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surance begins. Knowing, from the table, the amounts of the contri-
butions and the number of deaths and the time at which they become
due, it is to be ascertained what amount of money deposited at the
beginning of the period, improved at compound interest, would be
equivalent to the total of these sums.

The present value of 81 at the beginning of the year, at 4^ per
cent, interest, is S0"9569 ; that is to say, 80-9569 invested at 4^ per
cent, interest will amount to $1 at the end of the year. The present
value of $1 for two years is 80-9157, for three years 80-8763 ; or these
amounts, improved at 4^ per cent, compound interest, will become 81
by the end of these years.

Applying this principle to the class of 847 persons under considera-
tion, and assuming each contribution and each death-claim to be 81,
we need only multiply these by the present value corresponding to
each year, bearing in mind that the living pay in advance, while the
death-claims are due at the end of the year :



Age.
90..
91..



Livin-.


Deaths.




. 847 X $1 = $847 00


385 X


•9569 = $368 41


. 462 X -9569 = 442 10


246 X


-9157 = 225 26


. 216 X -9157= 197 79


137 X


-8763 = 120 05


. 79 X -8763 = C9 23


58 X


•8386 = 48 64


. 21 X -8386 = 17 61


18 X


•8025 = 14 44


3 X -8025 = 2 41


3 X


•7679 = 2 30



$1,576 14 S'779 10

The above calculation shows the present value of the 1,628 contri-
butions, at 81 each, to be 81,576.14, and the present value of the 847
death-claims to be 8779.10 ; therefore, to meet these latter, the con-
tributions need only be, instead of one dollai-, jWeV^f of one dollar, or
80-49432 (49 + cents). The item of interest has reduced the premium
to 80"49432, when, without it, it would have been 80*52027.



PRACTICAL BUSINESS OF LIFE INSURANCE. 735

Similarly to the annual premium, any other mode of payment may
be determined ; say, for instance, one single premium for life. At
age 90 the present value of all future death-claims is $779.10, and
there are 847 persons to provide for the same ; therefore, each one
must contribute ^J|'^, or $0"91987 in advance, that being the one sin-
gle premium for life.

The limits of a magazine article do not permit more extended
illustrations, but the reader can readily reason out for himself how-
premiums, insuring for life in a limited number of payments, and
various other adaptations in vogue, all based upon the same principles,
may be arrived at.

Let us now apply the annual premium of $0*49432, as above ascer-
tained, to the insurance fund, and follow its working to the end, com-
puting interest at 4| per cent. :

Age 90— Living 847 x -49432 = $418 69 x 1-045 = 8437 53

Death-claims at the end of the year, 385 00



Balance, 85'^ 53



Age 91 " 462 X -49432 = $228 37

Balance on hand, 52 53



S280.90 X 1-045 =$293 55
Death-claims at the end of the year, 216 00

Balance, 847 55



216 X -49432 = 8106 77
Balance on hand, 47 55

8154 32 X 1-045 = 8161 27
Death-claims at the end of the year, 137 00



Balance, 8-4 27



Age 93 " 79 X -49432= 8-9 05

Balance on hand, 24 27



863 32 X 1-045 = 866 18
Death-claims at the end of the year, 58 00



Balance, 88 18



Age 94 " 21 X -49432 = 810 38

Balance on hand, 8 18



818 56 X 1-045 = 819 39
Death-claims at the end of the year, 18 00



Balance, 81 39



Age 95 " 8 X -49432 = 8143

Balance on hand, 1 39



82 87 X 1-045 = 83 00
Death-claims at the end of the year, 3 00



IZ^'



THE POPULAR SCIENCE MONTHLY



It will be observed that, at the end of every year, with the exception
of the last one, an unexpended balance remains ; dividing this by the
number of survivors, we get the amount that applies to each individual
living at that period. This is called the net valuation, or, more com-
monly, the reserve for each policy.

At the ages we have under consideration, the reserve would be as
follows :



End of Year.


Living.


Balance.


Reserve for each.


