Popular Science Monthly/Volume 19/October 1881/The Practical Business of Life Insurance III

Popular Science Monthly Volume 19 October 1881  (1881) 
The Practical Business of Life Insurance III by Theodore Wehle



THE mortality tables, forming the theoretical basis of life insurance, having been explained, it remains to be shown how they are employed in practice. There is a fundamental difference between life and fire or marine insurance that must first be considered. The hazard attaching to a building or a ship may remain unchanged for a very long term of years, and the rate of premium once determined need not be altered. Such property is usually insured for one year at a time, and renewed as often as desirable. But the same methods can not be applied to human life. If the policy were to terminate annually, and a new examination could be demanded, many persons whose health had become impaired would be declined at the beginning of every new year. Then, as has been shown, from a very young age, upward, the rate of mortality constantly increases. That would necessitate a higher premium charge from year to year, so that, finally, a person who should be fortunate enough to reach the highest age of the table would have to pay one hundred per cent, for that one year. It requires no argument to prove such a system impracticable, and therefore the plan of fixing one uniform periodic premium for the whole term of the proposed insurance has been adopted.

The following table shows, in one column, the amount of net premium that must be paid at the beginning of every year to insure 81,000 for that year; and, in the other column, the equal net annual premium to insure for life.

By net premium is meant the amount calculated from a certain mortality table, and rate of interest, without any addition for expenses.

In all illustrations hereafter given the American Experience Table and four and a half per cent, interest will be employed, that being the official standard for the State of New York.

Age. Net premium
for one year.
Net annual
premium for life.
Age. Net premium
for one year.
Net annual
premium for life.
20 $7 47 $11 97 60 $25 54 $54 14
21 7 51 12 23 70 59 61 97 00
22 7 57 12 50 80 138 24 188 20
90 434 96 494 33
30 8 06 15 34 94 820 22 836 69
40 9 37 21 30 95 956 93 956 93
50 13 19 32 49

From this table it appears that, to insure $1,000 for one year at a time, it would cost $7.47 at age 20, and that the amount would have to be continually increased, until at age 90 it would be $434.96, while the same purpose would be accomplished for an equal annual premium of $11.97. The somewhat larger expense in the earlier years of insurance avoids the necessity of enormous charges at the high ages.

The method of arriving at the equal annual premium is based upon very plain reasoning, and can be explained in a simple manner.

Let us assume, with the American Experience Table, that, out of 100,000 persons at age 10, there remain 847 living at age 90, and that they die, according to the table, as follows:

Age. Number living. Number of
90 847 385
91 462 246
92 216 137
93 79 58
94 21 18
95 3 3
1,628 847

Were these 847 to form an association, based on the condition that the payments remain equal throughout, and be collected from the survivors at the beginning of each year, and that $1 be paid at the death of each member, there would be 1,628 contributions during the whole period, to provide for 847 death-claims. The requisite annual premium would therefore be 8471628 dollar, or $0.52027 (52 cents). Let us examine the working of this fund:

Age 90—living, 847 X ·52027 = contributions $440 67
Death-claims 385 00
Balance $55 67
Age 91—living, 462 X ·52027 = contributions $240 37
Balance 55 67
$296 04
Death-claims 246 00
Balance $50 04
Age 92—living, 216 X ·52027 = contributions $112 38
Balance 50 04
$162 42
Death-claims 137 00
Balance $25 42
Age 93—living, 79 X ·52027 = contributions $41 10
Balance 25 42
$66 52
Death-claims 58 00
Balance $8 52
Age 94—living, 21 X ·52027 = contributions $10 92
Balance 8 52
$19 44
Death-claims 18.00
Balance $1 44
Age 95—living, 3 X ·52027 = contributions $1 56
Balance 1 44
$3 00
Death-claims 3 00

One important element, however, the investment of money at interest, has been omitted in the above illustration, and will be introduced now. It has already been stated that premiums are payable at the beginning, while death-claims are due at the end, of the same year. To bring these different amounts and dates to a common basis we must determine the present value of each, at the age at which the insurance begins. Knowing, from the table, the amounts of the contributions 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 $1 at the beginning of the year, at 412 per cent. interest, is $0·9569; that is to say, $0·9569 invested at 412 per cent. interest will amount to $1 at the end of the year. The present value of $l for two years is $0·9157, for three years $0·8763; or these amounts, improved at 412 per cent, compound interest, will become $1 by the end of these years.

