-35
I-5S
27.750
472.16
1. 21
16.400
3H-5 1
1-57
28.000
475.I9
1. 2O
16.600
317.66
i-57
28 250
478.20
1.20
16.800
320.80
1-56
28.500
481.20
I.I9
17.000
323.92
i-55
28.750
484.18
i.iS
17.200
327.02
i-55
29.000
487.14
1.18
17.400
330.12
1-54
29.250
490.08
1.17
17.600
333-19
i-53
29.500
493.01
1.16
17.800
336.26
1.52
29.750
495.92
i-i5
18.000
339-31
i-5i
30.000
498.81
I-I5
18.200
34 2 -34
i-5i
30.250
501.69
1.14
18.400
345-36
1.50
30.500
504-55
1.14
18.600
343-37
1.50
30.750
507-39
i-i3
18.800
351-37
1.49
3I.OOO
510.23
1. 12
ig.OOO
354-35
1.48
3 I - 2 50
5I3-03
1. 12
19.200
357-31
1.48
31-500
515-83
I. II
19.400
360.27
1.47
3J-750
518.61
1. 10
19.600
363.20
1.46
32.000
521-37
1. 10
19.800
366.13
i-45
32.250
524.12
1.09
20.00O
369.04
i-45
32-500
526.8 5
1.08
20.250
372.66
1.44
33-ooo
532.26
1.07
20.500
376-27
i-43
33-500
537-62
1. 06
20.750
379-84
1.42
34.000
542.91
1.05
21.000
383-40
1.41
34-500
548.14
1.04
21.250
386.94
1.41
35-000
553-32
1. 02
21.500
390.46
1.40
35-500
558.43
1. 01
21.750
393-9 6
i-39
36.000
563.48
I.OO
22.OOO
397-44
1.38
36.500
568.48
99
22.250
400.90
i-37
37.000
573-42
.98
22.500
404-34
i-37
37-550
578.30
97
22.750
407.76
1-36
38.000
583.13
.96
23.000
411.16
i-35
38.500
587.90
95
23.250
4H-54
34
39.000
592.62
94
23.500
417.90
33
39-500
597-28
.92
23-750
421.24
33
40.000
601.89
.91
24.000
424.56
32
40.500
606.45
.90
24.250
427.86
3i
41.000
610.95
.90
24.500
43I-I5
30
41.500
615.41
.89
24-750
43441
30
42.000
619.81
.88
25.OOO
437-66
.29
42.500
624.16
.87
162
PRINCIPLES AND PRACTICE
TABLE No. LXIL (CONTINUED.)
VALUES AND DIFFERENCES FOR ^'CCLINTOCK'S METHOD OF VALUING
POLICIES, ADOPTED TO ANY TABLE OF MORTALITY AND RATE OF
INTEREST.
Difference.
Value.
Multifile of
Difference.
Difference.
Value.
Multiple of
Difference.
43.000
$628.46
.86
68.000
$791.07
.48
43- 5
632.72
85
68.500
793-46
47
44.000
636.92
83
69.000
795-83
47
44.500
641.08
.82
69.500
798. 16
.46
45.000
645-19
.81
70.000
800.47
.46
45.500
649.25
.80
70.500
802.76
45
46.000
653-26
79
71.000
805.02
45
46.500
657-23
.78
71.500
807.25
44
47-000
661.15
.78
72 coo
809.45
44
47.500
66v03
77
72.500
811.64
43
48.000
688.87
76
73-ooo
813-79
43
48.500
672.66
75
73-500
815.92
.42
49.000
676.41
74
74.000
818.03
.42
49.500
680. 1 1
73
74.500
820-11
.41
5O.OOO
683-77
7 2
75-000
822.17
.41
50.500
687-39
72
75-5 e o
824.21'
.40
51.000
690.97
7i
76. dcJo
826.22
.40
5*-5*i
694-5I
.70
76.500
828 21
39
52.000
698.00
.69
77.000
830.18
39
5 2 -5oo
701.46
.68
77-500
832.12
38
53.006
704.88
.68
78.000
834.04
38
53-5oo
708.26
.67
78.500
835-94
38
54.000
711.60
.66
79.000
837-82-
37
54- SCO
714.90
65
80.000
841.51
36
55.000
718.16
65
81.000
845.12
35
55- 5
721-39
.64
82.000
848.64
35
56.000
724.58
63
83.000
852.09
34
56.500
727-73
.62
84.000
855-46
33
57.000
73 -85
.62
85.000
858.75
32
57-50
73393
.61
86.000
861.96
3i
58.000
73697
.60
87.000
865.10
3i
58 5
7399 s
59
88.000
868.17
30
59.000
742.96
59
89.000
871.18
.29
59-500
60.000
745-90
74881
58
58
90.000
91.000
874.11
87697
.286
.280
60.500
751-69
57
92,000
87977
.270
61.000
754-53
56
94.01.0
885.18
259
61.500
75734
56
96.000
890-35
247
62.000
760.12
55
98.000
895.29
.236
62.500
762.86
54
IOO.OOO
900.00
.225
63.000
765-58
54
IO2.OOO
904.50
215
63-5CO
768.26
53
104.000
908.80
.205
64.000
64.500
770.91
77354
53
52
106 ooo
108 ooo
912.90
916.82
.196
.188
s~
65.000
7/6-13
5 1
no ooo
920.57
.163
65.500
778.69
5i
I2O.OOO
936.90
.130
66.000
781.22
50
130.000
949.88
.103
66.500
783-73
49
140.000
960.19
.082
.^C rf
67.000
786.20
-49
150.000
968.38
.065
67.^00
788.65
.48
1 160.000
974 88 i .050
OF LIFE INSURANCE.
