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THE
ABC
OF
Life Insurance.
By CHARLES E. WILLARD.
^ OF THE
\
NIVERSITY
OF .
ypOURTH
EDITION.
i
PUBLISHED BY
i THE :
SPECTATOR COMPANY
1
New
York.
1897
:t^ERAL
Entered in the office of the Librarian of Congress, at Washington, D. C, in
the year 1897, by The Spectator Company, New York.
PREFACE TO FIRST EDITION.
To ejcr^iain and illustrate some of the fundamental and ele-
mentary principles of Life Insurance so simply that they can
rpor^vJily fc understood by men who have not been specially
trained i>fnathematicians, or have not had their attention par-
iCIarly directed to the theory and mathematics of Life Insur-
ance, 4 tne aim of this Uttle book. For those who already
possess this elementary knowledge, there are many excellent
hand-books which carry the discussion much further, and
cover the entire subject in the ablest and most satisfactory
manner. But as an introduction to these, a beginning, an
**easy lesson," it is hoped that the following pages will have
their use. They owe their existence to the impossibility of
findmg among the text-books already published anything
which seemed exactly adapted to this purpose. C. E. W.
New York, November i, 1888.
^
PREFACE, TO FOURTH EDITION,
A demand for the ABC requiring a fourth edition to meet it
is evidence that every year a very considerable number of men
wish to know what Life Insurance is. It is a pleasure to pre-
sent to them a revised and enlarged edition of the book, con-
taining a more extended discussion of net premiums, a presen-
tation of the theory of surrender values and surrender charges,,
and a new table of *' Combined Experience, 4 per cent" net
premiums, and, in its references to the actual conduct of the
business, informing to the latest practice. C. E. W.
New ^'ork, November i, 1897.
THE
ABC
OF
LIFE INSURANCE
CHAPTER I.
A PRELIMINARY STUDY.
Insurance, in its simplest form, is indemnity for loss.
Or it may be described as a method of distributing an
individual's loss among a large number of other persons
who are willing to assume each his small share of it, ia
return for the certainty that if a similar loss falls upon any-
one of them, the loser, or those dependent upon him, will
in like manner be indemnified. If a building or stock of
goods is burned, so much capital is destroyed. If a pro-
ductive human life ends, so much capital in another form is
destroyed. For convenience in apportioning the loss, or
dividing it among those interested, the machinery and organ-
ization of a company are invoked. The company contracts
to pay the loss, the company collects the premium, the
company pays the loss if it occurs. Consequently, the com-
Note. — It is sometimes flippantly said that insurance is simply a form
of gambling, the company betting a large sum that a certain loss will not
occur, the insured bettinsf a small sum that it will; if the loss occurs, the
company pays the bet. In so foolish a statement as this, only the element
of chance is taken into account. No consideration is had of the fact that
the insured receives the worth of his money, in any event, in the protec-
tion afforded — the certainty that he will be indemnified if the loss falls on
him. A bet involves the payment of money without any equivalent in
return.
6 The A B C of Life Insurance,
pany is said to insure each individual, but it must be
remembered that the actual function of the company is
that of a medium through which the business is transacted,
and that the result is simply the apportionment of such
individual losses as occur, among a large number of insured
who assume the payment of these losses from year to year
in order that they may themselves claim a like indemnity
should the occasion arise. If this fact were thoroughly
understood in life insurance, as it is in fire, more correct
ideas of the values of life policies would prevail even among
those who have no technical knowledge of the subject.
Two or three elementary principles constitute the foun-
dation of all life insurance. They are so simple that they
need only to be presented to be comprehended by any
person of ordinary intelligence. Their practical application
to various contingencies may, and often does, involve
mathematical calculations which are not only very lengthy
but also very intricate. This fact has thrown a veil of
mystery over the whole subject, which does not properly
belong to it. One need not be an actuary or expert
mathematician to have a very fair knowledge of the funda-
mental principles. The following example will enable us
to study these principles :
// should be understood in advance that the supposed con-
ditions of this example^ so far as the rate of 7nortality {or
number of deaths in a year) is concerned, are not those
which we meet in actual experience. The ter7n of life is
shortened from ninety -six years to fifty, that the calculation
may be proportionately shortened. The number of deathc^
each year, and the amount of insurance on each individual^
are purposely such as to make the calculation very simple^
and susceptible of instant verification. Consequently, our
I
The A B C of Life Insurance.
results will not be the results of actual experience. The
premium will be very much too high, the annual cost of the
insurance very much too great, the accumulation of reserve
very much too rapid.
But the two or three elementary principles which we wish
to study are perfectly and exactly illustrated. As will be
shown later on, the same process applied to the conditions
which actually exist, will secure correct results.
Bearing the above in Mind :
Let us suppose that a company is formed of i ooo men ;
that the age of each man is 40 ; that each is insured for
$ijop^»that 100 men will die during the first and each
succeeding year ;* that every man remains in the company
until his death occurs ; that the company receives nothing
for interest on money in its hands, and pays nothing for the
expense of conducting the business. Suppose, also, that
for the sake of convenience these men agree to pay a uni-
form amount each year so long as they live, as a premium
for the insurance.
It is evident that the total amount of insurance to be
paid would be 1000 x $1100, or $1,100,000.
It is also evident that there would be 1000 men to pay
premiums the first year, 900 the second year, 800 the third
year, and so on. The total number of premium payments
made would be 5500. Each payment therefore must be
$1,100,000 -f- 5500, or $200, which, upon our assumption,
* As a matter of fact, we should expect that the number of deaths among
1000 men, age 40, would be but 9 or 10 the first year, and that i or 2 of
the 1000 men would survive the age of 90. To make our supposition
conform to these facts would extend our calculation over 50 years. The
assumption which is made above, reduces the term to 10 years, and so
avoids the tediousness of the calculation based upon the longer, actual
term.
8
The A B C of Life Insurance,
would be the anriTial, whole-life premium for an insurance ot
$1 loo upon the life of a man aged 40.
The results would be as follows :
i.cxx) X $200 =
100 X $1,100 =:
$200,000, Premiums received beginning of
110,000, Losses paid durmg
$90,000, Amount in hand at end of
900 X $200 = $180,000, Premiums received beginning of
$270,000, Total am't in hand beginning of
100 X $1,100 = 110,000, Losses paid during
$160,000, Amount in hand at end of
800 X $200 = 160,000, Premiums received beginning of
$320,000, Total am't in hand beginning of
100 X $1,100= iio.ooo, Losses paid during
$210,000, Amount in hand at end of
700 X $200 = 140.000, Premiums received beginning of
$350,000, Total am't in hand beginning of
100 X $1,100= 110,000, Losses paid during
$240,000, Amount in hand at end of
600 X $200 = 120,000, Premiums received beginning of
$360,000, Total am't in hand beginning of
100 X $1,100= 110,000, Losses paid during
$250,000, Amount in hand at end of
500 X $200 = 100,000, Premiums received beginning of
$350,000, Total am't in hand beginning of
loo X $1,100= iio.ooo. Losses paid during
$240,000, Amount in hand at end of
400 X $200 = 80,000, Premiums received beginning of
$320,000, Total am't in hand beginning of
ICO X $1,100= 110,000, Losses paid during
$210,000, Amount in hand at end of
First
Year,
Age 40.
Second
Year,
Age 41.
Third
Year,
Age 42.
Fourth
Year,
Age 43.
1 Fifth
\ Year,
I ^ge 44-
)
Sixth
S- ifear,
Age 45.
Seventh
Year,
Age 46.
300 X $200 = 60,000, Premiums received beginning of
$270,000, Total am't in hand beginning of
100 X $1,100= 110,000, Losses paid during
$160,000, Amount in hand at end of
200 X $200= 40,000, Premiums received beginning of
$200,000, Total am't in hand beginning of
100 X $1,100= 110,030, Losses p-^id during
Eighth
Year,
Age 47.
Ninth
Year,
Age 48.
$90,000, Amount in hand at end of j
100 X $200 = 20,000, Premiums received beginning of ^ T th
$110, oco. Total am't in hand beginning of Y Year,
100 X $1,100= 110,000, Losses paid during J 8' 49'
00
Now it is evident that the principles involved in fixing
the premium and collecting the necessary amounts to pay
losses in full, until the last contract is met, must be the
same whether the death rate be 9 or 100 per annum, and
the term 10 or 50 years. Let us see, then, what can be
discovered by a study of the above.
In the first place it is evident that the cost of the insur-
ance — i. e., the amount of the losses in any one year
divided by the number of men living at the beginning of
that year — ^varies from year to year, although the annual
premium remains the same. The losses for the first year
are $110,000. The number of men to pay premiums
is 1000. The cost of the insurance, therefore, is
$110,000-5-1000, or $110 per man. The second year
the losses are $110,000. There are but 900 men, how-
ever, to pay premiums, 100 men having died. Conse-
quently, the cost of the insurance is $110,000 -^ 900, or
$122.33 P^r man. In the same way the cost the third
year is $110,000.00-7-800, or $137.50 per man; the
fourth year, $110,000-^700, or $157.14 per man — and
so on. When we reach a point where more than one-half
lo The A B C of Life Insurance.
of the original number of men is dead, or will have died
before the end of the year, the cost will exceed the premium.
Thus, in the sixth year, the cost is $110,000 -^ 500, or
$220.00 per man. And, from this point, the cost con-
tinues to exceed the premium by an annually increasing
amount to the end.
It is evident, therefore, that a uniform or, as it is usually
called, a " level " premium, involves the annual payment of
a sum in excess of the current cost of the insurance during
a part of the term, and the annual payment of a sum less
than the current cost of the insurance during the remainder
of the term. Consequently; whatever is overpaid during
the former portion of the term must be held in hand,
reserved^ to provide against the deficit which would other-
wise occur during the latter part of the term.
The same fact appears from an inspection of the figures
above, without stopping to calculate the cost of the insur-
ance. Thus we see that the premiums received exceeded
the losses paid by $90,000 the first year, $70,000 the
second year, and so on up to the sixth year. Then the
losses began to exceed the premiums, the excess being
$70,000 in the ninth year, and $90,000 in the tenth year.
If, now, the company finding itself with $90,000 in hand at
the end of the first year, $160,000 at the end of the second
year, $210,000 at the end of the third year, had overlooked
the call to be made upon these funds in the future, and had
spent or, through carelessness or misfortune, lost some of
these funds, had failed to keep the full amount intact, there
would have been finally a deficit of exactly the amount so
lost or spent. Ten thousand dollars a year might be spent
for several successive years without affecting the company's
ability to pay its current losses, but the time would surely
come when the absence of the money would show itself in
The A B C of Life Insurance, ii
the inability of the company to carry its contracts of insur-
ance to the end. It is plain, therefore, that at the end of
each year the company would have in its possession a sum
of money which it must carefully reserve for the future
fulfillment of its existing contracts.
Another point. At the beginning of each year (for the
above example supposes that the company receives all its
premiums at the beginning of the year), there would be on
hand the money brought over from the preceding year plus
the premiums for the current year. A portion of this
total amount would have to be held for the payment of the
current losses of this year. To distinguish this from the
amount to be carried forward at the end of the year, we will
call it the insurance reserve. Since this would be paid out
at intervals during the year, as losses occurred, the sum left
in the company's hands would slowly diminish until, at the
end of the year, the insurance reserve would be entirely (and
properly) expended in the payment of losses, and only that
amount of money which must be held for the future would
remain. This latter amount, since it must be held for a
series of years, and might be invested in interest-bearing
securities, we will call the investment reserve.
This suggests another point, viz.: that while the reserve of
a policy may be said to increase each year that the insur-
ance is in force, this increase, so long as premiums are paid,
is not an absolutely uniform one. The reserve is greater at
the beginning of the year, because it includes both the
insurance and the investment portions ; diminishes during
the year, because the insurance portion is expended grad-
ually in the payment of losses ; but at the end of each year
is greater than at the end of the preceding year, because the
investment portion of that year is added to the investment
portion of the preceding year or series of years.
12 The A B C of Life Insurance.
If we divide the amount of money in the hands of our
supposed company at the end of the first year by the num-
ber of survivors at the end of that year, we have $90,000 -^
900, or $100. This is the amount of reserve for each policy
(or insurance) at the end of the first year. After the pre-
miums have been paid at the beginning of the second year,
and before any deaths have occurred for that year, the reserve
on each policy would be $270,000 -5- 900, or $300. At the
end of that year the reserve would be $160,000 -5- 800, or
$200 on each insurance. By putting the figures of reserves
at the beginning and end of several years in parallel col-
umns, this point will be more clearly seen :
Beginning End
of Year. of Year.
Reserve second year $3cx) $20c
Reserve third year 400 30c
Reserve fourth yeai 500 400
Reserve fifth year 600 500
This may be represented by a diagram as follows :
Fifth Year.
2
\A
'S
w
*s
a
•a
'&
•F5,
&
^
&
Perhaps the function of the investment reserve may be
shown in another way. Suppose that the company of 1000
I^n
The A B C of Life Insurance. 13
b had agreed to pay each year the exact cost of the
insurance for that year. Taking our figures of cost on page
8, the results would be as follows :
1,000 X $110 =$110,000, Premiums rec'd beginning of ^ p' st '
100 X $1,100 = 110,000, Losses paid during i Year,
00, Amount in hand at end of J & 4 •
I.
$122.23 = $110,000, Premiums rec'd beginning of ^ 5, ,
100 X $1,100 = 110,000, Losses paid during i Year,
— I Age 41
00, Amount in hand at end of j ^ "* '
800 X $137.50 = $110,000, Premiums rec'd beginning cf "^ Th' d
1
00, Amount in hand at end ot J
etc., etc., etc.
Here, as the increasing premiums take care of the current
losses for each year, there is no need of carrying any amount
forward from one year to another, and the investment re-
serve disappears altogether. The insurance reserve at the
beginning of each year is the full amount of the expected
losses for that year. As these losses occur and are paid the
reserve diminishes, and at any time during the year is
measured by the amount of expected losses for the re-
mainder of the year. At the end of the year, all losses
having been paid, it is nothing.