90


462

216

79

21

3


?52 53

47 55

24 27

8 18

1 39


eO-11370
0-22014
0-30721
0-38952
0.46261


91


92


93


94


95








While the reserve, as here given, is strictly correct in amount as
well as in principle, other methods of calculation are employed in prac-
tice ; but, for a simple explanation, the plan here adopted will proba-
bly serve better than any other. The difficulty has also been that
the very high age of ninety had to be selected for the above illus-
trations, because every computation has to be carried to the end of
the table, which would be very lengthy and tedious for a young age.
But, the explanation having been given, a closer inspection of the
reserves applying to age twenty will afford a broader insight into
the subject :

Age 20 — Net Annual Premium %11.97 per ^1,000.



End of Year.


Death-rate, per cent.


Cost of insurance.


Bcserve.


20


-780
-785
•790

-843
-979
1-083
1-116
1-378
2-669
6-199

85-714
100-000


$7 77
7 78
7 79

7 88

8 27
8 63

8 75

9 83
14 65
23 33

47 17
00 00


$4 74
9 67


21


22


14 82


30

40. . .


64 92
155 80


44 .. .


203 05


45


215 94


SO

60


286 56
451 27


70


623 60


94


944 97


95


1,000 00





From the above table it will be seen that the annual premium may
be looked upon as consisting of two parts, one defraying the annual
cost of insurance dependent upon the death-rate, the other put aside
as a reserve fund. Up to a certain period the premium is larger than



PRACTICAL BUSINESS OF LIFE INSURANCE, -j-^j

the actual cost of insurance, but a time arrives when it does not suffice,
and tlien a part of the interest on the reserve must contribute the
difference. It will be noticed that the reserve grows constantly, so
that by the end of the year 94 it is 8944.97, and, with the annual pre-
mium of $11.97, due at the beginning of year 95, amounts to §956.94,
which, invested at 4^ per cent, interest, will by the end of the year
produce the sum of $1,000. Theoretically, then, there is no loss from
a person dying according to the last year of the mortality table, be-
cause the whole amount of the sura insured has already accumulated
under the reserve.

This reserve, too, may in a certain sense be said to have a twofold
function : it not only provides for the future, but also annually re-
duces the amount at risk, whereby the cost of insurance becomes less
than it would otherwise be. Thus, by the above table for the year 45,
the cost of insurance is only 88.75, while the death-rate would amount
to $11.16 per 81,000. The fact that the reserve has reached 8215.94,
and the amount at risk is only 8784.06, reduces the cost from 811.16
to $8.75. For the year 94 the death-rate would amount to 8857.14
per 81,000, while the cost of insurance is only 847.17, since the reserve
has accumulated to 8944.97, leaving but 855.03 at risk.

As a final illustration of the whole method take the reserve at the
end of year 44, 8203.05, add the annual premium of 811.97, being
together 8215.02, invest at 4^ per cent, interest, and it will amount to
8224.69 ; deduct the cost of insurance, 88.75 (being the amount at risk
8784.06 X 1-116 per cent., the death-rate), and the balance remaining,
8215.94, is the reserve at the end of year 45.

But, however instructive these details, it may be well, to avoid con-
fusion, to sum up the whole process in the statement that the annual
premium is a device to collect a larger amount than the death-rate in
the earlier years of insurance, and to use these over-payments, improved
at compound interest, to meet the deficiencies which arise in later
years. The premium and reserve are so nicely adjusted that they ai-e
strictly equitable for the living as well as the dying at everv vear of
life.

The view of the reserve or net valuation here presented is distinc-
tively American. It has been embodied in State legislation, and has
an important bearing upon the question of surrender values, presently
to be considered. There are other methods for determing the valua-
tion, which take into account all future payments due, and all losses
and expenses to be incurred to the end of the table ; but these are
•juestions beyond the scope of this article.

To the net premium of which we have treated, a certain percentage
is added to defray expenses and to provide for contingencies ; it is
called loading, and together with the net premium constitutes what is
known as gross or office premium. In mutual companies, the only
ones that will be here considered, the loading is made higher than any
VOL. XIX. — 47



738 THE POPULAR SCIENCE MONTHLY.

probable exigency will deuiand, so as to be absolutely safe. At fixed
periods the amount collected, in excess of actual cost, is distributed
among the contributing members. It is erroneously called " profits "
or " dividends," when, in reality, it is only a j:eturn of unexpended
assessments. When the system was new and untried, it was not
thought prudent to make such restitution oftener than every live years.
Gradually experience led to greater confidence, and competition intro-
duced the practice of annual " dividends." These are principally de-
rived from the higher rate of interest realized than the legal standard
assumes, from a lower mortality than the table estimates, and from the
excess of loading over actual expenses. Various ways of distributing
this surplus have been in use, but the so-called "contribution plan,"
now universally adopted in the United States, is unquestionably the
most equitable ever devised, as it returns to every member precisely
his proportion of the over-payments. It may be best explained by an
illustration.