163
TABLE No. LXIII.
McCLiNTOCK's METHOD OF VALUING POLICIES; JOINT LIVES, AGE
NUMBERS, COMBINED EXPERIENCE, 4 PER CENT.
Tottno'tr
Age.
Equal
Ages.
2>/y. V
vl^YS,
5 JVars.
J9/^". in
Ages,
10 tears.
Diff. in
Age*.
15 1 ears.
Diff. in
Agts.
2O / ears.
Diff. in
Ages,
25 tears.
Diff. in
Ages,
30 Tears.
15
.000
.OOO
.OOO
.OOO
.000
.000
.OOO
16
.269
.302
346
405
.487
.604
753
17
550
.616
.706
.828
.996
1.239
i-536
IS
.842
943
1. 08 1
1.269
I -53
1.906
2-350
19
I.I47
1.284
1.471
1.729
2.089
2.6os
3-195
20
1.464
1.639
1.879
2.210
2.676
3-336
4-073
21
i-794
2.008
2-305
2.713
3.291
4.097
4-985
22
2.138
2-393
2.748
3-238
3-938
4.887
5-931
23
2.496
2 -794
3-210
3-788
4.617
5-711
6. 112
24
2.868
3-212
3.691
4-363
5-328
6.565
7.928
25
3-256
3-647
4.194
4966
6.071
7.451
8-983
26
3.660
4.101
4-7 r 9
5-599
6-845
8.371
10.073
27
4.080
4-573
^.268
6.264
7.649
9.326
11.207
28
4-5I9
<5-o66
5-843
6.962
8.485
10.316
12.381
2 9
4.976
5-581
6-444
7.692
9-353
11.342
I3-598
30
5-452
6.1 18
7-074
8-455
10.255
12.406
14.858
3.1
5-94S
6.678
7-73-5
9.251
11.189
13.509
I&I&
32
6.466
7:264.
8,429
10.077
12.159
14.65-1
17-: soft;
33
7.006
7.:S 7 S
- 9- l ST
10.936
13-165
15.835
I&S9J
34
7-569
8.520
9.920
11.827
14.208
17.062
20-3^4>
35
8-- 1 59
9,192.
10.718
12.754
15.290
18.334
.2J.797T
36
8-775
9.900
"550
13-717
16413
19.650
23-313
37
9-42J
10.644
12.415
14.717
I7-576
21.009
24.870.
38
10.098
11.425
J 3-3'7
15-757
18.784
22.413
26.470
39
10.808
12.246
14-255
16.836'
20.038
23.862.
28.113
40
"555
13-105-
I5-233
17-958
21.340
25-356
29.800
4i
12.342
14.005
16.252
19.124
22.490
26.896
31-533
42
13.171
14-944
17-313
20-337
24.088
28.484
33-312
43
14.046
15.926
18.419
21.600
25-535
30.117
35-I38
44
14.963
16.948
19.569
22.912
27.030
31-795
37-oi2
45
15.922
18.012
20.763
24.272
28.572
33-519
3S-939
4 6
16.922
19.116
22.OOI
25-679
3- I 58
35.288
40.894
47
I7-958
20.259
23.281
27.131
31.786
37.098
42.902
48
19.032
21-443
24.606
28.627
33-456
38.950
44954
49
20.144
22.667
25-977
30. 166
35 '66
40.845
47.047
50
21.297
23-934
27-394
,o o - -
3L750
36-919
ryQ H f A
42.781
A A *j(yCl
49.186
5 1
22.490
25.244
20.857
33-376
3 i3 -7 I 4
44.700
Aft 787
5 3
23-725
26.597
3 -364
35.O45
4O-55 1
At /nQ
4" /J
A S SAH
53
25.000
^/r - T Q
27.966
31.916
36-754
O o -. , .