It appears then, that, leaving out the question of ex-
penses, the level premium is made up of two parts — the
insurance portion, which pays the current losses of the
year, and the investment portion, whose sole purpose and
use are to keep the premium level. The investment reserve
(and this is what is usually meant by the term *' Reserve ")
may be defined as that part of a level or uniform premium,
not needed for current losses, which is set aside for pur-
1^ The A B C of Life Insurance,
poses of accumulation, to be used, with its accretions, im
payment of future losses.
Incidentally, it should be noted that the reserve of each \
policy in our example at the tenth or final year, plus the
premium for that year, is $iioo, and that the actual cost
of the insurance for that year is also $iioo,
From this preliminary study, then, it is evident that a
company must either collect an annually increasing pre-
mium, correctly adjusted to the annually increasing cost, or
must accumulate from a level or uniform premium an invested
reserve fund; that this reserve, if accumulated, must be
kept intact until needed for its legitimate purpose, viz.: the
payment of such a portion of each policy as that policy has
contributed to it; that the waste or loss of this reserve
means ultimate bankruptcy, on account of the increasing
cost of the insurance for which the level premium, without
the accumulated reserve, does not provide ; and that the
reserve upon any policy increases with the age of that
policy or the number of years it has been in force. We can
also see that the man who wishes insurance must continue
Note. — Another definition of a reserve is " The difference between
the present value of the insurance, and the present value of the future
premiums on that insurance." As an illustration of this definition, our
example is very crude, since it ignores the question of compound interest,
which is the important factor in determining present values. Neverthe-
less, it suggests the method of calculating the reserves for insurances at
different ages and under policies upon which premiums have been paid
for different terms of years, as actually practiced. Thus, in our supposed
company, at the end of the third year there were 700 survivors, upon each
one of whom there was an insurance of $1100, or a total of $770,000. The
total amount of premiums to be paid during the remainder of the term of
years covered by the example was $560,000. Of course, if interest is to
be ignored, there is no difference between present and future values.
Consequently, the present values of the insurances and of the future
premiums would be their full amounts. The difference, $210,000, is the
amount of the reserve at the end of the third year given in our example.
The A B C of Life Insurance, 15
to pay his premiums thereon ; that the men who die during
the earlier part of the term do not pay the company, in pre-
miums, an amount equal to the amount of their insurance ;
and that the men who live to the latter part or end of the
whole-life term pay, in premiums, more than the amount
of their insurance.
Simple and elementary as is the preceding discussion, it
will repay careful study by anyone unfamiliar with the
theory of insurance. And when its points have been mas-
tered thoroughly, the preparation will be ample for a
ready understanding of what follows in this little volume.
Our illustration was based upon the supposition that the
1000 men were all of the same age ; that no other men came
into the arrangement; that none of the original number
dropped out by the way ; that in each year the number of
deaths was exactly what it was expected to be when the
company was formed ; that nothing was realized for interest
by the investment of funds on hand ; and that there was no
expense connected with the transaction of the business. In
actual experience, men of all ages are insured in the same
company; new members are continually coming in; old
ones are dropping out ; new sets of reserves are taking the
places of those which have been applied in the payment of
losses or have been withdrawn ; the rate of mortality varies
more or less from the tabular rate ; interest is received on
investments; and expenses are incurred in various ways.
An attempt will be made in the following pages to discuss
some of these matters briefly and simply, but to carry the
discussion only so far as may be necessary to an intelligent
comprehension of the subject in a somewhat general way.
1 6 The A B C of Life Insurance.
CHAPTER II.
MORTALITY TABLES.
If insurance is simply a method of distributing or appor-
tioning individual losses among a large number of persons
who enter into the arrangement for mutual protection, the
fact will at once suggest itself that each person should pay
not only in proportion to the amount of his possible loss,
but also in proportion to the likelihood that that loss will
occur. Risks are classified for fire insurance according to
the hazard of fire. In like manner, the life most likely to
end should pay the highest premium. Asid : from the
special risk to which any individual hfe may, at any given
time, be subjected by reason of sickness or accident,
it is evident that the older a man grows the nearer he
is to death. Consequently, in determining the amount of
premiums which any individual should pay, it is evident
that his age must be the prime factor. The first thing,
then, to be determined is the effect of age upon the rate of
mortality — in other words, how many deaths within a year
may be expected among a given number of men of any given
age.
No business in the world has a more reliable basis upon
which to make its calculations than that of life insurance.
The rate of mortality among lives of different ages has
been made a matter of study and record for more than 150
years. The tabulated results are known as " Mortality
Tables" or "Tables of Mortality."
The A B C of Life Insurance, 17
The first used as a basis for life insurance was the North-
ampton Table. This was formed by Dr. Price from obser-
vations on the mortality in the town of Northampton, Eng-
land, from 1735 to 1780. This table is no longer used for
valuations, and has never been used in this country.
The Carlisle Table was formed by Mr. Milne from obser-
vations in the town of Carlisle, England, from 1778 to 1787.
It is still in use to a limited extent.
The Actuaries* or Combined Experience Table, published
in 1843, was compiled from the experience of seventeen
English companies. It is used in this country as the legal
standard for computing reserves with four per cent interest,
but in England has been largely superseded by the later
Actuaries' or H. M. (Healthy Males) Table.
The Farr Table, No. 3, was constructed by Dr. Farr from
observations upon the mortality of the entire population of
England, and was published in 1864. It is not now in use.
The American Experience Table was formed from the
experience of the Mutual Life of New York by Mr. Sheppard
Homans, actuary of that company. It is in general use in
this country for the computation of premiums, and as the
legal standard for computing reserves with four and one-
half per cent interest.
The experience of thirty American companies was tabu-
lated by Mr. L. W. Meech, and the results pubHshed in
1 88 1. This table is generally known as the Meech Table.
It is very valuable as a record of actual experience, but is
not used in valuations.
For present purposes it is necessary to give the Actuaries*
and American ExperienceTables only. These will be found
on pages 68, 71 and 72.
From the latter table anyone who is interested to do so,
and has the time to spare, can substitute the proper figures
i8 The A B C of Life Insurance.
for those given in the preHminary example, and can calcu-
late the necessary annual, whole-life premium for any age
without allowance for interest or expenses.
By dividing the number of deaths during any year by the
number of persons living at the beginning of that year, we
obtain the percentage of mortality as given in connection
with these tables.
From the mortality tables, also, by averaging the after-life
time of the number of persons living at any given age, we
obtain the table of the Expectation of Life given on page 50.
This table is interesting, but not particularly useful. It is
never employed in making calculations. The supposition
that the annual premium to be paid by a person of any
given age is the sum which, invested at four or four and a
half per cent during the "expectation" of that person,
would equal the amount insured ; or that the present value
of an insurance, payable at death, can be ascertained by
discounting the amount of the insurance at four or four and
a half per cent for the number of years represented by the
" expectation " of the insured, is wholly erroneous.
So, too, the average age of a number of Hves is not a
reliable measure of the risk upon them all. Thus, the
average age of 10 men aged 98, and 10 men aged 30,
would be 64 years. Among these 20 men we should
expect at least 10 deaths during the year, while among 20
men aged 64 we should not expect more than one death.
The A B C of Life Insurance, 19
CHAPTER III.
NET PREMIUMS,
A net premium is one in the calculation of which due
allowance has been made for the interest which a company
may receive upon its investments, but with no allowance for
the expenses of the business.
Thus far we have, for the sake of simplicity, neglected the
question of interest. But, since a company may realize con-
siderable amounts in the way of interest upon judiciously
invested funds, not needed for present use, it is plain that,
in determining the premium which it is necessary to charge,
due consideration of this source of income should be had.
Obviously, the rate of premium will be reduced by the fact
that interest receipts are to be added to the company's in-
come. If too great a reduction is made, however, the pre-
mium will not be sufficient. And, as life insurance contracts
may cover a very long period, premiums must be based
upon assumptions which are likely to be realized in actual ex-
perience through an indefinite term of years. With this fact
in view, 4 per cent has been taken as the probable rate of
interest, in ihe calculation of premiums.
The following explanation of the method of calculating a
net annual premium for an insurance for the term of five
years, presents only the very simplest form of such calcula-
tions, the design being rather to illustrate principles and the
method of their application, than to present or attempt to
demonstrate intricate mathematical problems.
20 The A B C of Life Insurance.
What should be the net annual premium (level) for an in-
surance of $1000, for the term of 5 years only, upon the life
•of a man aged 40, according to the American Experience
Table with 4 per cent interest ?
An annuity is the recurring annual payment of a uniform
amount. Consequently the annual premium is an annuity
paid by the insured to the company. Manifestly, there-
fore, the proper method of ascertaining the required pre-
mium is to ascertain the present value of the insurance, and
then to determine the amount of an annuity whose present
value is equal to the present value of the insurance. We
will calculate the present value of an insurance for $1 and
then find the corresponding annuity. The latter will be the
annual premium for an insurance of $1, which must be
multiplied by the number of dollars of any desired insurance
to obtain the necessary premium therefor.
In thiSy and in all similar calculations ^ the premium is
considered payable at the beginning of the year, and the loss
at the end of the year.
Present value of (or, in other words, single premium for)
an insurance of $1, for a term of 5 years, upon the life of
a man aged 40.
By the American Experience Table (page 68) it appears
that, out of 78,106 person living at age 40, there will die
In the I St year, 765 persons
In the 2d
" 774
In the 3d
'' 785
In the 4th
" 797
In the 5th
" 812
An insurance of $1, therefore, upon each person, would
require the payment of $765.00 at the end of the first year,
$774.00 at the end of the second year, and so on. From the
I
The A B C of Life Insurance. 21
table of present values of $1 (page 76) we find that the
Present value at 4 per cent of $1 payable in i year
is $0.961538.
Present value at 4 per cent of $1 payable in 2 years,
is $0.924556, etc.
Therefore the present value of the above losses is as
follows :
Of the $765.00. $765 X .961538 ^7355?
Ofthe 774.00, 774 X .924556 715.60
Ofthe 785.00, 785 X .888996 697.86
Of the 797.00, 797 X .854804 681.28
Of the 812.00, 812 X .821927 667 40
Total present value of losses $3,497-72
If the 78,106 persons living at the beginning of the term
were to divide this present value into 78,106 single pay-
ments, to be made at once, the result would be $3,497.72
-i- 78,106, or $0.04478, and this would be the present value
of an insurance of $1, and consequently the single pre-
mium which each man should pay in advance for such an
insurance.
But we wish to find an annual premium (or annuity)
whose present value shall equal the above present value of
the insurance. This will, of course, be an annuity for 5
years contingent upon the lives of 78,106 persons, aged 40.
We will first find the present value of such an annuity
for $1.
By the same table of mortality, we find that if each per-
son living at the beginning of each year should pay $1,
the company would receive
At the beginning ofthe ist year, $78,106.00.
At the beginning ofthe 2d year, 77,341.00.
Lt the beginning of the 3d year, 76,567.00.
Lt the beginning of the 4th year, 75,782.00.
At the beginning of the 5th year, 74.985.00.
22 The A B C of Life Insurance.
Of course, the present value of the first payment would
be the entire amount of that payment, since it is made at
once. The present value of the second payment would be
the present value of -that amount payable in i year ; of the
third, the present value of that amount payable in 2 years ;
and so on. Resorting again to the table of present values
of $1, we have
Present value of the $78,106.00 $78,106.00 1
Present value of the 77,341.00 = $77,341 x .961538 74,36631
Present value oi the 76.567.00 = 76,^67 x ,924556 70,790.48
Present value of the 75,782.00 = 75,782 x .888996 67,369.89
Present value of the 74,985.00 = 74,985 x .854804 64,097.48
Total present value of all the payments $354-73° i^
This total depends upon the lives of 78,106 persons — the
number living at the beginning of the first year. Conse-
quently, the amount depending upon the life of any one per-
son must be $354,73o-i6 ^ or $4.54164. This, then, is the
78,106
present value of an annuity of $1 for 5 years, contingent
upon the life of a person aged 40. This value is much
larger than the value of the insurance, which is only
$0.04478. Consequently the required annuity or annual
premium will be only . of $1, or $0.00986. This is
the net annual premium for an insurance of $1 for the
term of 5 years on a life aged 40. The premium for an
insurance of $1000 would be 1000 x $0.00986, or $9.86.
It will'be seen at once that, if the term of the insurance
instead of being limited to 5 years, had covered the entire
term of life according to the American Experience Table,
the result would have been the net annual, whole-life pre-
mium.
The A B C of Life Insuraui.^,
23
The following example carries the premium, interest, re-
serve and loss accounts through the five-year term, with the
above premium and with the rate of mortality shown by
the American Experience Table :
78,106 X $9.86 = $770,125 16, Premiums rec'd beginning of '
30,805.01, 4 per cent interest
765
77,341
774
76,567 X
785
^800.930,17, Total
765,000.00, Death claims during
$9.86 :
$35,930.17, Reserve end of
762.582.26, Premiums rec'd beginning of ^
512 43, Total beginning of
31,940.50, 4 per cent interest
$830,452.93, Total
000 = 774,000.00, Death claims during
$56,452.93, Reserve end of
).86 = 754,950,62, Premiums rec'd beginning of ^
$811,403.55, Total beginning of
32,456 14, 4 per cent interest
$843,859.69, Total
Jiooo = 785,000,00, Death claims during
75,782 X $9 86 :
797
74.985 X $9.86 :
812 X $1000 :
$58,859.69, Reserve end of
747,210.52, Premiums rec'd beginning of '
$806,070.21, Total beginning of
32,242.81, 4 per cent interest
$838,313.02, Total
797,000.00, Death claims during
$41,313.02, Reserve end of
739,352.10, Premiums rec'd beginning of ^
$780,665.12, Total beginning of
31,226.60, 4 per cent interest
$811,891.72, Total
: 812,000.00, Death claims during
First
Year,
Age 40.