Take a policy issued at 25, at an annual premium of 819.89, on
which a cash dividend of 86.72 haS been declared at the end of year 38.
Assume the expenses applying to this policy to be equal to about 10
per cent, of the annual premium, the average rate of interest realized
h\ per cent., and the actual mortality experience to be 10 per cent,
less than the table indicates, the account would then stand as fol-
lows :

Reserve at the end of year 37 §101 51

Gross premium §19.89 paid at beginning of year 38, being net premium 13 42

Loading §6 47

Less actual expenses incurred 1 99

4 48

8119 41
Interest earned at 5i per cent 57

§125 98

TJeserve at end of year 38 §111 74

Cost of insurance according to table §8 35

Less saving by actual mortality (10 per cent.) 83

7 52

119 26

Return due on policy §6 72

The same result may be shown in another way :

Legal reserve based on 4^ per cent, interest, actually earned 5 J per cent., being

gain of 1 per cent, on §111.74 §1 12

Loading exceeds actual expenses 4 48

Interest on same at 5^ per cent 25

Actual mortality less than assumed 83

Interest on same at 5i per cent 4

§6 72



PRACTICAL BUSIXESS OF LIFE IXSURAXCE. 739

Of course, there may be other items of gain or loss besides those
enumerated in the above ilhistration.

Most companies give poliey-hohlers the option of either taking a
cash return, or having the amount converted into a '' reversionary divi-
dend," payable with the policy ; that is, simply to purchase insurance
for a single premium. The above cash dividend of 86.7:i would give
a net reversionary dividend of 8^0.82 (the net single premium for
$1.00 at age 39 being 80-32283) ; but of course some deduction must
be made for expenses of management.

These reversionary additions form a very large item with old
institutions, one leading company alone having over §25,000,000 in
force.

Intimately connected with the reserves and dividends, and next
in importance, is the question how lapsed or forfeited policies should
be treated. Probably no theoretical point has been so hotly contested,
and certainly none has offered equal difficulties in practice. In the
early days of the institution, when it was prudent to err on the side
of safety, the view prevailed that a policy was a contract for life,
from which neither party could withdraw. Instead of a single pre-
mium in advance, annual account payments were accepted, but it
was thought that a violation of this condition could only be regu-
lated by absolute forfeiture of all previous contributions. As the
business grew in importance, and long experience proved it grounded
on reliable foundations, the harshness of this rule began to attract
attention.

In England Dr. Farr advised the issuing of non-forfeitable policies,
and the allowance of a definite cash surrender value on them. In this
country the Insurance Commissioner of Massachusetts first brought
the subject before the Legislature of that State, and a non-forfeiture
law was passed in 1861. In opposition to the views held by actuaries
of the old school, a tendency extreme in the other direction now began
to assert itself. It was contended that the reserve pertaining to each
policy should be considered equivalent to a deposit in a savings-bank,
to be withdrawn at the pleasure of each individual insurer. This posi-
tion was combated as wrong in theory, and as absolutely subversive
of the business in practice. Insurance when applied to the individual
becomes an absurdity, and it can only be safely conducted on averages
dependent upon large aggregates. A person that insures for life virtu-
ally agrees to contribute to the death-claims of other members as
long as lie himself lives, and should he withdraw ought to pay his
share of the liabilities assumed and the expenses of management
attendant thereon. It becomes the duty of an insurance company to
prevent the unnecessary withdrawal of its members, and self-preserva-
tion compels it to constantly strive to acquire new lives to retain the
institution in a prosperous condition. Therefore, while it would be
unjust to confiscate the Avhole accumulated reserve on lapsed policies,



740 THE POPULAR SCIENCE MONTHLY.

it is but fair that such charge be made as to fully compensate the
association for the loss of a withdrawing member.