42.420
40.047
r f\ f\c 2
54
26.310
/** AQ T
29.441
33-5 12
3 a -54
44-347
A f\ "?ri*7
5 U< 95^
C7 TOO
55
-f.
27.001
~ ,-.00
3-935
35- 1 5 2
->fi Q-jr
40.296
40.307
5 V 5- 1L * J
5"
29.000
3 2 -474
3- & 35
,q rf.r
42.130
3
30.540
3-1 -59
30.501
44.005
A C nT}
5
32.041
35-69 1
4-33
45-9 2 *
A>7 SS->
59
f<n
33-59 2
37-37 1
42.142
A f f\r&
47.002
An 8S?
VJ*J
it*
35-H9
tf\ R/i?
39.097
*r*i 9A-T
43.990
49.00.5
wi
flf
3-43
,C ,,Q
40. 007
\J&
f.-.
3 o -53
Ar\ >*?S
42.679
A 4 T"? T
3
f>A
tfU. / O
44o3 x
4
42.O62
^ ' * . | j j
164
PRINCIPLES AND PRACTICE
TABLE No - LXIV.
MCCLINTOCK'S METHOD OF VALUING POLICIES, AGE NUMBERS,
AMERICAN EXPERIENCE, 4^ PER CENT.
Age.
Whole Life.
Endotvmtnt at
Death, or 40.
Endoivmtnt at
Death, or 45.
J5nifo7vmfttl at
Death, or 50.
15
16
17
18
'9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
3 I
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
8
60
61
62
63
64
.OOO
.i6j
332
5'i
.698
895
Z.IOI
i-3i7
1-544
1.781
2.030
2.292
2.567
2-855
3-I58
. 3-476
3-Sii
4.162
4-531
4.919
5-326
5-755
6.205
6.679
7-177
7.700
8.250
8.829
9-438
10.079
10.752
11.460
12.204
12.985
13.804
14.662
15-559
16.497
17-477
18.501
19.568
20.681
21.839
23.046
24.301
25.605
26.959
28.364
29.821
3i-33o
.OOO
.891
1.^48
2.878
3-987
5.188
6.486
7-884
9.426
11.098
12.929
14.944
17.169
19.642
22.405
25-518
29-055
33-120
37-856
43-475
50-304
58893
70.271
86.750
115.708
.OOO
.638
I-3I9
2.047
2.825
3-658
4-551
5-510
6.541
7.652
8.852
10.150
11-558
13.090
14.762
16.592
18.605
20.829
23.298
26.058
29.166
32.697
36-755
41.483
47.091
53-9' J 8
62.482
73-843
90.301
119-235
.000
.472
973
1.506
2.072
2.675
3-3i8
4.003
4-734
5-5I5
6-352
7.248
8.210
9. 2 44
10-358
11.560
12.860
14.271
15.804
17.476
19.306
21.319
23-540
26.006
28.762
31-863
35-386
39-433
44.148
49.741
56.538
65.089
76.42!
92844
121-735
OF LIFE INSURANCE.
I6 5
TABLE No. LXIV. (CONTINUED.)
McCLiNTOCK's METHOD OF VALUING POLICIES, AGE NUMBERS,
AMERICAN EXPERIENCE, 4^ PER CENT.
Ag*.
Endowment at
Death, or 55.
Endowment at
Death, or 60.
Endowment at
Death, or 65.
Endowment at
Death, or 70.
15
.COO
.OOO
.OOO
.OOO
16
357
.282
.230
.197
17
757
579
.472
403
18
I-I39
893
.670
.621
19
1-565
1.225
.996
849
20
2.017
1-575
1.279
1.090
21
2.496
1.946
l '57&
1-343
22
3.004
2-337
1.892
i. 608
23
3-544
2-751
2.223
1. 888
24
4.117
3-189
2-573
2.182
25
4.727
3652
2.942
2.491
26
5-377
4.144
3332
2.817
27
6 609
4.665
3-743
3.161
28
6.808
5.218
4*79
3-522
2 9
7-597
5.806
4.638
3-904
3
8.440
6.430
5-125
4.306
3i
9-344
7.094
5.640
4730
3 2
10.313
7.801
6.186
5-I78
33
H355
8-555
6.764
5-65I
34
12-475
9 2 59
7378
6.151
35
13684
10.218
8.029
6.679
36
14.990
11.138
8.722
7-237
37
16.406
12.123
9-458
7.828
3S
17-944
13.180
10.242
8.453
39
19.620
14.316
11.076
9.114
40
21-453
15-540
11.967
9.816
4 1
23.466
16861
12.917
10-559
42
25.688
18.290
13-934
11.348
43
28.152
19841
15-023
12.186
44
30-903
21.529
16.191
I3-077
45
3399 s
23373
17-447
14.025
46
37-5"
25-395
18.800
I5-034
47
41-544
27.621
20.259
16.110
48
46.240
30.088
21.837
17-257
49
51.808
32-835
23-549
18.483
50
58.572
35-920
25.412
19.792
5'
67.079
394H
27-445
21.193
52
78.356
43.418
29.675
22.695
53
94.711
48.074
32.135
24.309
52
123.521
53-588
34876
26.049
re
60 78 c
7*7 0^2
27 Q1O
OJ
r<5
*J\J* ^O^
68.710
o/-y-*
4.1 lid.