Second
Year,
Age 41.
Third
Year,
Age 42.
Fourth
Year,
Age 43.
Fifth
Year,
Age 44,
Excess of death claims, $108.28
The excess of the death claims, $108.28, represents about
one-seventh of a cent for each person living at the end of
24 The A B C of Life Insurance,
the fifth year. It is impossible to express the premium
more exactly, in dollars and cents, than $9.86. A premium
of $9.87 would show an excess of receipts over death claims
of about $4,207.52, or 5.6 cents for each person living at
the end of the term.
Endowment policies, so-called, are, strictly speaking, en-
dowment insurance policies. To the agreement to pay say
$1000 in the event of death within the endowment term, they
add the agreement to pay $1000 also provided the insured
shall live to the end of that term. Thus if A has what is
usually called a " twenty-five-year endowment " policy, his
beneficiaries will receive $1000 if he shall die within the
twenty-five years, and he will himself receive $1000 if he
shall live out the twenty-five years. Manifestly here is
a double provision, the one contingent upon death and the
other upon life. The former is pure insurance, the latter is
pure endowment.
What should be the net annual premium for a five-year
endowment insurance of $1000 upon the life of a man aged
40, according to the American Experience Table, with four
per cent interest ?
The net premium for the insurance part of this contract
we have just found to be $9.86. If, then, we ascertain the
net premium for the endowment part and add it to the
$9.86, the result will be the net premium for the double
contract.
Pure endowment provides nothing for the beneficiaries of
those who die, but is solely concerned for those who live.
Consequently for our immediate purpose we wish to know
the probable number of persons who will be living at the
beginning of each year to pay premiums, and the probable
number who will survive the fifth year and, on the first day
of the sixth, will be living to claim the endowment. The
I
The A B C of Life Insurance, 25
probable number of premium payments will, of course, be
the same as in the preceding example. A glance at the
American Experience Table shows that the probable num-
ber of persons who will live out the five-year term and reach
age 45 will be 74,173. A pure endowment of %\ for each
of these will, of course, amount to $74,173. The method
of computing the net annual premium necessary to provide
this amount is practically the same with the method of com-
puting the insurance premium already explained, viz.: as-
certain the single premium for the pure endowment, and
then the equivalent five-year annuity.
Since no part of the pure endowment is payable until the
expiration of five years, while at that time the whole must
be paid, it is evident that the present value would be the
present value at four per cent of $r, payable in five years,
multiplied by the total amount of the pure endowment.
$745173 X .821927 =$60,964.79, the present value. If the
78,106 living at the beginning of the term were to divide
this into 78,106 single payments, to be made at once, the
result would be $60,964.79 -f 78,106 = $0.78050, which
would be the net single premium which a man aged 40
should pay in advance to secure a pure endowment of $1 at
the end of five years.
Now, as we found on page 22, the present value of an
annuity of $1 for five years, contingent upon the life of a
person aged 40, is $4.54164. This is larger than the value
of the pure endowment, and consequently the required an-
nuity will be ^ '^^^ of $1, or $0.17186, which is the net
454,164
annual premium for a five-year pure endowment of $1 on
the life of a man aged 40. The premium for such an en-
dowment of $1000 would be, of course, 1000 x $0.17186,
or $171.86. Add the pure insurance premium, $9.86, to
26 The A B C of Life Insurance,
the pure endowment premium, $171.86, and we have
$181.72 as the net annual premium for an endowment in-
surance (ordinarily termed endowment) of five years on the
life of a man aged 40.
On page 23 an example carried the insurance part of this
contract through the five years. The subjoined carries the
endowment part through the same period.
78,106 X $171.86 = $13,423,297.16, Prems. rec'd beginning of ^ p. .
536,931.89, 4 per cent interest j. Year,
* Age 40.
$13,960,229.05, Reserve end of J
77,341 X $171.86 = 13,291,824.26, Prems. rec'd beginning of ;
$27,252,053.31, Total
1,090,082.13, 4 per cent interest
$28,342,135.44, Reserve end of
76,567 X $171.86 = 13,158,804.62, Prems. rec'd beginning of ^
Second
Year,
Age 41.
Third
Year,
Age 42.
Fourth
Year,
Age 43.
$4 [,500, 940. 06, Total
1,660,037.60, 4 per cent interest
$43,160,977.66, Reserve end of
75,782 X $171.86= 13,023,894.52, Prems. rec'd beginning of
$56,184,872.18, Total
2,247,394.89, 4 per cent interest
$58,432,267.07, Reserve end of
74,985 X $171.86= 12,886,922.10, Prems. rec'd beginring of ")
$71,319,189.17. Total [ ™^^
2,852.767.57, 4 per cent interest 1 Age 44.
$74,171,956.74, Fund in hand end of )
r Amount required to pay \
74,173 X $1000 = 74,173,000 00, ■? endowments at the be- | Sixth
(^ ginning of \ Yea'-,
Age 45.
Excess of endowments, $1,043.26, j
This excess of the endowments over the fund in hand is
less than a cent and a half for each person living at age 45
and consequently entitled to draw $1000 from the fund.
The addition of one cent to the annual premium would
I
^H The A B C of Life Insurance. 27
have made the fund in hand exceed the amount required
for the endowment by about $3275.
For the sake of the demonstration and of the lessons'*
which may be learned from the illustration, we will now
take the net premium, $181.72, for the pure insurance
and the pure endowment combined, and by an example
which will be, of course, a combination of that on page 23
and that on page 26, will carry the premium, interest, death
loss, reserve and endowment accounts through the five-year
term.
78,106 X $181 72 :
765 X $1000 :
77,341 X $181.72 :
774 X $1000 :
76,567 X $181.72 :
785 X $1000 :
75,782 X $181.72 :
797 X $1000 =
: $14,193,422.32,
567,736.90,
$14,761,159.22,
: 765,000.00,
$13,996,159.22,
: 14,054,406 52,
$28,050,565.74,
1,122,022.63,
$29,172,588.37.
774,000.00,
$28,398,588.37,
■• 13.913.75524,
$42,312,343.61,
1,692,493.74,
$44,004,837.35,
785,000.00,
$43,219,837 35,
: 13,771,105.04,
$56,990,942.39,
2,279,637.70,
$59,270,580.09,
797,000.00,
$58,473,580.09,
Prems. rec'd beginning of
4 per cent interest
Total \
Death claims during
Reserve end of
Prems. rec'd beginning of ")
Total beginning of
4 per cent interest
Total
Death claims during
Reserve end of
Prems. rec'd beginning of '
Total beginning of
4 per cent interest
Total
Death claims during
ResTve end of
Prems. rec'd beginning of '
Total beginning of
4 per cent interest
Total
Death claims during
Reserve end of
First
. Year,
Age 40.
Second
Year,
Age 41.
Third
Year,
Age 42.
Fourth
Year,
Age 43.
28 The A B C of Life Insurance,
74.985 ^ $181.72 = 13,626.274.20, Prems. rec'd beginning of ^
$72,099,854.29, Total beginning of
2,883,994.17, 4 per cent interest
•ay "^ Sixth
in- > Year,
) Age 45.
Fifth
Year,
$74,983,848.46, Total I Age 44.
812 X $1000 = 812,000.00, Death claims during
$74,171,848.46, Fund In hand end of
C Amount required to pay
74,173 X $1000= 74,173,000.00, ^endowments at begin-
Cning of
Deticit... $1,15154
This deficit is made up of the " excess of death claims,
$108.28," found on page 23, and the "excess of endowments,
$1,043.26," found on page 26. An addition of five-six-
teenths of a cent to the premium would be more than suffi-
cient to cover it.
A comparative study of these three examples on pages 23,
26 and 27 can be made interesting and instructive. Note that
in the first (five-year term insurance) the reserve increases
for a while, then decreases, and finally is exhausted in the
payment of the fifth year's death claims ; that in the second
(pure endowment) the reserve increases steadily to the end
of the term, and is then exhausted in the payment of the
endowments ; that in the third (endowment insurance) the
reserve steadily increases from year to year, is always at the
end of any given year the sum of the reserves for the cor-
responding year in the first and second examples, and is
finally exhausted in the payment of the fifth year's death
claims and of the endowments. Note also that the reserve
at the end of any year contains a certain amount, greater or
smaller as the case may be, which has been derived from
premium payments (with interest thereon) made by persons
who have died. Note also the part which compound inter-
est plays, and the vital importance of the interest earnings
to any company.
The A B C of Life Insurance. 29
Still further, in term insurance, as illustrated in the first
example, the fund in hand at the end of the fifth year is not
equal to the total amount of the outstanding insurance, but '
is equal to the amount of insurance which is to be paid as
death claims during that year. Under the endowment in-
surance the fund in hand at the end of the fifth year is equal
to the total amount of the outstanding insurance, because
every person insured will have a claim upon the fund either
because of his death during the fifth year or because of his
survival to the beginning of the sixth. Whole-life insurance
must provide a fund at the end of the last year which shall
equal the total amount of the outstanding insurance,
because, by the end of that year, the few survivors who
began the year will have died. It is often said that a
whole-life policy (American Experience Table) is " prac-
tically an endowment at age 96.'' This is correct to the
extent that the reserve under such a policy at age 96 will
equal the face of the policy — the full amount of the insur-
ance. It has happened at least once in the history of life
insurance in this country that a man holding a whole-life,
annual-premium policy carried the policy and paid the pre-
miums until he was 96 years old. According to the Mor-
tality Table he should have been dead. He had made all
the payments theoretically required under his contract, and
the accumulated reserve under his policy was equal to the
full amount of his insurance. Very properly, the company
in which he was insured paid him his money without waiting
for his actual demise.
For the sake of brevity a five-year endowment was chosen
for our example. In actual practice so short endowments are
rarely issued, and consequently the very great disproportion
between the insurance and the endowment elements which
Vears in the preceding examples exists in frequen tly in
30 The A B C of Life Insurance.
practice. The premiums under longer endowments — ten,
fifteen, twenty-five or more years- — must, of course, make
provision for a greater amount of death claims during the
term, and for a smaller amount of endowments at its end.
The foregoing illustrations show that a considerable
amount of work is involved in determining the premium for
ordinary forms of insurance for one age only, and for so
short a term as five years. It will be seen at once that the
computation of premiums for every age and for long terms
would be an exceedingly laborious process. And when dif-
ferent forms of insurance and contingencies involving more
than one life are to be considered, the mathematical prob-
lem may be one of great intricacy and difficulty. Log-
arithms, the processes of algebra, and various devices, such
as ** Commutation Columns," for lightening the labor of
computation, are employed by the actuaries or expert mathe-
maticians who make the calculations. One who desires to
acquaint himself with the mathematics of Hfe insurance can
find a large number of text books from which to choose.
For our purpose it is unnecessary to follow the subject
further. Tables of net annual and single whole-life pre-
miums will be found on pages 69 and 73.
The A B C of Life Insurance . 31
CHAPTER IV.
GROSS OR OFFICE PREMIUMS.
To the net premium must be added a certain amount
with which to pay the expenses of conducting the business
and to provide for contingencies. This amount is called
the margin or loading. It is usually a percentage of the
net premium. The loading and net premium together con-
stitute the gross or office premium — that which the com-
pany charges for the insurance. Thus, from our example
illustrating the computation of a net premium we have
Net premium for a five-year term insurance of $1000, age 40 $9.86
Margin or loading, say 33^^ per cent 3.29
Gross or office premium $13-15
The loading is usually a percentage of the net premium.
Its amount varies with the form of the insurance and the
objects which the company has in view. If it is intended
to return a portion of the premium in the shape of divi-
dends to the policyholder, the loading will be higher than
when no such return is contemplated. Premiums so loaded
are called "mutual" or "participating" premiums. Those
from which no dividend is paid are called "stock " or " non-
participating " premiums.
All annual premiums are supposed to be paid at the
beginning of the policy year. If, by consent of the com-
pany, the premiums are paid semi-annually or quarterly, the
unpaid installments of the annual premium are called
"deferred" premiums. Interest is charged on them, and
32 The ABC of Life Insurance,
their amount is always deducted from the amount of the
insurance in case of a claim. As has already been stated,
premiums are computed upon the theory that the full
annual premium is paid at the beginning of the year, and
the premiums are smaller than they would otherwise be.
Consequently the company is fairly entitled to retain the
unpaid installments. This is equity also between different
poh'cyholders. One man pays a full annual premium and dies
within three months. Another who has taken his insurance
at the same premium rate, theoretically, pays but one-
quarter of his annual premium and also dies within three
months. Manifestly equity between these two men, insur-
ants in the same company, would be observed by deducting
from the amount of insurance on the latter the amount of
the three unpaid quarters of his annual premium.
An analysis of the first year's whole-life premium at differ-
ent ages, showing what portion of the net premium is in-
tended for death claims and what for reserve, the amount of
a uniform loading of forty per cent at all ages, and the
gross premium made up of these three items, is given on
page 70. Special attention is called to the note regarding
this table on page 77.
The A B C of Life Insurance. 33
CHAPTER V.
RESERVES J LOANS ; REINSURANCE,
But little need be added to what has already been said
concerning reserves. Their nature and function have been
fully explained. Nor is it necessary to attempt an explana-
tion of the method of calculating them. Remembering the
definition of a reserve, " the difference between the present
value of the insurance and the present value of the pre-
miums thereon," it will be seen that compound interest is
again an important factor. The interest received upon the
fund representing the reserve, or upon the securities in
which that fund is invested, may be added to the fund from
time to time, thus lessening the amount of the principal
which must be set aside for investment.