Applying this principle to the class of 847 persons under consideration, and assuming each contribution and each death-claim to be $1, 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. Living. Deaths.
90 847 X $1= $847 00 385 X ·9569 = $368 41
91 462 X ·9569 = 442 10 246 X ·9157 = 225 26
92 216 X ·9157 = 197 79 137 X ·8763 = 120 05
93 79 X ·8763 = 69 23 58 X ·8386 = 48 64
94 21 X ·8386 = 17 61 18 X ·8025 = 14 44
95 3 X ·8025 = 2 41 3 X ·7679 = 2 30
$1,576 14 $779 10

The above calculation shows the present value of the 1,628 contributions, at $1 each, to be $1,570.14, and the present value of the 847 death-claims to be $779.10; therefore, to meet these latter, the contributions need only be, instead of one dollar, 77910157614 of one dollar, or $0·49432 (49 cents). The item of interest has reduced the premium to $0·49432, when, without it, it would have been $0·52027.

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 779.10847, or $0·91987 in advance, that being the one single 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 ascertained, to the insurance fund, and follow its working to the end, computing interest at 412 per cent.:

Age 90—Living 847 X ·49432 = $418 69 X 1·045 = $437 53
Death-claims at the end of the year, 385 00
Balance, 52 53
Age 91" 462 X ·49432 = $228 37
Balance on hand, 52 53
$280.90 X 1·045 = $293 55
Death-claims at the end of the year, 246 00
Balance, $47 55
Age 92" 216 X ·49432 = $106 77
Balance on hand, 47 55
$154 32 X 1-045 = $161 27
Death-claims at the end of the year, 137 00
Balance, $24 27
Age 93" 79 X ·49432 = $39 05
Balance on hand, 24 27
$63 32 X 1·045 = $66 18
Death-claims at the end of the year, 58 00
Balance, $8 18
Age 94" 21 X ·49432 = $10 38
Balance on hand, 8 18
$18 56 X 1·045 = $19 39
Death-claims at the end of the year, 18 00
Balance, $1 39
Age 95" 3 X ·49432 = $1 43
Balance on hand, 1 39
$2 87 X 1·045 = $3 00
Death-claims at the end of the year, 3 00

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 commonly, 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 $52 53 $0·11370
91 216 47 55 0·22014
92 79 24 27 0·30721
93 21 8 18 0·38952
94 3 1 39 0.46261
95 . . . . . . . . . . .

While the reserve, as here given, is strictly correct in amount as well as in principle, other methods of calculation are employed in practice; but, for a simple explanation, the plan here adopted will probably serve better than any other. The difficulty has also been that the very high age of ninety had to be selected for the above illustrations, 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. Reserve.
20 ·780 $7 77 $4 74
21 ·785 7 78 9 67
22 ·790 7 79 14 82
30 ·843 7 88 64 92
40 ·979 8 27 155 80
44 1·083 8 63 203 05
45 1·116 8 75 215 94
50 1·378 9 83 286 56
60 2·669 14 65 451 27
70 6·199 23 33 623 60
94 85·714 47 17 944 97
95 100·000 00 00 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 the actual cost of insurance, but a time arrives when it does not suffice, and then 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 $944.97, and, with the annual premium of $11.97, due at the beginning of year 95, amounts to $956.94, which, invested at 412 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, because the whole amount of the sum 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 reduces 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 $8.75, while the death-rate would amount to $11.16 per $1,000. The fact that the reserve has reached $215.94, and the amount at risk is only $784.06, reduces the cost from $11.16 to $8.75. For the year 94 the death-rate would amount to $857.14 per $1,000, while the cost of insurance is only $47.17, since the reserve has accumulated to $944.97, leaving but $55.03 at risk.