*/ 'yjr*
2Q O72
o"
C7
79.886
T i- O/T
4C 722
*y 71
72 IOQ
Jt
rk
06 T27
45-0^*
A(\ OO7
o^-^W
74. 6j.2
O
CO
yU.l.ij
T 24 7OO
TV-V^a
CC 724.
OT""T -
77, -142
2 y
60
i ^T-/y j
J.V J^T
61.906
O/ -JT*
4O.7.48
61
TO IOI
T^-' JT V
4.7 77O
62
/u. iyi
Sr TOO
T- J / f*
47.?8l
61
LA> j-yy
OT 27C
T/'.I'-'J
C2 O47
u j
64
y/'^JJ
125.666
O^-^TJ
57-3"
i66
PRINCIPLES AND PRACTICE
TABLE No. LXV.
McCLiNTocK's METHOD OF VALUING POLICIES, AGE NUMBERS,
COMBINED EXPERIENCE 4 PER CENT.
Age.
Whole Life.
Endowment at
Death, or 40.
Endowment at
Death, or 45.
Endowment at
Death, or 50.
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3 1
32
33
34
35
36
37
38
39
AO
.OOO
.222
453
.694
944
1.205
1.476
1-758
2.052
2.358
2.676
3.607
3-320
3-7"
4.085
4-475
4.8^1
5-304
5-745
6.205
6.6S6
7.187
7.711
8.260
8-833
.OOO
973
2.013
3.128
4-324
5.609
6.994
8.490
IO.II2
11.874
13-795
15.901
18.218
20.782
23.638
26.842
30-471
34.628
39-456
45- 1 66
52.086
60.766
72-234.
88.803
96.588
.OOO
715
1-473
2.279
3-137
4-051
5.026
6.067
7.182
8-377
9.661
11.045
12.538
14.156
I5-9H
17.831
19.930
22.240
24.994
27.640
30-832
34.448
38-590
43-402
49-095
r C.QQ7
.OOO
543
1.117
1-723
2.364
3-043
3-762
4-525
5-334
6.195
7.111
8.087
9.130
10.245
11.440
12.724
14.105
I5-596
17.210
18.962
20.873
22.964
25.266
27.812
30-647
n S'o
64. 6s6
77 ,17,1
*?6 IO7
A I c6d.
A1
Q^^dS
4.6.76.1
107.716
C2.O4.2
rS Q27
45
46
67 CC7
4 U
1 3*v4
78.960
47
A&
OC.4.C7
no ccc
49
IO./45
5 1
5 2
1 9*93
oJ
54
55
c6
5
- J 3'39 1
cA
*4o,>
5
(a
2 5'//
60
^G Tj-l
6l
*33J
62
67
fiA
04
65
.53-9 01
35-475
OF LIFE INSURANCE
TABLE No. LXV. (CONTINUED.)
167
MCCLINTOCK'S METHOD OF VALUING POLICIES; AGE NUMBERS,
COMBINED EXPERIENCE, 4 PER CENT.
Age.
Endowment at
Death, or 55.
Endowment at
Death, or 60.
Endowment at
Death, or 65.
Endowment at
Death, or 70.
15
.OOO
.OOO
.OOO
.000
16
.426
346
293
.258
17
875
.710
599
.528
18
1-347
I.ogi
.920
.810
'9
1.844
I. 49 I
I - 2 55
1.104
20
2.368
I.gll
1.606
1.411
21
2.920
2.351
1.972
I-73I
22
3-52
2.814
2-356
2.065
23
4.116
3-3o
2.758
2.414
24
4-765
3.810
3- '79
2778
25
5-45 1
4-348
3.620
3-159
26
6.177
4-9'3
4.082
3-557
27
6.946
5-59
4-567
3-973
2S
7.662
6.138
5.076
4.408
2 9
8.629
6.800
5.611
4-863
30
9-550
7.500
6.172
5-339
3 1
10.532
8.240
6.762
5-S38
32
n-579
9.024
7-383
6.361
33
12.698
9-853
8.037
6.908
34
13.896
10-733
8.726
7-4S3
35
15.182
11.669
9-453
8.087
36
16.565
12.665
IO.22I
8.721
37
18.058
13.726
11.034
9-388
38
19.674
14.861 .