These views may be considered as the equitable, middle course
between two extreme positions, and they are now very generally con-
ceded and adopted in practice. Policies are made non-forfeitable after
two or three annual payments, and when lapsed, if presented within
reasonable time, either paid-up insurance is granted or a percentage
of the reserve allowed as cash surrender value. A few, indeed, have
gone further, and printed in the contract the fixed cash surrender value
that may be obtained at the end of every year. This innovation is
not unlikely to be permanently ingrafted upon the business, and even
now there is hardly a reputable company that declines to purchase its
own policies when presented at the proper time ; and the amounts
thus expended are far greater than is generally known. One leading
company of this State, whose annual premium income for 1879 was
about 812,500,000, paid over $4,500,000 for surrendered policies. Vari-
ous intricate formulas have been devised by actuaries to determine the
strictly equitable surrender value, which, however, as far as the general
reader is concerned, all culminate in a larger or smaller percentage of
the reserve.

While proper agitation, competition, and a sense of justice, brought
about a fair adjustment of cash surrender values, the question of paid-
up insurance has been definitively determined in New York by the
enactment of a statute, which went into effect January 1, 1880. It
provides that when a policy shall lapse for the non-payment of pre-
mium, after being in force three years, the reserve and dividend addi-
tions on such policy shall, on demand made xoithin six months after
such lapse (unless the provisions of the statute had been specifically
waived), be taken as a single premium at the published rates of the
company, and be applied either to continue the policy in force at its
full amount, so long as such single premium will purchase temporary
insurance for that amount, or to purchase paid-up insurance, payable
at the same time as the original insurance ; provided, however, that
the net value of the insurance given for such single premium shall in
no ease be less than two thirds of the entire reserve. That is to say,
that the whole amount of the policy shall remain in force for such a
length of time as no less than two thirds of the net reserve will pur-
chase, or that the amount of the policy shall be reduced correspond-
ingly, and be made to expire at the time originally fixed by the policy.
In principle, therefore, the question may be considered as permanently
settled, and new methods will certainly be devised to adjust minor
practical difficulties upon an equitable basis.

Still, many crude ideas yet prevail among the insuring public, which
lead to misunderstandings that ought not to exist. Some intelligent
men, even, imagine that a company should be compelled to reinstate
a lapsed policy without reexamination of the insured life, or that, at



»1!3^:



PRACTICAL BUSINESS OF LIFE IXSURAXCE. 741

least, the whole amount of premiums paid ought to be returned, since
no loss has occurred. However absurd such notions, they have caused
much dissatisfaction, and, as they spring from a total misconception
of the aims and functions of the institution, they ought to be dispelled.
The companies themselves are not free from blame, however, for per-
mitting many false impressions to gain ground. Nothing can be more
mischievous than the assertion that life insurance is a profitable invest-
ment for money in the ordinary acceptation of that phrase. It is a
provision against a contingency to which every human being is sub-
ject. A proper appreciation of its great benefits would prompt most
men to seek its protection as far as their means permitted. To the
majority of insurers, however, it is an actual expense, though allotted
among them upon the most equitable basis. On the other hand, the
amount of premiums paid can never be totally lost, since every life-
policy must eventually become a death-claim. But only those should
insure who really require it and can continue payments to the end.
Had this always been understood, many policy-holders would have
been spared disappointment and suffering when sober reaction followed
a period of wild inflation.

One of the evils resulting from dissatisfaction with insurance com-
panies has been the formation, all over the country, of so-called coop-
erative (latterly mutual benefit) life associations. They are based on
what has already been shown as utterly impracticable — the collection
of contributions on the death of members, with no fixed premiums or
adequate accumulation of reserves. When the lives are newly se-
lected, and not much above middle age, there is, at first, an appearance
of saving over regular premiums. But, as they get older and the rate
of mortality rises rapidly, the contributions become onerous, and, there
being nothing to forfeit, the healthy lives withdraw, leaving a con-
stantly increasing preponderance of impaired lives. The association
breaks up, and those most in need of insurance can no longer obtain
it from regular companies. The fallacy consists in assuming a continu-
ous increase of new young lives that are willing to bear the burdens
of the old members ; an infatuation that never lasts long. It seems
almost incredible that, in the face of well-established scientific princi-
ples and a century's experience, such crude experiments should again
be introduced, as though they were a new invention. They deserve
no better name than frauds, originated either by designing men to
plunder the credulous or by those so grossly ignorant as to be no less
culpable. Well have they merited the name current in insurance par-
lance, " the co-duperatives."

