In the case of insurance to run for life there is apparently a new element introduced. since the indemnity is certain somer or later to hceome a claim. But the difference is only in appear ance. If the Actuaries' table be 0 w hob- life policy taken out at age twenty-five may be treated as a term policy for seventy-fonr years, since the table assumes the death of the last survivor at ninety-nine. In calculating the risk for the seventy-fourth year the fraction represent ing the probability of death becomes and the risk assumed for that year equals the face of the policy. This risk would then be dis vomited at 4 per cent. compound discount for seventy-four years, and the result added to re sults similarly obtained for previous years. On the other hand, tile promise to pay :zit each year for life ceases to have tut\ value for any year after the seventy-fourth. since on the sev enty-fifth year the numerator of the fraction rep resenting the probability of survival becomes zero.
Endowment insurance to-day is Trite as mach in evidence as pure life insurance. An endow ment is a promise to pay a person a stated sum at a future day provided the person is living at that day. Endowment insurance 11.11;11Iy proviilis also for the !payment of an insurame indemnity if the insured dies before the end of the (.11 dowinent period. The two transactions. 'however, the insurance and the endowment. are entirely distinct and could perfectly well be carried of by different companies. In tl e ease of endow Ment the pre111111111 eolitnins two eve to pay for the endowment. the other to par for the insurance. Let us consider how each is determined.
What risk does a company assume which promises a boy of ten that if he is alive at age thirty it will pay him $1000? From the table we find that the probability that he will survive is represented by the fraction Multiplying $1000 by that fraction, we find that the risk is $S6•.92. if we discount this amount at compound discount for twenty years, we have the present value of the risk. or the single ad vance premium equivalent to the risk. At 4 per cent. discount the result would he $393.82. To find the net animal level premium for the en dowment. divide this single premium by the pres ent value of the promise at age ten to pay $1 al lllll ally for twenty years contingent on sur VIving. The promise to pay $1000 if the insured dies before the end of the period is an insnranee eontract, for which the net single premium pay able in advanee, ascertained according to the method already described, is $92.75. This pre mium covers the chance of dying, as the endow ment premium covers the chance of surviving. The net single premium for the endowment life insurance policy is therefore $393.82 plus $92.75. or $4$6.57. The net annual level premium will be found by dividing this amount by the present value of the contingent promise to pay $1 an nually for twenty years from age ten.
Limited-payment life policies grant insurance for life in return for a limited number of annual payments. The net single premium for such a policy might be ascertained by computhig the present value of the risk assumed by the com pany as in the ease of whole-life insurance, and the level annual premium might be ascertained by dividing this amount by the present value of the premiise to pay $1 for a stated number of years of living. Or the risk may he divided into two parts, term insurance while the payments are going on, and life insurance after the end of the period of payments. The single premium for the term insuranee would be found ill the way already described. The single premium for the life insurance would then be found by calculating the single premium necessary to pay for an en dowment to come due at the end of the limited payment period and to be large enough to eon stitute a single premium for whole-life insurance at the age which the insured will then have reached. hi whatever way the single premium
is determined, the level premimn will be ascer tained by the usual method.
Keen competition for new business has led life insurance companies to devise a bewildering va riety of pnlivies, emInslying many different ods of settlement. It is unnecessary, however, to eons ider in detail these different forms. How ever complieated they may be. they are all ca pable of being analyzed in such a way that the net premiums may he ascertained by the appli eat ion of the same principles. namely, probability and discount. If different companies use the same table of mortality and the same rate of diseount. they must adopt what are essentially the same net premium rates. One form of policy may be better suited to the peculiar needs of the insured than another. but the apparent ceonornic advantage of one form over another is purely Lo.tmxo. In the matter of loading. however. there is room for great diversity. The loading is the addition to the net premium which is in tended to cover contingencies and expenses of management. The contingencies to be prepared for are a rate of mortality in excess of that in dicated by the mortality table in use, and a rate of interest below that assumed in discounting fu ture payments. Preparation to meet these con tingencies alone would require but a small addi tion to the net premium in the form of loading. The larger part of the loading is for the purpose of meeting the expenses of management. The loading varies greatly in different kinds of poli cies. Where natural premium rates are used it is commonly per cent, of the net premium plus $4 per $1000. Gil term policies of all kinds it is per cent.; on whole-life policies it varies from 25 per cent. to 40 per cent., while for the endowment policy it is commonly 20 per cent. to 25 per cent. Of the gross premium, therefore, from 16% per cent. to 30 per cent, is loading.
It is difficult for an outsider to discuss intel ligently in detail the expenses of life-insurance companies, but that they are excessive is the unani lllll us testimony of disinterested investiga tors. Greater expenses mean higher premiums, and higher premiums mean a smaller number of insured and a larger proportion of lapses and sur renders. The effort to secure new business leads to the adoption of more and more costly methods of solicitation rather Ilan to a reliance on the attractive powers of ton premiums. The item of commissions to agents represents over a half of the entire cost of management of the life-insur ance business. In the first year of a policy the commissions encroach heavily on the net pre mium; for while the loading is from 16 per cent. to 20 per cent. of the gross premium, the cony mission to the *gent is on the average more than 50 per cent. of the gross premium. The cost of the agency system is not confined to the com missions paid to the agents. Allowance must be made for the extra-hazardous risks foisted upon the company through the desire of the agents for commissions, and for the enormous number of lapses by persons who either do not need insur ance or cannot afford to carry it, but are induced to take it out through the persistence of the solicitors. More than one-half of the lapses oe cu• before the second premium is paid. and ac cording tee the testimony of the eompanies them selves every such lapse represents a net loss to the company.