11.895
10.1-91
39
21.428
16.075
12.809
10.832
40
23-34I
17-379
13.780
ii 614
4i
25-436
18.782
14.813
12.441
42
27.741
20.296
15.916
i33 J 7
43
30.291
21-934
I7-093
14.244
44
33-128
23.710
18.351
1^-256
45
36.308
25.641
19.695
16.263
46
39-93
27-747
2LI33
17-359
47
44.013
30-053
22.673
18.517
48
48.780
3!-592
24.327
19.741
49
54-4H
35-408
26.109
21.036
50
61.239
38.556
28.036
22.412
5i
69.802
42.109
3- I 3
23-874
52
81.131
46.167
32.416
25-43I
53
97-534
50.872
34.926
27.0(98
54
"7-454
56.43
37-702
28.884
cc
6? 167
J.O.7OO
30.806
J.T
r6
u o* lu /
71 627
T" / jfv
44.2SS
o
32.886
J>
C7
/ "/
82.836
^-(.. <-JV--
48. 268
7C I -l6
Ji
cS
OO. IOI
C2 S7O
O - ' T
77.610
o u
CQ
124 77O
i> **/;
c8."?2S
JI .'"V
4.0.746
3V
60
**T- / j"
J^'J"^
f\A O76
T 1 ^ OT
41.77S
61
"T'V-J"
TI.IA-I
T*> .>/
i6.ciS7.
62
1 j"*tj
8l 272
f^" V -J
50.656
6-1
U T * /
IOO.22s
54.7^2
64
172 67s
-IT / 1
6().O74
U T
65
*.}* "jj
v /I
66.^28
1 68
PRINCIPLES AND PRACTICE
TABLE No. LXVI.
VALUATION COLUMNS.
AMERICAN EXPERIENCE, FOUR AND A HALF PER CENT.
Aff.
Cm
**
A,
15
I-05304
7-305
7.692
18.5509
16
I -05307
7-331
7.720
18.4818
17
1.05310
7-357
7.748
18.4095
18
I-053H
7-394
7.786
18.3339
19
1.05318
7-43i
7.826
-18.2550
20
1.05322
7-469
7.826
18.1726
21
1.05328
7-5 i 7
7.917
18.0665
22
1-05333
7.566
7.969
17.9968
23
I-05336
7.616
8.022
17.9032
24
1-05344
7.666
8.075
17-8055
25
I-05350
7.717
8.130
17.7036
26
1 -05357
7.780
8.196
17.5972
27
1.05364
7.844
8.264
17.4862
28
I-0537I
7.909
8-333
I7-3705
29
1.05380
7.986
8.415
17.2497
30
1.05388
8.064
8.498
17.1238
31
1 -5397
8.144
8-583
16.9926
32
.05407
8.237
8.681
16.8557
33
.05419
8.342
8.794
16.7131
34
0543 *
8.451
8.909
16.5646
35
05443
.8.<;6i
, 9.027
16.4099
36
05458
8.697
8.172
16.2487
37
05474
8.837
9.320
16.0811
38
05493
9.003
9-497
15.9066
39
-05512
9.174
9.679
I5-7253
40
05534
9-373
9.891
15.5669
4i
05556
9-577
10.109
I5-34I3
42
05583
9.811
10-359
15.1382
43
.05611
10.064
10.629
14.9275
44
1.05644
10.363
10.947
14.7059
45
1.05680
10.682
11.289
14.4826
46
1.05722
11.064
11.687
14.2484
47
1.05769
11.484
12.146
14.0065
OF LIFE INSURANCE.
TABLE No. LXVI (CONTINUED.)
VALUATION COLUMNS.
169
AMERICAN EXPERIENCE, FOUR AND A HALF PER CENT.