We have now touched upon most of the distinctive features of life
insurance that interest the general reader, and but little remains to be
said of the general management. It has been shown that next in im-
portance to the collection of premiums is the accumulation of a reserve,
which must earn at least the minimum rate of interest assumed as the



742 THE POPULAR SCIENCE MOXTHLY.

basis of calculation. This is no easy task in the present condition of
the money market, and exceptional skill, prudence, and forethought,
are required to secure safe and profitable investments. It must be
remembered, too, that theoretically all the funds on hand are supposed
to bring interest, while in practice a considerable part must always
remain unemployed, so that the average rate realized is less than the
cui-rent rate of interest. On the other hand, well-managed companies
accumulate a surplus over the net reserve, and have their interest in-
come largely increased from this source. Still more important is
the fact, as far as Xew York is concerned, that, since Massachusetts
and some other States have established four per cent, as the legal
standard for reserve, and all companies desire to transact business
in those States, they keep their surplus sufficiently high to be vir-
tually on a four per cent, basis. Whether a lower rate than this
will be realized on safe investments in the next quarter of a cen-
tury, expert financiers and economists seem hardly prepared to an-
swer ; but, should a reduction to a three and a half per cent, standard
become necessai-y, it would only temporarily incommode our sound
offices.

With mortality tables as reliable as any human estimate can make
them, and with reserves based on a sufficiently low rate of interest, the
management of a life-insurance company does not materially differ
from that of other moneyed institutions. The proper selection of
business and the safe investment of funds require prudence and sa-
gacity, and devolve great responsibility upon executive officers. But
mutual-insurance companies (and nearly all stock companies in the
United States also embody the mutual principle) have a margin far
above any probable exigency, in the excessive loading of premiums.
This very safeguard, it is true, may be perverted, and in some cases
has been a temptation to abuse and extravagance. A life-insurance
company once fairly established, however, ought to be as safe as any
other financial institution, and, where failure occurs, it may always be
traced to either gross mismanagement or intentional fraud. State super-
vision, which has been of great benefit to the system and to the com-
munity, can never supplant individual judgment or probity. In fact,
it ought to be limited to prescribing minimum reserves, the character
of investments, and the publication of truthful statements of the con-
dition of companies.

While life insurance is of comparatively recent date in the United
States (the oldest company now in business having been organized in
1843), its development has been so rapid as to have probably surpassed
that of every other country. The following table shows the condition
of the business, as reported to the Jsew York department, in its in-
fancy in 1859, its period of highest inflation in 1870, and at the lowest
point of reaction in 1879 :



HOW TUB EARTH IS WEIGHED.



743



1S50.


No. of
com-


Number

of
poUcies.


Amount

of
insurance.


Gross assets.


Surplus.


New York State....
Other States


8
6


23,690
25,918


$72,197,426
69,300,541


$11,629,085
8,907,000


$3,630,706
1,440,442




14


49,608


$141,497,967


$20,586,085


$5,071,148


New York State. . . .
Other States


41
30


377,437
370,370


$1,039,662,517
984,222,438


$133,119,187
136,401,253


$19,673,246
28,815,048




71


747,807


$2,023,884,955


$269,520,440


$48,488,294


lS-9.
Now York State. . . .
Other States


12
19


261,799
833,687


$730,648,500
709,312,665


$202,562,832
198,932,901


$32,887,465
32,390,256




31


595,486


$1,439,961,165


$401,515,793


$65,277,721



The number of companies rose from fourteen to seventy-one in eleven
years, and fell to thirty-one in the following nine years, while the amount
insured was only reduced by about 25 per cent. Compared with other
institutions, this shrinkage during a period of general retrenchment is not
large. With about 600,000 policies in force, $400,000,000 of assets and
805,000,000 of net surplus, the success of life insurance is really aston-
ishing. As a cooperative enterprise, in the truest sense of the word,
it outranks every other in the means employed. Scientific principles
are applied to the solution of an intricate social problem, and result in
the most equitable division of burdens. The aims and purposes are



Online LibraryD. S. (David Samuel) MargoliouthThe Popular science monthly (Volume 19) → online text (page 93 of 110)