To put it in another way, it is evident that if a company
is to receive interest on its investments, it need not reserve
so much money at the present time to meet a certain
amount of future liabilities as it would have to reserve if no
interest were to be received. Also, the higher the rate of
interest the smaller the reserve required. If you must have
$1000 at the end of a year, and can get but 4 per cent
interest, you must put aside or reserve at the beginning of
the year $961.54. But if you can get 10 per cent you
need reserve only $909.09. Reserves are usually calculated
upon the basis of the Actuaries' Table with 4 per cent
interest, or the American Experience Table with ^\ per
cent interest. Of course those calculated on the latter
basis are the smaller. The following table shows the
34 The A B C of Life Insurance,
reserves on a policy of $1000, issued at age 35, computed
according to the different standards:
American Experience Actuaries'
with \%, per cent Interest, with 4 per cent Interest.
End of 1st year $9.82 $11.48
End of 5th year S3.20 6134
End of loth year 1 17-45 133 41
End of 15th year 193-43 21430
End of 20th year 279.59 301.35
The percentage of difference decreases with the age of
the policy, that is, the number of years it has been in force.
Tables of Reserves according to the higher standard, the
Actuaries' Table of Mortality with 4 per cent interest, are
given on pages 74 and 75. These are the reserves on pre-
mium-paying, ordinary life policies. The reserves on paid-up
policies are, of course, the net single premiums given in the
table on page 73.
There are many forms of insurance, as will be seen from
chapter VI I. Each corresponding form of policy has its own
special premium, which must, of course, provide for its own
sufficient reserve. The net premiums and reserves given in
the tables herewith, are those on the most ordinary form of
life policy only. These are sufficient, in the wav of
elementary illustration, for the present purpose.
From the nature of a reserve, it is always reckoned a
liability of the company. It must be kept intact for its
proper use, as already explained. If it is not, and the im-
pairment is too great to be made good, the laws of the dif-
ferent States require, under differing conditions, the winding
up of the company, upon the theory that, although the
company may be amply able to pay its current claims, the
time will surely come when it will be unable to do so.
Consequently the matter of suitable investments which shall
be safe, and at the same time shall return a fair rate of in-
The A B C of Life Insurance, 35
terest, is one of prime importance to a company. The
laws of most States prescribe the forms of investments which
a company may make.
It should be noted in passing that the larger the reserve
on a poHcy, the less the amount which the company has at
risk in the insurance. Thus, if the reserve on a policy of
$1000 is $500, it is evident that the company need add but
$500 from its current income to make up the full amount
of the insurance. From this point of view, and regarding
the reserve in the light of a deposit made by the policy-
holder with the company, Mr. Elizur Wright gave to the re-
serve the definition of " self-insurance." The actual loss to a
company through death claims is not the total amount of
those claims, but the difference between that amount and
the total amount of the reserves credited to the policies
under which the claims are paid.
The following table shows the accumulation of the re-
serve under a policy of $1000, ordinary Hfe plan, issued at
age 40. Column i gives the portion of the premium which
is set aside each year for reserve. This diminishes each
year, as the actual cost of insurance increases each year.
Column 2 gives the total amount of the reserve held by
the company at the end of each year. Of course, at the end
of the first year, this is the reserve portion of the first year's
premium, with one year's interest at four per cent added. At
the beginning of the second year, the reserve portion of the
second year's premium is added to the total amount of reserve
held at the end of the first year. To this sum, one year's
interest at four per cent is added, and the total is the reserve
at the end of the second year. And so on for each year.
The net amount at risk is obtained by subtracting the re-
serve held by the company at the end of each year, from
$1000, the full amount of the insurance.
36
The A B C of Life Insurance.
Accumulation of Reserve; Decrease of Amount
AT Risk.
Amount insured, $1000. Ordinary life plan. Age at
issue, 40. Reserve computed according to American Ex-
perience Table, with four per cent interest.
Year.
Reserve Portion
of Premium.
Accumulated Re-
serve at End of Year
Net Amount
at Risk.
1st
$13.06
12.99
12.91
12.82
12.70
12.57
12.40
12.22
12.00
11.73
11.43
11.08
10.71
10.29
9.83
9.34
8.80
8.23
7.65
6.96
etc.
$13.59
27.65
42.18
5720
72.70
88.68
105-13
122.05
139.41
157.19
175.37
193-91
212.80
232.02
251-52
271.30
291.31
311-52
33191
352.42
etc.
$986.41
972.35
957-82
942 80
927.30
911.32
894.87
877-95
860.59
842.81
824.63
806.09
787.20
2d
Qd ,
o*-* •
4th
5th
6th
7th
8th
Qth
lotn
nth
i2th
iqth
14th
767.98
748.48
728.70
15th
i6th
17th
708.69
688.48
668.09
i8th
19th
20th
647-58
etc.
etc.
Premiums are sometimes paid, by consent of the com-
pany, partly in cash and partly in notes. These notes are
available as a part of the reserve. The cash part of the
premium is used to pay expenses and current losses, and
the note is laid away as part of the reserve. Such notes
are called " premium notes " and in reality constitute a loan
to the policyholder. The premium note system has not
always proved very satisfactory. The notes accumulate and
finally constitute a considerable lien upon the insurance,
which is deducted from the amount of the insurance in case
The A B C of Life Insurance. 37
of claim. In companies whose dividends are large, the
accumulation of these notes is diminished by applying the
dividends towards their payment. There are very few com-
panies at present which use the note system.
Policies having a large reserve value are sometimes used
as collateral for loans. Their main value for such purpose
lies in the reserve. The insurance itself is payable only
upon the happening of a certain contingency, /. ^., the death
of the insured, and, of course, constitutes a very indefinite
form of security. Endowments (policies payable when the
insured reaches a certain age, or at prior death) are more
available as collateral security, but even here the definite
value of the collateral is largely dependent upon the amount
of the reserve.
The amount of money allowed by a company for the
surrender of a policy is governed by the reserve, unless
the insured is in poor health. In that case the prospect of
his early death, which would make the policy a claim for
the full amount of the insurance, would give an added
present value to the policy. It is evident, however, that,
if the insured be in good health, the reserve on his policy
represents his entire equity in the insurance, since the
remaining portion of his premiums has been used for the
payment of current losses and expenses. As a matter of
fact, the reserve represents more than the entire equity of
the policyholder and, for that and other reasons, should be
subject to a " surrender charge." This will be considered
in a subsequent chapter.
In cases of reinsurance, the reserve is again the important
element of the transaction. If a company wishes or is
forced to withdraw from business, it sometimes reinsures its
risks, i. <?., transfers them to another company. This latter
company assumes the contracts of the former, and charges
38 The A B C of Life Insurance,
the same premium tor the insurance which each policyholder
was paying the original company. To enable it to do this,
the reserve fund accumulated by the original company
must be transferred to the reinsuring company, else the lat-
ter company would be the loser by the transaction, by at
least the deficiency of the reserve. Consequently, a com-
pany which has impaired its reserve to any considerable
extent cannot reinsure its risks.
The reserve is sometimes called the "reinsurance" re-
serve.
The A B C cf Life Insurance, 39
CHAPTER VI.
SURPLUS J DIVIDENDS,
The surplus of a company is the excess of its assets over
its liabilities. The former include such real estate as the
company may own, cash on hand and in course of trans-
mission, stocks, bonds, mortgage loans, loans on collaterals,
premium notes, accrued rents and interest, and deferred
premiums less the loading. The liabilities include the re-
serve, unpaid death claims and all unpaid bills or current
obligations. The reserve will be the largest item of liability ,
unless the company has been doing business but a very
short time. If it is calculated upon a At\ per cent basis
it will be smaller than if upon a 4 per cent basis.
Consequently, the surplus at 4^ per cent will be larger than
at 4 per cent, by exactly the difference between a 4 per
cent and a 4^ per cent reserve. In some of the older and
larger companies this difference amounts to several million
dollars.
The principal sources of surplus are ordinarily:
A lower rate of mortality than was assumed in the compu-
tation of the premiums ;
A higher rate of interest, actually received, than was
assumed in that computation ; and
The use of a less amount of money for expenses than was
provided for by the loading of the premiums.
If exactly the tabular rate of mortality were experienced,
exactly the assumed rate of interest were realized, and ex-
40 The A B C of Life Insurance.
actly the amount of the loading were used for expenses, the
company would at all times have its reserve on hand, but
not a dollar of surplus. (Surplus and reserve should be
carefully distinguished. They are entirely separate and dis-
tinct. One is an asset, the other a liability. One can be
used for such purposes as the company thinks best. The
other should be used only in the manner and for the pur-
pose which have been so fully explained and illustrated in
the preceding pages.)
The rate of mortality in any well-managed company
should be less than the assumed or tabular rate.
The rate of interest has for many years averaged more
than 4 per cent. For at least ten years subsequently to
1865 it averaged 8 per cent. Its constant tendency, how-
ever, is to become lower. Consequently, one exceedingly
important factor in producing surplus in earlier years has
grown less and less important in later years.
The amount used for expenses ought not to equal the
loading in any company which has a considerable amount
of business, especially if the premiums are heavily loaded.
After retaining a surplus sufficiently large to provide for
contingencies, it is customary among companies which issue
policies on the mutual or participating plan to divide the
remainder of the surplus among such of its policyholders as
are entitled to share in it. This is, in reality, the return of
Note— Formerly, if a policy " lapsed," the entire reserve was forfeited
to the company, and thus no inconsiderable additions were made to the
surplus. Now, however, a more equitable practice prevails, and the ad-
ditions to the surplus from this source are now less than formerly. In
general, the most considerable gain from lapsed policies, at present,
arises from forfeitures of contingent dividends and a portion of the reserve
under the " Tontine " system as explained on page 57. As the Tontines
form a special class, they are not included above in considering sources of
surplus.
The A B C of Life Insurance, 41
an overcharge, but it is customary to call it the payment of
a dividend.
The principal plans upon which dividends are distributed
are the percentage plan and the contribution plan. The
former allows dividends as a percentage, either on the
amount of the insurance or on the sum of all premiums
paid. The latter takes account of the sources of surplus
and of the amount which each individual policy has contrib-
uted. For example: if the mortality has been but 80 per cent
of the tabular rate, 20 per cent of the cost of the insurance
under A's policy is credited to him ; if interest has been 6 per
cent, instead of 4 per cent, 2 per cent upon the reserve
under his policy is also credited A ; if the expenses have
been 90 per cent of the loading, 10 per cent of the loading
of A^s premium is also credited him. The sum of these
three items is the amount of the dividend received by A.
This plan, now almost universally adopted, was devised by
Mr. Sheppard Homans, assisted by Mr. D. P. Fackler.
Dividends are paid sometimes in cash, sometimes in
reduction of the next year's premium, sometimes by the
addition of a certain amount of insurance to the original
amount of the policy. In the latter case they are known as
" reversionary " dividends.
The frequency with which the accumulated surplus is
divided, and, consequently, the periods at which dividends
are declared, vary with different forms of policies and the
practice of different companies. Sometimes dividends are
paid annually. In other instances, as under policies written
upon the twenty-year distribution plan, they are paid once
in twenty years, and only upon such policies as are then in
force.
42 The A B C of Life Insurance.
CHAPTER VII.
TERMINATIONS AND SURRENDER VALUES.
Policies of insurance which from any cause cease to be in
force are said to " terminate." The methods of termina-
tion may be classified as follows : By " death," when the
policy becomes a claim on account of the death of the in-
sured; by "maturity/* when an endowment, for instance,
becomes payable because the end of the endowment period
has been reached; by " expiry," when a term insurance has
been carried to the end of the term for which it was issued
and consequently is no longer in force ; by " lapse," when
the policy is terminated solely by reason of the non-pay-
ment of a stipulated premium when due ; by " surrender,"
• when the legal liability of the company under the policy is
voluntarily canceled by the insured and beneficiary for a
consideration allowed by the company, which consideration
is called the " surrender value."
Evidently the payment of a death claim or an endowment
when due meets the full measure of a company's responsi-
bility under such a policy. From what has been said in the
preceding pages the reader will understand that a five-year,
ten-year or any other purely term insurance which has ex-
pired has no subsequent value. But in the case of a lapsed
whole-life or endowment policy, for example, to what con-
sideration in the way of a surrender value is the insured
equitably entitled?
It is not at all unusual for such a person to say, " The
I
The A B C of Life Insurance. 43
company has paid out nothing under my policy. I have
not died nor has my pohcy matured ; consequently my in-
surance has cost the company nothing. I ought to have
my premiums returned to me, to say the least, and even then
the company will have had the interest on my money." The
obvious answer to this is that the risk carried by any com-
pany is the total amount of its insurance in force, not
simply that portion of the total amount which becomes a
claim by death or maturity ; that each policy is a part of
the aggregate, and consequently contributes to the total
cost as well as to the total income; and that while the
total loss is, so to speak, individualized by the death of cer-
tain persons, nevertheless the cost actually, and properly,
falls on all the insured, those who do not die receiving the
full worth of their money in the protection afforded. The
aggregate of all the premiums paid by all the insured is
used to pay expenses and death losses so far as it is re-
quired for that purpose, and from each individual premium
is taken its proper proportion.
On the other hand, in the early history of life insurance
no surrender value was allowed in case of lapse. Under
this practice no account was taken of the fact that, after de-
ducting the cost of his insurance and his proper contribu-
tion to expenses, the insured had still paid to the company
an amount in excess of both these items, which was repre-
sented by the " reserve," and for which at the date of lapse
he had received no consideration. Gradually this fact and
the equities involved in it were recognized, and out of this
recognition, stimulated to some extent by legislation and to
a much larger ex'ent by the competition of the companies
for business, has grown the elaborate modern system of sur-
render values.
In discussing this system let us use for the purpose of
44 Tf'i^ A B C of Life Insurance,
illustration the whole-life policy only, while recognizing the
fact that endowments, annuities and other forms are issued'
by the same company, and that what is said concerning the
whole-life policy may require some modification in apply-
ing the general principle to a specific instance of another
form of insurance.