Agt.
z
c *
*,
4
48
1.05824
11-771
12.668
13.7569
49
1,05888
12,542
13.280
13.4998
50
1.05960
13.188
13-974
13-2358
51
1.06042
13.915
14-755
12.96151
52
1.06133
14.726
15-629
12.6880
53
1.06235
15-630
16.604
12.4049
54
1.06350
16.6.1;
17.704
12.1160
55
1.06478
17.771
18.922
11.8218
56
1.06020
19.031
20.289
11.5228
57
1.06778
20.416
21.800
11.2194
58
1.06953
21.948
23-474
10.9121
59
1.07149
23.656
25-347
10.6013
60
1 .07366
25-544
27-425
10.2877
61
1.07608
27.637
29-739
9.9718
62
1.07876
29.949
9-6544
63
1.08 72
32.481
35-I36
9-3360
64
1.68501
35.285
38.285
9.0172
65
1.08869
38.401
41.807
8.6987
66
1.09276
41.825
45-704
8.3814
67
1.09728
45-596
50-031
8.0662
68
1.10232
49.763
54-855
7.7536
69
1.10789
54-318
60.178
7.4446
70
1.11406
59-323
66.090
7.1399
71
1 . 1 2084
64.752
72.576
6.8402
72
1.12818
70.557
79.602
6.5460
73
1.13609
76.725
87-167
6.2569
74
1.14461
83.280
95-323
5.9723
75
1.15389
90.307
104.204
5.6914
76
1.16410
97-905
"3-971
5.4133
77
1- '7556
106.211
124.941
5-1376
78
1.18862
115.621
137-433
4.8640
79
1-20355
126.061
1151.720
4.5928
So
1.22156
138.245
168.861
4.3241
1 70
PRINCIPLES AND PRACTICE
TABLE No. LXVI (CONTINUED).
VALUATION COLUMNS.
AMERICAN EXPERIENCE, Six PER CENT.
Age.
-.
..
*,
*
15
16
1.06813
1.06818
7.202
7.227
7.692
7.720
15.1368
15.1003
17
1.06821
7-253
7-747
15.0617
18
1.06825
7.289
7-787
15.0208
19
1.06830
7-326
7.826
14.9778
20
1.06834
7-363
7.866
I4-9325
21
1.06839
7.411
7.917
14.8846
22
1.06845
7-4S9
7-969
14.8342
23
1.06850
7.508
8.022
14.7811
24
1.06856
7-558
8.076
H-7252
25
1.06862
7.608
8.130
14.6662
26
1 .06869
7.670
8.197
14.6039
27
1.06877
7-733
8-265
I4-5383
28
1.06882
7-797
8333
14.4694
29
1.06892
7-873
8-415
14.3964
30
1.06901
7-950
8.499
H-3'97
31
1.06910
8.029
8-583
14.2388
32
.06920
8.120
8.682
14-1536
33
.06932
8.224
8-795
14.0639
34
.06944
8.331
8.910
13-9695
35
.06957
8.440
9.027
13.8701
36
.06972
8- 574
9.172
I3-7655
37
.06988
8.711
9.320
I3-6555
38
.07007
8.876
9.498
13-5399
39
.07026
9.044
9-679
13-4185
40
I .07048
9.240
9.891
13 2911
41
1.07071
9.441
10.109
I3-I574
42
1.07098
9.672
10-359
13.0174
43
1.07127
9.922
10.629
12.8701
44
1.07160
10.216
10.947
12.7160
45
1.07197
10.531
11.289
1 2-5549
46
1.97240
10.907
11.697
12.3865
47
1.07287
11.321
12.146
12.3108
OF LIFE INSURANCE.
TABLE No. LXVI. CONTINUED.
VALUATION COLUMNS.
171
AMERICAN EXPERIENCE, Six PER CENT.
A ff e.
e ,-
**
A x .
48
1-07343
11.801
12.668
12.0278
49
1.07407
12.364
13.280
11.8376
50
1.07481
13.001
13-974
11.6404
51
1.07564
I3-7I7
H755
"4365
52
1.07657
14.518
15.629
11.2259
53
1.07760
15.409
16.604
11.0089
54
1.07877
16.411
17.704
10.7859
55
1.08006
17.520
18.922
10-5563
56
1.08150
18.760
20.289
10.3214
57
1.08311
20.128
21.800
10.0811
58
1.08488
21.637
23-47,4
9-835S
59
1.08687
23.321
25-347
9-5858
60
1.08907
25.182
27-425
9-33I7
61
1.09152
27-245
29-739
9-0738
62
1.09424
29.520
32.302
8.8127
63
1.09725
32.022
35-136
8.5490
64
1.10058
34.786
38.285
8.2831
65
1.10431
37-858
41.807
8.0156
66
1.10485
41-233
45-704
7-7475
67
1.11303
44-951
50-031
7.4792
68
1.11815
49.058
54-S54
7.2116
69
1.12379
53-549
60.178
6-9455
70
1.13006
58.484
66.090
6.6815
7i
1.13693
63.836
72-576
6.4204
72
1.14438
69-559
79.602
6.1626
73
I-I5239
75-94
87.167
5-9079
74
1.16104
82.102
95-323
5-6559
75
1.17046
89.029
104.205
5-4057
76
i.iSoSi
96.519
113-97 1
5-1567
77
1.19244
104.778
124.941
4.9082
78
1.20568
113.988
137-433
4.6603
79
1.22082
124.277
151.720
4-4i3i
80
1.23899
136.288
168.861
4.1669
172
PRINCIPLES AND PRACTICE
TABLE No. LXVI (CONTINUED.)