As a final illustration of the whole method take the reserve at the end of year 44, $203.05, add the annual premium of $11.97, being together $215.02, invest at 412 per cent, interest, and it will amount to $224.69; deduct the cost of insurance, $8.75 (being the amount at risk $784.06 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 confusion, 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 are strictly equitable for the living as well as the dying at every year of life.

The view of the reserve or net valuation here presented is distinctively 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 determine: the valuation, 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 questions 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 probable exigency will demand, 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 return of unexpended assessments. When the system was new and untried, it was not thought prudent to make such restitution oftener than every five years. Gradually experience led to greater confidence, and competition introduced the practice of annual "dividends." These are principally derived 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 $19.89, on which a cash dividend of $6.72 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 512 per cent., and the actual mortality experience to be 10 per cent, less than the table indicates, the account would then stand as follows:

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
$119 41
Interest earned at 512 per cent 6 57
$128 98
Reserve 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 28
Return due on policy $6 72

The same result may be shown in another way:

Legal reserve based on 412 per cent, interest, actually earned 512 per cent., being gain of 1 percent, on $111.74 $1 12
Loading exceeds actual expenses 4 48
Interest on same at 512 per cent 25
Actual mortality less than assumed 83
Interest on same at 512 per cent 4
$6 72

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

Most companies give policy-holders the option of either taking a cash return, or having the amount converted into a "reversionary dividend," payable with the policy; that is, simply to purchase insurance for a single premium. The above cash dividend of $6.72 would give a net reversionary dividend of $20.82 (the net single premium for $1.00 at age 39 being $0·32283); 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 premium in advance, annual account payments were accepted, but it was thought that a violation of this condition could only be regulated 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 position 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 virtually agrees to contribute to the death-claims of other members as long as he 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-preservation 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 whole accumulated reserve on lapsed policies. 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 conceded 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 $12,500,000, paid over $4,500,000 for surrendered policies. Various 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 premium, after being in force three years, the reserve and dividend additions on such policy shall, on demand made within 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 case 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 purchase, or that the amount of the policy shall be reduced correspondingly, 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 reëxamination of the insured life, or that, at 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 permitting many false impressions to gain ground. Nothing can be more mischievous than the assertion that life insurance is a profitable investment for money in the ordinary acceptation of that phrase. It is a provision against a contingency to which every human being is subject. 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 companies has been the formation, all over the country, of so-called cooperative (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 selected, 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 constantly 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 continuous 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 principles 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 parlance, "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 importance to the collection of premiums is the accumulation of a reserve, which must earn at least the minimum rate of interest assumed as the 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 current rate of interest. On the other hand, well-managed companies accumulate a surplus over the net reserve, and have their interest income largely increased from this source. Still more important is the fact, as far as New 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 virtually on a four per cent, basis. Whether a lower rate than this will be realized on safe investments in the next quarter of a century, expert financiers and economists seem hardly prepared to answer; but, should a reduction to a three and a half per cent, standard become necessary, 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 sagacity, 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 supervision, which has been of great benefit to the system and to the community, 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 condition 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 New York department, in its infancy in 1859, its period of highest inflation in 1870, and at the lowest point of reaction in 1879:

1859 No. of
Gross assets. Surplus.
New York State. 8 23,690 $72,197,426 $11, 629,085 $3,630,706
Other States. 6 25,918 69,300,541 8,907,000 1,440,442
14 49,608 $141,497,967 $20,536,085 $5,071,148
New York State. 41 377,437 $1,039,662,517 $133,119,187 $19,673,246
Other States. 30 370,370 984,222,438 136,401,253 28,815,048
71 747,807 $2,023,884,955 $269,520,440 $48,488,294
New York State. 12 261,799 $730,648,500 $202,562,832 $32,887,465
Other States. 19 333,687 709,312,665 198,952,961 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 $65,000,000 of net surplus, the success of life insurance is really astonishing. 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 most exalted, too. Other associations combine individuals to cooperate with a view to their own present support and immediate enjoyment, while this institution is based upon abstention, self-imposed for other future beneficiaries.

With its usefulness not yet fully appreciated, its wide field of application not thoroughly understood, we may well be thankful for what it has already accomplished, and be proud of it as an exponent of the civilization and of the times in which we live.