What is the exact status of both parties to an ordinary
whole-life contract? The insured has requested in his
"application" that the company, in consideration of the
annual paymen*^ of a specified premium so long as the in-
sured shall live, shall bind itself to pay a specified amount
to the designated beneficiary whenever the insured shall die.
The company, in compliance with this request, has issued ai
contract (policy) by which it is so bound. The presumption
is that this is a contract which will be maintained during
the lifetime of the insured, and the company relies upon the
annual payments of premium as a revenue from which it
will derive a certain contribution to the payment of its
death losses, another to the payment of its expenses^,
another to the making of a reasonable profit from its busi-
ness. The company has exactly the same right to expect ;
these things which the insured has to expect the prompt
payment of his loss when it occurs. If, now, the policy-
holder fails to pay all the premiums contemplated by his
contract, the company is at once cut off from that source of
income and profit, and, at considerable expense, must seek
another customer to replace the one which it has lost. The
policyholder has had his insurance at its cost plus expenses,
and has an equity in the accumulated reserve. That he
" owns " the specific amount of the reserve on his individual
policy, as has been vehemently asserted in some quarters,
cannot be true. In the first place, there has never been a
year in which the reserve credited to his policy has been
The A B C of Life Insurance, 45
made up entirely of his own money with interest accretions,
and consequently it is not true that that reserve stands
e xactly in the light of a deposit made by fiimself out of his
own funds. Part of the reserve was contributed by men
who died in prior years. If the reader is interested to work
out an illustration of this fact for himself, let him take any
one of the three examples on pages 23, 26 and 27. and note
the number and amount of premiums in excess of the actual
cost of the insurance paid each year by those who die dur-
ng that year, and compute their aggregate with compound
nterest accretions. Of course, under the pure endowment,
page 26, since there is no insurance there can be no cost of
insurance, and the reserve at the end of each year includes
every cent which has been paid by all those who have died.
If the reader has followed the discussion carefully from the
first page to the current one, he will readily understand that
the amount of contribution to the reserve by those who have
died will vary very largely with the form of policy and the
length of time during which the insurance has been in force,
being in some cases of considerable, and in others of incon-
siderable, importance. But that any such contribution, of
greater or of less amount, has been made, is sufficient to
nuUify the alleged ** ownership " of the reserve. The fact
is that the insured agrees to pay so much a year for so much
insurance ; as a rule he knows little of the theory or practice
of the business, and concerns himself less. He has a very
hazy idea of a ''reserve," and wouldn't know what was
meant if he should be told that he " owned " it ; he does
not buy a reserve nor stipulate for such a purchase ; he ex-
pects the company to live up to its contract and to treat
him fairly ; and, even if he expected or desired it, the com-
pany could not sell him the ownership of his reserve unre-
stricted by conditions and enforceable at any time. Conse-
46 The A B C of Life Insurance,
quently what shall be done with the reserve under a lapsed
policy is, apart from legislative interference, purely a ques-
tion of equity between the two parties to the contract.
In determining what is equity, the company on its sirle
must at least consider another question in some respects far
more important than the loss of income and profit in case
of lapse. The man who is in sound health will be likelier
to surrender his insurance than the man who has reason to
believe that his health is impaired and his chance of life
diminished. This is simply human nature, and in this re-
spect the " selection," as it is termed, is always against the
company. By this it is not meant that none but '* good risks '*
will allow their insurance to terminate, Financial difficul-
ties, altered circumstances, the death of beneficiaries for
whom consequently the provision of insurance is no longer
needed, a multitude of reasons for discontinuing insurance
affect alike the. good and the poor risks, and in many cases
are imperative. But where there is any choice in the mat-
ter, the man of impaired health, because he values his insur-
ance the more, will make the greater effort to continue it.
The consequent result of a high rate of lapse is to reduce
the average standard of the risks which remain, and thus to
increase the death rate, a consideration of the utmost im-
portance.
There are other questions which might be considered if
this little book were intended as an exhaustive discussion of
the topics presented, but for its less ambitious purpose it is
not necessary to take them up. Enough has been said to
make it evident that, as a matter of self-protection to the
company, and, in fact, of equity between the retiring
policyholder, the company and those who remain, a reason-
able forfeit might well be demanded by the company from
the man who lapses his policy. This forfeit is known as a
■
7 he A B C of Life Insurance, 47
surrender charge." What should be the amount of this
charge is a vexed question. Eminent actuaries differ in
regard to it, the practice of the companies is not uniform,
£,nd the laws of such States as attempt to regulate the mat-
ter by statute are widely apart in their provisions. Without
a.ttempting to decide or even to suggest where doctors fail
jto agree, let us consider for a moment in what form that
portion of the reserve which remains after deducting the
surrender charge, shall be available.
It has been said that life insurance companies exist for
, the purpose of selling life insurance and not of buying it.
Tliat used to be true, but the modern surrender-value sys-
jtem has largely modified the actual functions of an insurance
company. Theoretically, if A has purchased a policy of life
insurance, and B an endowment, and C an annuity, they
would be entitled, in the event of lapse, to receive as a con-
sideration for their respective reserve equities an equivalent
amount of their respective forms of insurance upon which
no further payment of premium would be necessary. Thus
iVs reserve equity would be applied as a single premium to
purchase insurance payable at his death, B's would be
i applied as a single premium to buy an endowment payable
at the same date at which his original endowment would
have been payable, and C's to purchase an annuity payable
[It the same time and under the same conditions with his
original annuity. All of these policies would be known as
** paid-up" policies. Their amount would necessarily be
less than the amount of the originals.
Example. — A took a whole life policy of $5000 at age
40, carried it ten years and lapsed. To what amount of
paid-up insurance would he be entitled as a surrender
value ?
4^ The A B C of Life Insurance.
Reserve on such a policy (see table on page 75)
would be 5 X $162.97 or $814.85
Surrender charge, say 10 per cent 81.49
' — -^— ^^— — —
Net equity in reserve $7 3336
A at the time of lapse is, of course, 50 years old. Single
premium for insurance at that age is $481.92 for each $1000
(see table on page 75). Consequently A's equity would
purchase ^^^^ of $1000, which would be $1520.
48162
In this case, then, instead of having a policy of $5000
on which he must pay a premium every year, A would have
a policy of $1520 on which he would have to pay no more
premiums.
There is another way in which the reserve equity might
be appHed to the purchase of insurance. Instead of issu-
ing a paid-up policy for a less amount but in force until
terminated by the death of the insured, the company might
continue the full amount of the insurance (in the example,
$5000,) in force during such a term as the reserve equity
would pay for. If the insured should die during that term
his beneficiaries would be paid the full amount of the policy,
but if he should outlive the term, the policy would ter-
minate by expiry and the insurance would cease. An
arrangement of this description is called "extended''
insurance.
It is also evident that any person's reserve equity under
one form of insurance might be used to purchase an equiv-
alent amount of paid-up or extended insurance of another
form. Thus B might have the reserve equity under his
endowment policy applied to the purchase of paid-up
whole-life insurance.
The above surrender values which, not so very many
The A B C of Life Insurance, 49
years ago, were about all that were offered or allowed by
the majority of companies — unless in exceptional instances
or under very special forms of policies — have in recent times
been supplemented and largely superseded by the popular
cash surrender value. Practically there are many cases in
which the insured, when he lapses his policy, has no further
need for insurance, but has urgent need for money, and in
which to insist upon applying his reserve equity to the pur-
chase of any form of insurance, and to refuse to give it to
him in cash, works a hardship. Consequently a policy
which provides for a cash value is attractive to anyone who
thinks he may sometime need the cash more than the insur-
ance, and would rather have a contract right to call for the
cash than to be obliged to negotiate for it and perhaps find
the company unwiUing to pay it. Partly as a concession to
possible necessity on the part of the insured and partly as
an effective method of competing for business, the com-
pany began to make cash surrender values a feature of more
and more of their policies until at the present time a policy
without such provision is rather the exception than the rule.
In the beginning a good deal of caution was exercised on
the theory that it might not always be convenient for a com-
pany to pay the reserve equity in cash. It is necessary that
a company should obtain a certain rate of interest on its
assets, and it cannot afford to keep on hand too large an
amount of uninvested money. Investments must also be
made in the best class of securities and in those having a
long time to run. A life insurance company must also pro-
tect itself against the results of a financial panic and must
not open the way for a possible " run " upon itself by treat-
ing its reserves practically like individual deposits in a bank.
These and other similar arguments seemed to have great
weight at first, and in consequence cash values were not
50 The A B C of Life Insurance,
allowed whenever the policies might lapse, but only at stated
intervals, five, ten, fifteen years, and so on. Moreover, the
portion of the reserve which would be paid in cash was
smaller than the amount which would be applied to pur-
chase insurance, in other words, when cash was paid the
surrender charge was increased. But gradually all this has
been done away with. This may be partly due to the fact
that the evil effects which were anticipated from the free use
of cash surrender values, were not realized, and partly to the
efforts of the different companies to outdo each other in
competition for patronage, but, whatever the reason, cash
values are to-day the rule among the '^ options " given by
policy contracts whenever the policy lapses, and surrender
charges have diminished in proportion. Practice in this
case, as in many others, does not conform to theory. It is
the aim of this discussion to present the latter clearly. He
who seeks an exemplification of the former by examining
the current forms of policies issued by the several com-^
panics will find that the reserve equity — pretty nearly the
entire reserve, for that matter — and the contingent interest
of the insured, if any, in dividends are made the foundation
upon which is reared a structure of numerous options avail-
able in the settlement of lapsed policies. The relative
value and equity of these options in any particular case
cannot be determined by one who has no knowledge of the
elementary principles of life insurance. The man who
decided to patronize one company rather than another be-
cause the surrender values of the former were based upon
" the reserve with ^ per cent interest," while those of the
latter were based upon " the reserve with 4 per cent inter-
est," made a mistake due to his ignorant belief that the 4^
per cent reserve was the larger.
p'or information in regard to surrender values actually
i
The A B C of Life Insurance, 5 1
allowed, the reader is referred to the published literature of
the companies. .«
The most elaborate statutory provisions are contained in
the so-called "Non-forfeiture Law" of Massachusetts.
This, with its accompanying tables, constitutes quite a for-
midable document. At the present time the law is under
criticism by the Massachusetts companies, the Insurance
Commissioner of that State and the majority of American
actuaries for the alleged reason that it is based upon an
erroneous and inequitable theory of surrender values.
52 The A B C of Life Insurance,
CHAPTER VIII.
FLANS OF INSURANCE,
The words " insurance " and *' policy " are often usee
interchangeably, thus : " An insurance of five thousanc]
dollars," or " A policy of five thousand dollars."
Life Policies. •
A policy payable only upon the death of the insured is
known as a life policy. When the premiums are paid an-
nually (or in semi-annual or quarterly installments) during ;
the lifetime of the insured, the policy is called an ordinary,
whole-life policy.
When the payments are to be completed in a given num-
ber of years, the term limited-payment life policy is used.
Or, the exact term is mentioned, as " ten-payment Hfe,"
^* fifteen-payment life," etc. The payment of a single pre-
mium constitutes a single-payment life policy. Of course, \
all limited-payment premiums are higher than ordinary pre- ■
miums, since the equivalent of payments during a lifetime
must be contained in the limited number of payments made. \
Consequently, the reserve or self-insurance element is also
larger.
On all limited payment policies it is customary to give
paid-up insurance for as many proportionate parts of the
original amount as there have been premiums paid. Thus 4
premiums paid on a ten-payment life policy of $1000 would
secure paid-up insurance of $400 payable at death ; 7 pre^
miums paid on a len-payment endowment of $1000 at 6c
would secure a paid-up endowment of $700 payable at 60.
I UNIVERSITY )
The A B C of Lg%Jns^r,^nf^^^ 53
Joint-life policies are contingent upon two lives (some-
times more than two), both of which are insured under one
policy, the insurance being payable to !he survivor upon the
death of either. The premium is higher than that upon a
single life, but is not equal to the sum of the full premiums
on both lives. Policies of this form are not in favor with
American companies at the present time. Very intricate
calculations are involved in the computation of joint-life
premium rates.
Term insurance is insurance covering a specified term.
This provides for payment on account of such deaths only
as occur during the term. The example on page 23 is an
illustration of a five-year, term insurance. As will be seen
by examination, out of 78,106 persons living at age 40,
only 3933 will die during the succeeding five years. If the
term of the insurance, then, is limited to five years, the pre-
mium need be only large enough to provide for 3933 deaths,
while a whole-life insurance would require provision for
78,106 deaths. The term premium is consequently lower.
When the policy provides for insurance for a specified term,
with the privilege of renewing the insurance at the end of
that term for another similar term, upon payment of a pre-
mium adjusted to the cost of each successive term, it is
called a renewable term policv. The length of the term is
indicated by such nomenclature as "yearly renewable term,'*
or " ten-year renewable term."
Annuities.
These policies provide for the payment of a certain
yearly sum to the insured, or to the beneficiary named in
the policy, during the life-time of the annuitant The
premium may be paid in one payment, or in annual pay-
ments for a given number of years. Its amount depends
54 -^^ A B C of Life Insurance,
upon the relative ages of the insured and the annuitant.
Thus if A, being 25 years old, insures his life for the bene-
fit of his mother, 60 years old, with the understanding that
the insurance is to be an annuity, payable, in the event of
his death, during the remainder of his mother's life, the
premium would be very small. For the probability is chat
A will survive his mother — in which case the company
would have to pay nothing — or, in any event, that he will
pay a considerable number of premiums to the company,
while his mother will not live many years after his death
to receive her annuity. On the contrary, if B, the insured,
were an old man, and his daughter, the beneficiary, were
young, the chance would be that B would pay comparatively
few premiums, while the daughter would survive him many
years to receive her annual stipend. In such a case, the
premium would be very high. Annuities, while quite pop-
ular in Europe, are Httle sought after in this country.
Endowments.