VALUATION COLUMNS.
Age.
COMBINED EXPERIENCE, FOUR PER CENT.
D x
c x
c x
Ni
A *" ^
u x
" x+1
JD X A *
15
1.04727
6.677
6.992
19.9976
16
1-04733
6-733
7.052
19.8957
17
1.04740
6.791
7-"3
19.7901
18
1-04757
6.860
7-185
19.6807
'9
1.04755
6.929
7-259
'9-5675
20
1.04764
7.010
7-344
19.4504
21
1-04773
7-093
7-432
I9-3293
22
1.04782
7-U7
7.520
19.2041
23
1.04793
7-273
7.622
18.0747
24
1.04803
7.371
7-725
18.9410
25
1.04814
7.471
7.830
18 8027
26
1.04827
7.583
7-949
18.6589
27
1.04839
7.698
8.071
18.5122
28
1.04854
7.826
8.206
iS-3597
29
1.04868
7-956
8-344
18.2023
30
1.04884
8.101
8.497
18.0396
31
1.04900
8.248
8.652
17.8718
32
1.04958
8 410
8.824
17.6985
33
1.04936
8.576
8.999
17.5196
34
* -04955
8746
9.179
I7-3350
35
1.04975
8-931
9-375
17.1444
36
1.04996
9.122
9-576
16.9475
37
1.05017
9.3I3
9.782
l6 -7443
38
1 .05040
10.005
16.5342
39
1.05064
9741
10.235
16.3172
40
.05089
9963
10.470
16.0929
4 1
.05116
10.204
10.726
15.8610
42
.05146
10.476
11.014
15.6212
43
05183
10.818
"379
I5-3736
44
05231
11.247
11.836
15.1186
45
.05286
11.742
12.363
14.8571
46
05353
12-345
13.006
14.5896
47
05425
12.996
13.701
14.3170
OF LIFE INSURANCE.
TABLE No. LXVI (CONTINUED.)
VALUATION COLUMNS.
173
Agt.
COMBINED EXPERIENCE, FOUR PER CENT.
D x
c x
c x
Nx A
n Ux
L/x + i
*>,~ c *
D 9 + l k *
D x
48
1 -05504
13-711
14.466
14.0394
49
1.05590
14.482
15.291
I3-757I
50
1.05684
*5-326
16.197
I3-4703
5i
1.05788
16.248
17-189
13.1792
52
1.05901
17-257
18.275
12.8841
53
1.06024
iS-359
19.464
12.5853
54
1.06156
*9-532
20-735
12.2832
55
1.06303
20.831
22.144
11.9779
56
1.06462
22.237
23.674
11.6698
57
1.06632
23-730
25-304
"3593
58
1.06819
25-37I
27.101
11.0463
59
1.07023
27.160
29.068
I o-73 I 3
60
1.07254
29.169
31-285
10.4149
61
1.07506
31-357
33-7"
10.0977
62
1.07786
33-770
36.399
9.7805
63
1.08090
36-384
39-32S
9.4641
64
1.08427
39-255
42-563
9.1489
65
1.08796
42.386
46.115
8-8355
66
1.09199
45.782
49-994
8.5248
67
1.09644
49.494
54.268
8.2170
68
I.IOI26
53-490
58.907
7-9!30
69
1.10648
57-776
63.928
7.6130
70
I.II222
62.436
69.442
7-3I72
7i
I.IIS47
67.460
75-452
7.0261
7^
I-I2530
72.889
82.022
6.7400
73
I-I3275
78-734
89.186
6-4593
74
1.14093
85.065
97-054
6.1840
75
1.14988
91.885
105-657
5.9146
76
I-I5965
99.211
115.050
5-6512
77
I.I7047
107.182
125-453
53-938
78
1.18242
115.812
136.938
5.1428
I 9
I.I9549
125.062
149.511
4.8986
80
1.20087
135.006
163.340
4.6607
INDEX.
PACK
Accumulation formula, Wright's 150
" " Fackler's 150
" " McClintock's 144
American Experience Mortality Table 33. 68
' ' Commutation Columns, 4 % per cent 70
" Commutation columns, 6 per cent , 74
Annuities Certain, At Compound Interest 19
1 ' Deferred 23
" Formulae for 143.