A pure endowment, as has already been explained, is an
agreement to pay a certain sum of money when the insured
shall have reached a certain age, but nothing if he shall die
before reaching that age. Although a few policies of this
description have • been issued in this country, this form,
unmodified, is almost never used, but there is added to it
an agreement to pay the sum insured if the person insured
shall die before reaching the specified age. Thus, an endow-
ment assurance of $1000 at 60 means that the company
will pay $1000 if the insured reaches the age of 60, or upon
his death at any time before that. The premium, therefore,
must be the sum of two premiums, one covering the insur-
ance for the term, and the other providing for the endow-
ment at the end of the term. This has been fully ex-
plained and illustrated in Chapter III.
The A B C of Life Insurance. 55
Endowments are sometimes classified by the age which
the insured must attain in order to receive the amount of
the poHcy; thus, an "endowment at 60," an ** endowment
at 70." They are more commonly classified by the term
covered. Thus, an endowment on a hfe, age 40, payable
^t age 55, would be called a *' 15 -year endowment." If
a premium was to be paid each year during this term, the
policy would be called an " ordinary 15-year endowment/'
If, however, the premiums were to be paid in 10 years, the
policy would be called a ^^ten-payment, 15-year endow-
ment."
The rate of premium depends upon the age of the in-
sured, the length of the endowment term and the number
of payments.
Return-premium Policies, Instalment Policies,
Bonds, Etc., Etc.
The preceding policies, three only in number, include just
about everything, in principle^ which is possible in life insur-
ance. And since annuities are so little in vogue in this
country, it is within the truth to say that the life policy and
the endowment are the principal part of the seventy- five or
more differently named policies which are to-day offered to
the public. To describe any considerable number of these
would not be worth the space which it would require. We
mention two or three.
Some policies, either life or endowment, stipulate that
upon the death of the insured, within a specified number of
years, the amount of the premiums paid by him shall be
returned in addition to the amount named in the policy.
Other policies guarantee the payment of the amount of the
insurance with 6 per cent interest thereon. Of course, in
either case and in all similar cases, the addition to the
56 The A B C of Life Insurance.
amount named in the policy is just so much additional
insurance, and an additional premium must be, and always
is, charged therefor.
The instalment principle has been widely applied to both
life and endowment policies. Thus the contract of a whole-
life insurance may stipulate that, whenever the policy
matures as a death claim, the amount of the insurance shall
be paid in a specified number of equal annual instalments.
The premium for this would be less than for the same form
and amount of insurance payable in one sum at the death
of the insured, for the very obvious reason that the risk is
not at any time the full aggregate amount of the instalments,
but only the present value of those instalments. Thus if a
policy which nominally insures for ^20,000 stipulates that
that amount shall be paid in twenty equal annual instal-
ments, the measure of the risk actually assumed by the com-
pany under that policy is the present value of twenty instal-
ments of ^1000 each, the first payable at once, the second
at the end of one year, the third at the end of two years,
and so on, the last one being payable at the end of nineteen
years. From the table of present values, page 76, we find
this to be $14,138, or a little more than seven- tenths of the
nominal insurance.
The foregoing will serve as examples. A most admirable
ingenuity has been displayed in the numerous combinations
of life and endowment insurance with the return of all pre-
miums, or a portion of them, with the payment of interest,
at different rates and for longer or shorter terms, and with
the payment of the principal sum insured in instalments
covering any number of years desired, and themselves of
uniform or varying amounts. In the keen competition for
business almost every possible wish or necessity of the in-
suring public has been met by one or another of the com-
The A B C of Life Insurance. 57
panics. The nomenclature by which these different forms
are known is equally ingenious and sometimes decidedly
picturesque. "*
Tontines.
In 1648, Lorenzi Tonti organized a fund in Naples, the
conditions of which were as follows : Each subscriber paid
a certain sum of money into the fund. The total fund was
invested, and the interest on the amount of each subscrip-
tion was paid, during the lifetime of the subscriber, to such
person as he named. At the death of a subscriber his sub-
scription was forfeited to the fund, and the interest thereon
was divided among the subscribers, who, for this purpose,
were divided into classes according to age. At the death
of the last subscriber the entire capital subscribed reverted
to the crown.
It will be seen that this is the converse of life insurance,
since those who live longest receive the greatest benefits.
The principle of forfeiture on the part of those who die and
of accumulation for those who live is known as the " Ton-
tine " principle, and is perfectly illustrated in the pure en-
dowment, page 26. That application of this principle to
life and endov/ment insurance policies which has given to
such policies, as a cluss, the name *' Tontines," is as follows :
As has already been explained, a policyholder who has
paid premiums for several years and then given up his in-
surance, paying no further premiums, leaves in the hands
of the company the reserve credited to his policy, and also
any share in the surplus which might fairly be considered
his, but which has not been actually paid to him in the
form of dividends. Under the early Tontine practice the
entire amount of this reserve and of this surplus was credited
by the company to the other policies of the same form and
class. If any policy became a death claim the face of the
58 The A B C of Life Insurance,
policy only was paid, and any accrued but undivided sur-
plus thereunder was credited in like manner. Finally, at
the end of a specified number of years, known as the Tontine
period, the gains from these sources were divided among the
policies of the same form and class which then remained in
force.
This practice has been modified so that in many cases
the Tontine principle is now applied, after the policy has
been in force three years, to surplus only, the retiring
policyholder receiving an equitable consideration in paid-up
insurance (see page 47) for his reserve. The Tontine
principle is applicable to any form of policy written upon
mutual or participating premiums. The methods of ap-
plication are quite numerous, and the policies are variously
designated as Semi-Tontine, Free Tontine, Five, Ten, Fif-
teen or Twenty-year Distribution policies, etc. The extent
to which the principle is applied can be determined only
from a knowledge of the terms and conditions of the policy
in each case. The different companies writing this kind of
policies furnish estimates of the probable results.
The A B C of Life Insurance^ 59
CHAPTER IX.
CERTAIN CONDITIONS IN POLICY
CONTRACTS.
Payments of Premiums, — Premiums are always payable
at the home office of the company, but, for the convenience
of the policyholder, are allowed to be paid at some bank or
agency near him. Prompt payment of premiums is also re-
quired. In actual practice, this is often waived, although
there would seem to be no good reason why the insured
should not pay his premiums with the same promptness
which he expects and demands from the company in the
payment of its losses.
Residence and Occupation, — The conditions of policies in
regard to these matters are usually exceedingly liberal. '
Residents in notoriously unhealthy localities, or persons en-
gaged in extra-hazardous occupations, would not be
insured by any company at the usual rates of premium.
Policies provide that, after being insured at the usual rate,
the policyholder shall not reside in such localities or engage
in such occupations without first obtaining the company's
consent and paying an extra premium therefore. The
written consent of the company is called a " permit."
Use of Stimulants and Narcotics, — Some policies provide
that the insured shall not indulge in the use of stimulants
or narcotics to such an extent as to impair his health or
shorten his life.
Suicide, — The practice of different companies differs as
to suicide. Some policies provide that death by suicide,
whether the insured be sane or insane, shall not constitute
6o The A B C of Life Insurance,
a claim against the company. In others, death by suicide
from insanity is treated as the natural termination of the dis-
ease. In others, no reference is made to suicide.
Non- Forfeiture, — As already stated, every company now
allows some equitable return, in the way of paid-up or ex-^
tended insurance, and most likely in cash, for the reserve
left in its hands by the lapse of a policy. Provision for this
is made by the terms of the poHcy, and consequently the;
reserve equity is not forfeited by failure to pay a stipulated
premium.
Incontestability. — Most policies provide that, subject to
the conditions of the policy in regard to residence, occu-
pation, and the payment of premiums, the insurance shall be
incontestable after a certain number of years (two or three).
The exact phraseology of this provision differs with dif-
ferent companies and policies. The general effect of the pro-
vision, however worded, is to waive, in case of claim against
the company after the specified term, all defenses of a merely •
technical nature, or such as might be based upon misstate-
ments in the application, made without fraudulent intent.
No company ought, perhaps, to waive its right to contest a
fraud, or to be estopped from making such defense if good
grounds for it exist. The sensible man will undoubtedly admit
that there is no more reason why attempted fraud upon an ;
insurance company should not be resisted, than there is for
non-resistance to any other form of fraud. Attempts of this
sort sometimes occur, and are either fought out in the courts
or settled by compromise as a matter of expediency. Resist-
ance to such claims is always creditable to a company, and
should have the support of agents and policyholders. On
the other hand, the fact that a company frequently resists
the payment of claims or forces compromises, may be ac-
cepted without hesitation as proof that something is wrong
in the management.
The A B C of Life Insurance, 6i
In general, there are two things which should be said
in regard to the conditions of the later .^policy contracts.
No one can determine what are all the conditions of any
policy by an examination of the policy only. Every con-
tract of insurance consists of two parts, the request for the
insurance known as the '* application/' and the policy, and
these two are in legal effect one. Consequently any stipu-
lations or conditions recited in the application and consented
to by the applicant, as witnessed by his signature thereto,
are as much a part of the contract as they would be if
printed in the policy. The practice of the companies is not
uniform in this respect, and in one case the majority of the
conditions appear in the policy, while in another they are to
be found in the application.
The general tendency in late years has been toward
fewer conditions and restrictions, and greater liberality.
Certain rights and obligations of both parties have been
definitely established in practice and by legal decisions,
while others have been made matters of statutory pro-
vision. The supposed necessity for some restrictions has
not been demonstrated by experience to be a real necessity,
and in the case of some others where it cannot fairly be
said that experience has demonstrated anything, thus leav-
ing the matter in doubt, the companies have given their
patrons the benefit of the doubt. The life insurance
manager of fifty years ago, comparing a "latter day"
policy with one of his own lengthv, verbose and minutely
restricted contracts, would be more than likely to mistake
the former for a promissory note.
62 2"he A B C of Life Insurance.
CHAPTER X.
APPLICATIONS; RISKS; MEDICAL
EXAMINERS.
When a person desires insurance, he makes application
therefor upon printed forms furnished by the company. It
is intended that this form, when properly filled out and
accompanied by the report of the Medical Examiner, shall
furnish the company with information which will enable it
to decide whether or not the applicant is a desirable risk.
His family history as to longevity, existence of hereditary
diseases, etc. ; his own personal history as to health or
disease, residence, occupation, etc.; his present residence
and occupation, and, last but not least, his present physical
condition, must all be taken into the account.
It is here that the Medical Examiner plays a most
important part. It is his duty to ascertain the present
physical condition of the applicant, and from the results of
his examination, together with the personal and family
history of the appHcant, to determine the probability of a
long or short life, and consequently to recommend or reject
the risk. No one performs a more important duty in
connection with the whole business of life insurance. If
Medical Examiners are incompetent or careless, the best
plans of insurance and the ablest management will end in
nothing but disaster. The fact that not one of the import-
ant failures of life insurance companies in this country has
The A B C of Life Insurance, 63
been due primarily to excessive mortality, speaks volumes
for the skill and fidelity of the MedicaUExaminers.
It might appear, at first sight, that a rigid medical exam-
ination should result in a large saving to the companies by
securing for them an exceedingly row rate of mortality. It
is true that the rate is generally very low for a year or two
among newly selected risks, but the effect of the medical
selection disappears more rapidly than is usually supposed,
and but a comparatively short time elapses before the aver-
age normal rate is experienced. The very low cost of
insurance in assessment organizations, newly organized, is
due to the fact that the risks are newly selected, but it is
idle to expect that the cost can be kept down to that point
by the infusion of "new blood," or by any other process.
If impaired or doubtful risks were not summarily rejected,
the selection against the company, already alluded to, would
assert itself at the very outset. The better class of lives
would drop out, and the company would find itself over-
whelmed by the mortality among the poorer risks remaining.
Companies have been formed for the insurance of im-
paired lives at an adequate rate of premium. It has been
found very difficult to determine what premiums are ade-
quate, but some of the later experiments in this direction
are giving promise of a successful solution of the problem
of insuring "sub-standard" risks.
If sufficient space were available, it would be interesting
to note the variations between the standards which the dif-
ferent companies make in the matter of risks. Probably
it would be correct to say that, in a very general way,
all Medical Directors agree as to what constitutes a desir-
able, and what an undesirable, risk, but within the lines of
this general agreement there is plenty of disagreement on
minor points.
64 The A B C of Life Insurance,
Beside its presentation of the applicant as a risk, the
application has another purpose which has already been
mentioned — it forms the basis of the insurance contract.
The applicant asks for the insurance, declares such and such
things to be true in regard to his age, place of birth, per-
sonal history, present residence, occupation, etc., and agrees
that the policy may be issued to him upon certain con-
ditions. In all of this he acts as agent for the bene-
ficiary named in the policy and for any and all other
persons who may in the future acquire any interest in the
insurance. It is not necessary to suggest that an applica-
tion should be prepared with care, and that the applicant
ought to acquaint himself with all its terms before signing it.
/*
The A B C of Life Insurance, 65
CHAPTER XI.
ANNUAL STATEMENTS; RATIOS,
The laws of the different States require companies to file
annually statements of their transactions during the pre-
ceding year, and of their financial condition at the close of
the year. The forms prescribed by the Insurance Depart-
ments of the various States are very complete. The results
in detail are published in the annual reports of the Depart-
ments, and are frequently accompanied by tables of per-
centages and ratios. In determining the value of these,
some knowledge of the business of life insurance, and more
common sense, are necessary. For instance :
Percentage of expenses to income is not always a reliable
standard by which to judge economy of management.
Premiums may be very heavily loaded for certain forms of
insurance, and the current year's expenses may exhaust but
a small part of that loading. Or the investment part of the
premiums may be very large, and the premiums, con-
sequently, very high. The amount used for expenses
would, in either case, constitute but a comparatively small
percentage of the gross premiums. On the other hand, the
loading, or the investment part, or both, of premiums may
be very small, in which case, although expenses may be
kept within the loading, they may still constitute a com-
paratively large percentage of the premiums. Consequently
66 The A B C of Life Insurance.
equal economy of management will not necessarily result in
the same, or even nearly the same, percentage of expense
to premium income.