' ' Life 43
Average Duration of Policies 66
Combined Experience or Actuaries Table of Mortality^ 34, 69, 98
" Experience Commutation Columns, 4 per cent 72
Commutation Columns, How Made 36'
Contribution Explained . 50
Formulae, Homans's 151
Cost of Insurance Explained 48, 120
Single Premium, Whole Life Policy, American Experience,
4% per cent 121
" Combined Experience,
4 per cent 121
" Whole Life Policy, American Experience, 4^ per cent 122
" Ten Payment Life " " 123
" Ten Year Endowment " " 124
" Fifteen Year Endowment " " 125
" Twenty Year Endowment " " 126
" Twenty-five Year Endowm't " " 127
" Thirty Year Endowment " " 128
" Whole Life Policy, Combined Experience, 4 per cent 129
" Ten Payment Life " " 130
" Ten Year Endowment " -" 131
" Fifteen Year Endowment " " 132
Twenty Year Endowment " " 133
Twenty-five Year Endowment " 134
Thirty Year Endowment " " 135
Decimal Parts of a Year, to January ist following 140
Definitions n
Discount 21
Endowment, Simple 42
' ' Insurance 43
" Insurance, Formulae for 144, 146
INDEX. ^5
PAGK
Equation of Life 57
" Table of 58
" Formulas for 151
Expectation of Life 55
Table of 56
" Not Adapted to Determine Premiums 57
Formulas for 151
Forfeiture of Policies and Paid-up Insurance 62
Formulae for Verifying Commutation Columns 151
Gross Valuation 46
Insurance Paid-up 62
1 ' Term 42
' ' Values, Mr. Wright's Formulae for 151
Interest 16
" Compound 16
' ' Rate of 34
Joint Life Policies 59
' ' Valuation of Chandler's Method 156
" Valuation of Chandler's Table for 157
' ' Formulae for 146
Life Contingencies 32
Life Insurance, Explanation of 37
1 ' Formulas 142'
Massachusetts Non-Forfeiture Law. 63
" " Net Single Premiums Applied -to 130
" ... " Insurance on Lapsed Whole Life Policies,
According to 136
Monetary Tables, 4 per cent 24
4^ " 25
5 " 26
" 6 " 27
" 7 " 28
" 8 " 29
9 " 3
10 " 31
Mortality, Tables of 33
Mortality Table, American Experience Table 68
' ' Combined Experience 69
Net Premiums American Experience, 4^ per cent 76
" Combined Experience, 4, per cent 77
" Joint-Lives, Combined Experience 114
" Term Insurance, American Experience, 4^ percent 78
" Term Insurance, Combined Experience, 4 per cent 78
Net Valuation 4 6 . 8o
Net Values, Whole Life Policies, American Experience, 4^ per cent. . 82
' ' Ten Payment Life " 84
" Ten Year Endowment " 86
" Fifteen Year Endowment 88
" Twenty Year Endowment " ....:.... 90
" Twenty-five Year Endowm'nt " " 9 2
" Thirty Year Endowment " " 94
" Thirty five Year Endowment " " 9 6
!^6 INDEX.
PAGE
Net Values, Whole Life Policies, Combined Experience, 4 per cent ico
1 ' Ten Payment Life " " 102
" Ten Year Endowment " " 104
" Fifteen Year Endowment " " 106
' ' Twenty Year Endowment " " 108
" Twenty-five Year Endowment " " no
" Thirty Year Endowment " " 112
" Joint Life Policies, Equal Ages " 115
" " Diiference in Ages, 5 Years " 116
" " " 10 Years" 117
IS Years " 118
Premiums, Life, Explained 38
Present Values 21
Probability of Life 35
Return Premium Plan 60
' ' Formulae for 147
" Loaded Annual Premiums, Formulas for 147
" Net Annual Premium for Return of Gross Premiums,
Formulas for 147
' ' Limited Payment 148
Single Return Premium 148
' ' Loaded Return Premium 148
Return Premiums, Disadvantage of, Illustrated 61
Risk, Amount at 47
Surplus, Distribution of 49
" Formulas for, Roman's 151
Surrender Values 64
" Prof. Bartlett's Formulas for 152
Tables of 155
Sinking Fund, see Monetary Tables.
Term Insurance, Formulae for 144, 146
" Net Premiums 78
Tontines, and Tontine Dividends 53
Valuation Tables, American Experience, 4}^ per cent 168
" " 6 " 170
" Combined Experience 4 " 172
Valuation of Policies, Net and Gross 45, 148
' McClintock's Method 158
Whole Life Policy, Formulas for 144, 146
V
University of California
SOUTHERN REGIONAL LIBRARY FACILITY
405 Hilgard Avenue, Los Angeles, CA 90024-1388
Return this material to the library
from which it was borrowed.
A ~~' MI "iiiiiiniiilllll/||/||