The ratio of assets to liabilities is of little consequence
until both assets and liabilities have reached respectable
proportions. If A has but one dollar in the world, and
owes nothing, the ratio of his assets to his liabihties is
infinity. If B, however, is worth $200,000, and owes
$100,000, the ratio of his assets to his HabiHties is only two
to one. Of course, after a company has been in business
for a number of years and has placed a large amount oi
insurance on its books, the percentage of its assets to its
liabilities is a question of the highest importance.
The percentage of death losses to the mean amount in-
sured during the year affords the basis of a fairly close esti-
mate of a company's mortality experience. But an exact
determination of that experience cannot be made without a
knowledge of the ages of all the persons insured, and conse-
quently of the percentage of mortality expected by the com-
pany and provided for in the premium charges.
The percentage of interest {including rents and profits on
sales of stocks^ bonds and real estate) to mean amount of
assets, is important. If premiums are calculated and
reserves held upon a basis of 4 per cent, that rate, at least,
ought actually to be reaHzed.
The ratio of expenses to a^nount of new business secured
may be of much or little importance, depending entirely
upon the proportion of expense fairly chargeable to the
securing of new business, as well as upon the provision for
that expense made in the premiums charged.
The ratio of assets to amount of insurance in force
is of Uttle value, the main question always being whether
present accumulations, together with future premiums,
^e
The A B C of Life Insurance,
67
'e sufficient to provide for future claims. If future pre
miums alone are sufficient, the question of present accumu-
lation is of less consequence.
And so on. Persons of a statistical turn of mind are
constantly furnishing tables of ratios and percentages, com-
parative tables, etc., etc. Most of the statistics thus compiled
are interesting, many of them are valuable, a few are vital.
Anyone well grounded in the elementary principles of life
insurance, and fairly familiar with the practical workings of
the business, can decide for himself to which class belong
such statistics as come under his observation.
"Expectation" Table. — Assured Lives.
(Constructed from the American Experience Table of Mortality.)
Age.
10
II
12,
13
14,
IS
16
17
18,
19
20
21
22.
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Expecta-
tion,
Years.
48.7
48.1
47-4
46.8
46.2
455
44-9
44.2
43-5
42.9
42.2
41.5
40.9
40.2
39 5
38.8
38.1
37.4
367
36.0
35 3
34-6
33 9
332
325
31.8
311
Age.
37...
38--.
39---
40...
41...
42...
43- ••
44...
45...
46...
47...
48...
49---
50...
51...
52...
53...
54...
55...
56...
57...
58...
59-..
60...
61;..
62...
63...
Expecta-
tion,
Years.
304
29 6
28.9
28 2
27.5
26.7
26.0
25.3
245
23.8
23.1
22.4
21.6
20.9
20.2
19.';
18.8
18.1
17.4
16.7
16. 1
154
14.7
14. 1
135
12.9
12.3
Age.
64
65
66
67
68
69
70
71
72,
73
74
75
76
77
78
80
81
82
83
84
85
86,
87
88
89
90
Expecta-
tion,
Years.
2 5
2 2
1.9
1-7
1.4
68 The A B C of Life Insurance.
American Experience Table of Mortality.
c
bXI
u
G O
B
0,;
.^^
H
.2 h-^ bo
^1
o.S
r
^ W)
Ho^
M
;z;
5-PQ
ICO.OCO
749
.007490
99.251
746
007516
98.505
743
•037543
97,762
740
.007569
97,022
737
.007596
96,285
735
.007634
95.550
732
.007661
94,818
729
.007688
94.089
727
.007727
93,362
725
.007765
92,637
723
.007805
91,914
722
.007855
91.192
721
.007906
90471
720
•007958
89.751
719
.008011
89 032
718
.008065
88314
718
.0 8130
87596
718
.008197
86,878
718
.008264
86,160
719
.008345
85,441
720
.0 8427
84.721
721
.008510
84.000
723
.008607
83.277
726
.008718
82.551
729
.008831
81,822
732
.008946
81,090
737
.009089
80.353
742
.OC9234
79.611
749
.009408
78,862
756
.009586
78 106
765
.009794
77.341
774
.010008
76.567
785
.010252
75.782
797
.010517
74.985
812
.010829
74.173
828
.011163
73.345
848
.011562
72497
870
.012000
71,627
896
.012509
70,731
927
.013106
69,804
962
.013781
68,842
1,001
.014541
67,841
1,044
.015389
Age.
53
54
55.
56^
57-
58.
59-
60,
61.
62.
63.
64,
65
66,
67.
68.
69.
70
71
72
73 ■
74
75
76
77
78
79
80
81
82.
83
84
85
86
87
88
89
90
91
92
93
94
95
l4
hfl
^ *
C
l>
c
^u
.t wi
^f>
hJ.S
•>•>
a
Pi
^•^
PQ
^
66.797
i,c9i
65.706
1. 143
64563
1,199
63.364
1,260
62,104
1325
60.779
1.394
59.385
1,468
57,917
1,546
56.371
1,628
54.743
1. 713
53.030
1.800
51.230
1,889
49341
1,980
47.361
2,070
45.291
2,158
43.133
2243
40,8qO
2 321
38,569
2,391
36,178
2,448
33.730
2,487
3^243
2505
28,738
2.501
C6237
2,476
23,761
2431
21,330
2369
i8,q6i
2 291
16,670
2,196
14.474
2,091
12,383
1,964
10,419
I 816
8603
1,648
6.955
1,470
5,485
1,292
4,193
1,114
3.079
933
2,146
744
1,402
555
847
385
462
246
216
137
79
58
21
18
3
3
The A B C of Life Insurance,
69
Net Premiums for a Whole- Life Insurance of $1000.
Based upon the American Experience Table of Mortality, with 4 per ceilt interest.
Age.
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
^i
36.
38
39
40
41,
42
43
44.
45'
46
47
48,
49
SO.
51
52.
S3
S4.
56.
57
58
59
60
61
62
64
65
Single Pre-
miums
which are
also Net
Reserves
on Paid-up
Policies,
$247.77
251-85
256.08
260.47
265.04
269.79
27474
279.87
285 21
29075
296.51
302 50
308 71
315 17
321.86
328.81
33602
34850
35124
359-27
367-57
376.17
385.06
394-25
403-75
41355
423 66
434.06
444.76
455-74
466.99
47848
490.21
502.15
514.31
526.65
539.15
551 81
564.59
577.48
590.46
603.49
616.56
629.63
642.69
655.70
Annual
Premiums
During
Life.
$12 67
^2.95
13.24
13-54
13-87
14.21
14.57
14-95
15-35
1577
16 21
f6.68
17 18
17.70
18.25
18.84
19.46
20.12
20 82
21.57
22.35
23.19
24 08
2503
26.04
27.12
28 27
29.50
30. 8 E
32.21
3370
3529
36.98
3879
40.73
42.79
45.00
47-35
49.87
5257
55-45
58.54
6t 84
65 39
69 18
7325
Annual
Premiums
for
Twenty
Years.
$18.73
19.05
19-38
19.72
20.08
20.46
20.85
21.26
21.68
22.13
22.59
23.08
23.59
24.12
24-67
25.26
2587
26.51
27.18
27.88
28.68
29.41
30.24
31 II
32.03
33.00
3404
35.14
3630
37.55
38.86
4027
41.76
43.36
4506
46.88
48.84
50.93
53-17
55-59
58.18
60.98
63-99
67.24
7075
74 54
Annual
Premiums
for
Fifteen
Years.
SP22.53
22.91
23.30
23.71
24.14
24.58
25.05
25-53
26.03
26.56
27.10
27.67
28 27
28.89
29-53
30.20
30.91
3164
32-41
33-21
34.05
34-93
35-85
36.82
37.83
38.90
40.02
41.21
42.45
43.76
45 14
46.60
48-13
49.76
51.47
53-29
55.21
57.26
59-44
61.76
64.25
66.90
69.74
72.79
76.07
7959
70
The A B C of Life Insurance.
Annual Premiums— Analysis of First Year's Premium,
Different Ages, $icxx) Whole-Life Insurance.
Participating Rate.
AGE.
Net Premiums, American Ex-
perience Table of Mortality,
with 4 Per Cent Interest.
Portion
for Death
Claims.
$7-71
7.76
7.Z2,
7.88
7.96
803
8.11
8.20
830
8.40
8.51
8.64
877
8-93
9 TO
9.29
9.49
9.71
9-95
10.24
10.5s
10 92
11.32
11.79
12.34
12.97
13.67
1445
15.33
16 30
17-38
18.60
1993
21.40
23.10
24.85
Portion
for
Reserve.
$650
6.81
7- 13
7-47
7.8r
8.18
8.57
8.98
9.40
986
IO-33
10.82
11-35
11.89
12.47
1306
13.70
1437
15.08
15.80
16.57
17.35
18.18
19 02
1987
2073
21.62
22.53
23.46
24-43
25.41
26.40
27.42
28.67
2953
30.60
Total
Net
Premiums
$14.21
1457
149s
15-35
1577
16 21
16.68
17 18
17.70
18.25
18.84
19.46
20.12
20.82
21.57
22.35
23.19
24 08
2503
26.04
27.12
28.27
2950
30.81
32.21
3370
3529
36.98
3879
40.73
42.79
4500
47.3s
49.87
52.57
55-45
Loading.
$5-63
583
5.98
6.13
6.30
649
6.67
6.87
7.08
7-30
7-54
7 79
8.05
8.33
8.62
8.9s
9.28
9.64
10.02
10.42
10.85
IT. 31
11.80
12.32
12 88
1348
14 IT
14.80
15.52
16.29
17 12
18.00
18.94
1995
21.03
22.18
See Explanatory Notes on Page 77.
The A B C of Life Insurance.
71
^^K Actuaries' or Combined Experience Table
^^ OF MORTALfTY.
The following 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. Some
of the objections advanced against it are that certain lives
have 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 average duration of all
the policies was a little less than eight and a half years. The
later Actuaries' or H. M. (healthy males) Table is now more
generally used in England. The American Experience Table
furnishes a better standard than either for American lives.
Age.
|i
3
Ratio of Deaths
During the Year to
Number Living at the
Beginning of the Year.
Age.
:>o
►J bJO
is
I
3
3
10
IT
12
13
14
15
16
17
18
19
20
21
22
23
24
100,000
99.324
98,650
97.978
97.307
96,636
95.965
95.293
94,620
93.945
93.268
92,588
91.905
91,219
90,529
676
674
672
671
671
671
672
673
675
677
680
683
686
S^
694
.006760
.006786
.006812
.006848
.C06896
.006944
.007003
.007062
.007134
.007206
.007291
.007377
.007464
.007564
.007666
25
26
27
28
29
30
31
32
33
34
p:::::::
P:::::::
39
89.835
89.137
^7,726
87,012
86,292
85.565
84.831
84,089
83.339
82,581
81,814
81,038
80.253
79.458
698
703
708
714
720
72.7
734
742
750
758
767
776
785
Q S **
fi3^
.007770
.007887
.008006
.008139
.008275
.008425
.008578
.C08747
.008919
.009095
.009288
.009485
.009687
.009906
.010131
72
The A B C of Life Insurance,
Actuaries' or Combined Experience Table
OF Mortality.
{Continued front preceding ^age^
•r 5 ^
1) 4) «
5 «
78,653
77.838
77,012
76.173
75.316
74.435
73.526
72,582
71,601
70.580
69.517
68,409
67.253
66,046
64,785
63,469
62,094
60658
59.161
57.600
55.973
54.275
52,505
50,661
48,744
46,754
44.693
42.565
40.374
38,128
^2
815
826
839
857
881
909
944
981
1,021
1,063
1,108
1. 156
1,207
1,261
1,316
1.375
1.436
1.497
1,561
1,627
1,698
1,770
1,844
1.917
1,990
2,061
2,128
2,191
2,246
2,291
•5 rt rt*^
.0 10362
.010612
.010894
.011251
.011697
.012212
.012839
.013517
.014260
.015061
•OI593Q
.0^6898
.017947
.019093
.020313
.021664
.023126
.024679
.026386
.028247
.030336
.032612
.035120
.037840
.040826
.044082
.047614
.051474
.055630
.060087
70
71
72
73
74
75
1^
77
78
79
80
8i
82
83
84
85
86
87
88
89
90
9C
92
93
94
96
97
98
99
4> U
,£i OS
i!<
t>
«.•
^^
^2
'l>
1^
%-i
9
^^
55
35.837
2.327
33.510
2,351
31.159
2,362
28,797
2.358
20,439
2.339
24,100
2,303
21,797
2,249
19.548
2,179
17.369
2,092
^S^277
1,987
13.290
1,866
11,424
1.730
9.^94
1,582
8,112
1.427
6,685
1,268
5.417
1,111
4.306
958
3.348
81E
2,537
673
1,864
545
1.3^9
427
892
322
570
231
339
155
184
95
89
52
37
24
13
9
4
3
I
I
The A B C of Life Insurance,
73
Net Premiums for a Whole-Life Insurance of $1000.
Based upon the Combined Experience Table of Mortality, with 4 percent interest.
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36.
37
38.
39
40.
41.
42.
43-
44.
45-
46.
48.
49.
50-
51-
52.
53-
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64,
65.
$251.88
256.57
261.38
266.34
271.49
276.80
282.29
287.98
293.84
299.91
306.14
312.61
319-31
326.15
33327
340.61
348.16
356.00
364.08
372.42
381.04
38996
399- 18
408.69
418.49
42857
438.84
449-34
460.04
470.88
481.92
493"
504.46
515-97
527-59
539-32
551-15
563-12
57515
587.27
599-43
611.62
62385
636 00
648.11
660.19
$12.95
' 13.27
13.61
13.96
M-33
14.72
15 13
1556
16. OT
16.48
16.97
1749
18.04
18.62
19.23
19.87
20.54
21.26
22 02
22.82
23.68
2459
25-55
26.58
27.68
28.85
30.08
31-39
32.77
3423
35-78
37.42
39-15
41.00
42.95
4503
47-23
4957
5207
5472
5756
60.57
6378
67.20
70.84
74.72
Annual
Annual
Premiums
Premiums
for
, for
Twenty
Fifteen
Years.
Years.
$19.00
$22.86
' 19-37
23.29
1976
23-75
20.15
24.22
20.57
2471
21.00
25 21
21.44
25-74
21.90
26.28
2238
26.84
22.88
27-43
23-39
28.03
2393
28.65
24.49
29.30
25.07
29-97
25.68
30.67
26.32
31.40
26.98
32.15
27.67
32.94
28.40
33-76
29.17
3462
29.98
35-53
30.83
3647
31-74
37-47
32.69
3852
3371
39-63
34-77
40.78
3590
41.99
37.08
^53-25
38.32
44.57
39-63
45-95
41 02
47-38
42.48
48.89
4402
5046
45-66
52.12
47-39
53.86
4924
5569
51.20
57.63
5329
59.67
55 53
61.84
57-92
64.15
60.49
6660
63.24
69.21
66.18
71.99
69-33
74.96
72.71
78.12
7634
81.50
74
The A B C of Life Insurance,
Ordinary, Continued-Payment, Whole-Life.
net value, or reserve of a premium-paying policy of
$1000, at the end of various years, actuaries*
table, 4 per cent
ist
Year.
7.60
7.91
8.24
8.58
8.93
9-31
970
lO.II
10.54
11.00
II 48
11.99
12.55
13 12
1374
14.41
15 12
15.85
1659
17.30
18.01
18.69
1939
20.10
20.86
21.62
22.39
23.19
24.00
24.85
25.72
26.61
27.56
28.52
29.50
3045
ad
Year.
15-45
16.09
1675
17.43
18.16
18.91
19.70
2054
21 42
22.35
23.33
24.39
2551
26.69
27.96
29.31
30.73
32.18
33-59
34.99
3636
37.71
39.10
40.54
42.02
43-52
4506
46.63
48.26
49.94
51.65
53.43
55-29
57.18
5905
60.90
3d
4th
5th
6th
7th
Year.
Year.
Year.
Year.
Year.
$
$
$
$
$
2356
31.94
40.58
49-51
58.73
24.52
3324
42.24
51-52
61. II
2553
34.60
4396
53.62
6359
26.58
36.02
4576
5581
6620
27.68
37.50
47.64
58.12
68.93
28.83
3906
49.63
60.54
71.80
30.03
40.70
51 71
63.08
74.84
31.31
42-43
53.91
65.78
7804
32.65
44-25
56.25
68.63
81.43
34.07
46.20
58.71
71.65
85.03
35.59
48.25
61.34
74-86
88.84
37.19
50.43
64.11
78.26
92.87
38.90
52.75
67.08
81.87
97.09
40.72
55-22
70.20
85.62
101.43
4^.65
57.83
73.46
8948
105.88
44.70
60.55
76.79
93-42
110.36
46 81
6329
80.16
97-35
114.85
4891
66.04
83-49
101.26
119.32
5100
68.73
8678
105.13
123 80
53.02
71.38
90.04
109.02
128.28
55.04
7403
.93 34
11294
13280
57.05
76.72
96.67
116.90
137.38
59.14
79.47
100.09
120.95
142.05
6128
82.30
103-57
125.09
146.83
63.47
85.19
107.14
129.34
151-73
65.70
88.13
110.79
133.67
15672
67.98
91.14
114-53
138.09
161.84
70.33
94-24
118.34
142.64
167.09
72.74
97.42
122 29
147.32
172.47
75.22
100.70
12635
152.12
177-93
77.78
10408
130.51
156.98
183.46
80.42
107.55
134-72
161.90
189.01
83-15
III. 07
138-99
166.84
194-59
85.88
114 59
14323
171.76
200.14
88.60
118 08
147 46
176.66
20563
91.28
121 54
151-63
181.49
2ir.02
See Explanatory Notes on Page 77.
The A B C of Life Insurance. 75
Ordinary, Continued-Payment, Whole-Life.
net value, or reserve of a ^remium-paying policy of
$1000, at the end of various years, actuaries'
table, 4 per cent.
( Continued from preceding page. )
gth
Year.
$
7806
8452
87.99
91.64
95-48
99-53
103.82
108.36
11315
118. 16
12335
128.69
134.10
139.60
145-14
150.73
156.33
161.94
167.56
17324
179.12
184.90
190.90
197.06
203.34
209.76
216.27
222.86
229.51
236. 19
242.87
249-54
256.13
262 63
269.02
loth
Year.
$
88.20
91.76
95-50
99-43
103.56
107.91
112.51
117-37
122.50
127.86
133-41
139-13
144.97
150 89
15689
162.97
169.09
175.22
181.37
187.54
193-79
2C0.13
206.59
213.19
21995
226.84
233.82
240.88
248.00
255.18
262.35
269.52
276.63
283.65
290.58
297.42
iSth
Year.
$
144.12
149.99
156.17
162.65
169.41
176.42
183.65
191.06
198.65
206.39
214.30
222.36
230.54
238.83
247.22
255-70
264.25
272.83
281.47
290. 19
299.01
307.89
316.86
325-89
33498
344-07
353-18
362.24
37^-25
380.21
389.11
397.92
406.65
415.26
423-74
432.09
20th
Year.
$
209.84
218.13
226.62
23531
244.20
25329
262.57
272,02
281.64
291.42
301-35
311.42
321.60
331 91
342.33
35284
363-37
37390
38439
394.86
40530
415-71
426.07
43637
446.62
45679
466.88
476.87
48676
496-55
506.21
515.79
525-16
534-43
543.52
552.49
25th
Year.
$
283 60
29372
30403
314-51
325.18
336.02
347.02
358-17
36949
380.94
392.53
404.18
41589
427.60
439-31
450.97
462.54
47398
485-29
496.45
507-49
518.41
52923
53992
55049
560.91
571 20
581.36
591-36
601.20
610 89
620.47
630.03
639 68
649.52
659.75
^oth
Year.
$
362.97
374.60
386.39
398.34
410.44
422 68
434.90
447.38
459.80
472.23
484.64
497.00
50927
52142
533 44
545-32
55702
568.53
57985
59097
601 90
612 65
623.26
633.69
64393
654.00
663.94
673.82
68374
693-81
70415
714-83
72588
737.37
749.24
761.42
35th
iTear.
446. IT
458.86
471.67
48452
497.38
510.21
52301
535-72
548.34
560.83
57320
58542
597-47
609.34
621 01
63247
644.11
654-71
665.47
67599
686.30
696.43
706.46
716.50
726.61
73693
747-48
758.32
769.48
780.92
79251
804 24
815.99
827.41
838.15
847-87
See Explanatory Notes on Page 77.
76
The A B C of Life Insurance.
Present Value of $i Due at End of Year in from
One to Forty Years from the Present Time.
No. OF Years.
3
4
c
6
7
8
9
lO
TI
12
13
14
15
i6
17
i8
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Four Per
Cent.
,961538
924556
888996
854804
821927
790315
759918
730690
702587
675564
649581
624597
600574
577475
555265
533908
513373
493628
474642
456387
438834
421955
405726
3901 2 I
3751 17
360689
346817
333477
320651
308319
296460
285058
274094
263552
253415
243669
234297
225285
216621
208289
Four and
One-Half
Per Cent.
956938
915730
876297
838561
802451
767896
734828
703185
672904
643928
616199
589664
564272
539973
516720
494469
473176
452800
433302
414643
396787
379701
363350
347703
332731
318402
304691
291571
279015
267000
255502
244500
233971
223896
214254
164525
196199
877501
179665
I 71929
Five Per
Cent.
952381
907029
863838
822702
783526
746215
710681
676839
644609
613913
584679
556837
530321
505068
481017
458112
436297
415521
395734
376889
358942
341850
325571
310068
295303
281241
267848
255094
242946
231377
220359
209866
199873
190355
181290
135282
164436
156605
149148
142046
Six Per
Cent.
The A B C of Life Insurance. 77
EXP LAN A TOR*y NO TES.
Pages 74 and 75. — Reserves are calculated upon the basis qj net pre- ,
miums. The amount of loading, added to the net premium to make the'^
gross premium, does not aftect the reserve. Upon the same kind of a
policy, issued at the same age and with the same number of premiums
paid, the reserve would be the same, no matter what amount of annual
premium might be charged for the insurance.
Under premium-paying policies, the amount of the reserve depends
upon the age of the insured at the time the policy was issued, and
the number of premiums paid. Under paid-up insurance, the amount of
the reserve depends entirely upon the age of the insured at the date
for which the reserve is computed.
The reserves given are based upon the Actuaries' Table of Mortality,
with 4 per cent interest. See pages 33 and 34. For the sake of exactness
it should be said that, while these reserves are for the most part greater
than those based upon the American Experience Table, with 4^ per cent
interest, the latter are the greater at the very highest ages. The reason
for this is that according to the American Table the term of life ends with
age 95, while according to the Actuaries' it continues to age 100.
Page 73. — The net single premiums given are also the net values
or reserves of a paid-up pohcy of $1000 at the different ages. To esti-
mate pretty nearly the amount of paid-up insurance which a company
would allow for the surrender of an ordinary whole life policy with pre-
miums payable annually, ascertain the reserve on that policy according to
the table of reserves on pages 74 and 75, and divide 90 per cent of it by
the single premium given for the age actually attained by the policyholder
at the time of surrendering his original pohcy for paid-up insurance.
Page 70.— This table shows the component parts of both the net and the
gross (or office) premiums at different ages, for an insurance of $1000,
payable at death. This analysis, however, is correct for ihejftrst year of
the insurance at each age only. Each subsequent year the portion of the
premium used for death claims is greater, and the portion used for reserve
is smaller than these respective portions for the first year. The accumu-
lated reserve incre^ises each year by the addition of that year's reserve
portion of the premium and of interest, as is shown in table on page 36.
The "loading" remains the same theoretically for each year of the insur-
ance, although the amount actually collected by the company will vary
wirh the amount of dividend allowed on that account.
WH/T IS THOUGHT OF THE/ B C OF LIFE INSURAp.
OPINIONS OF EXPERTS.
COL. J A COB L» GREENE, President Connecticut Mutual Life Insurance
Company y Hartford^ Conn.
*' I find it, as I expected from its authorship, to be a clear and concise statement
of the matters therein treated, and I should think that it would be useful for the
purpose which I presume it is intended to serve — the instruction of new agents.
It has the advantage of some other elementary works which I have seen, of much
greater brevity."
HON. JAMES G. BATTERSON^ President Travelers Insurance Company.,
Hartford^ Conn.
" It is a very plain and intelligent statement of the case. I am glad that you
have kept out of the actuarial field. The various propositions stated arithmetic^
ally can be easily comprehended. Clear away mysteries from life insurance and
the people will take it. You have done a good and useful work."
DAVID PARKS FACKLER, Consulting Actuary, New York.
*' I have endeavored to read through your little treatise with the attention due
to its compact and masterly style For the purpose it has in view it
seems to excel anything I have seen, and I hope it will have the wide circulation
it merits."
SHEPPARD HOMANS, Consulting Actuary, New York,
" The ' A B C ' is the modest title of a manual of life insurance which should
•be studied by every canvassing agent. It is not ©nly full of valuable information
relating to the fundamental principles of the business, couched in language free
from algebraic formulas, but it contains information concerning the practicdl
application of these principles which is of great value to the student,"
OPINIONS OF PRACTICAL FIELD MEN.
SUDLOW &> MARSH, Indianapolis, Ind.
** We have looked it over very carefully, and are very glad to say that we think
it will subserve a most desirable purpose in the education of agents. Further, the
tables contained therein are very simple, decidedly good, and will prove of great
assistance in soliciting business. It meets our hearty commendation."
R. L. DOUGLAS, Philadelphia, Pa,
*' It is an exceedingly instructive and enjoyable production. What a contrast
between to-day and twenty years ago ! Then, and even at a much later period, it
was generally supposed that the subject of life insurance was a mystery beyond
the reach of ordmary intellects. Mr. Elizur Wright and Mr. Sheppard Homans
punctured that illusion. This book of yours is another long stride in advance
You take the bed rock and build from it "
The A B C of Life Insurance, 79
WHAT IS THOUGHT OF THE A B C OF LIFE INSDRANCE.-c.«/.««.rf.
HON. JOHN A. FINCH, the well-known insurance lawyer of Indianapolis,
in a recent lecture before the senior class of the Medical College of Indiana of the
University of Indianapolis, commended A B C OF LIFE INSURANCE as
follows:
If your interest should be general in the subject (of life insurance), so that you
wish to know something of the principle or principles which underlie the business
of life insurance, I know of no better work to recommend you to than a little book
called A B C OF LIFE INSURANCE, published by The Spectator Company,
New York. There is also a book by M. M. Dawson, entitled ELEMENTS OF
LIFE INSURANCE; also THREE SYSTEMS OF LIFE INSURANCE,
both by the same publishers, all of which you will find profitable.
Mr. Finch has also given the following endorsement of A B C OF LIFE
INSURANCE :
I believe I have in my office as nearly a complete set of books on the subject of
life insurance as can be collected, and I am free to say that I think there is more
meat in A B C OF LIFE INSURANCE than in any single book for the
beginner in the study of the principles of life insurance. I think the insurance
companies would do themselves and the public service if they would buy this
little book and give a copy to each student in the law schools of the country. I am,
perhaps, a little over hopeful, but I believe the popular impression of life insurance
as reflected in the decisions of the courts and the acts of our legislatures is very
largely attributable to ignorance ; and I believe this could be removed by proper
missionary work.
I
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