LIFE INSURANCE. 228 LIFE INSURANCE. What risk does a company assume which promises a hoy of ten that if he is alive at age thirty it will pay him .$1000? From the table we liiid that the probability that he will survive is represented by the fraction /."oVo- Multiplying .$1000 by that fraction, we find that the risk is .$802.92. If we discount this amount at compound discount for twenty years, we )iave the present value of the risk, or the single ad- vance priMiiiuni ecjuivalent to the risk. At 4 per cent, discount the result would lie .$:i!l3.82. To find the net annual level premium for the en- dowment, divide this single premium by the pres- ent value of the promise at age ten to pay .$1 annually for twenty years ecmlingent on sur- viving. " The promise to pay ,$1000 if the insured dies before the end of the period is an insurance contract, for which the net single premium pay- able in advance, ascertained according to the method already described, is .$02.7."). 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 $3!l.'?.82 plus .$!»2.7.i, or .$48ti.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 fur life in return for a limited number of annual payments. The net single premium for such a policy might be a.scertained by computing the present value of the risk assumed by the com- pany as in the case of whole-life insurance, and the level annual iiremium might be ascertained by dividing this amount by the present value of the promise to pay $1 for a staled number of years of living. Or the risk may be 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 insurance woidd be found in the way already described. The single premiimi 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 con- stitute a single premium for whole-life insurance nt the age which the insured will then have reachetl. In whatever way the single premium is detennined. the level premium will be ascer- tained by the usual method. Keen ccmipetiticm for new business has led life- insurance companies to devise a bewildering va- riety of policies, embodying many dilferent niethj ods of settlement. It is unnecessary, however, to consider in detail these different forms. How- ever complicated 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- cation of the same principles, namely, probability and discount. If different companies use the same table of mortality and the same rate of discount, 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 economic advantage of one form over another is purely illusory. T.OADlN'fi. Tn 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- 1 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 purjiose of meeting the expenses of managi'ment. The loading varies greatly in dilVerent kinds of poli- cies. Where natural premium rates are u.sed it is conunonly 33 'ij per cent, of the net j)remium plus .$4 per $1000. On term policies of all kinds it is 33V;t i)er cent.; on whole-life policies it varies from 25 per cent, to 40 per cent., while for the endowment policy it is commonly 20 y>CT cent, to 2.5 per cent. Of the gross premium, therefore, from 10% per cent, to 30 per cent, is loading. It is dillicult for an outsider to discuss intel- ligently in detail the expenses of life-insurance companies, but that they are excessive is the unanimous testimony of disinterested investiga- tors. Greater expenses mean higher premiums, and higher premiums mean a smaller lunnber of insured and a larger proportion of lapses and sur- renders. The effort to secure new business leads to the ado))tion of more and more costly methods of solicitation rather Uian to a reliance on the attractive powers of low 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 Hi per cent, to 20 per cent, of the gross premium, the com- mission to the agent is on the average more than fjO per cent, of the gross [iremium. The cost of the agency systexn is not conlined to the com- missions ])aid to the agents. Allowance must be made for the extra-hazardous risks foisted upon the comjiany 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 atTord to carry it, hut arc induced to take it out through the persistence of the solicitors. More than one-half of the lapses oc- cur before the second premium is ])aid. and ac- cording to the testimony of the eom])anies them- selves every such lapse represents a net loss to the cimipany. Medical Examination. The early mortality tables were constructed on the basis of the mor- tality of the general population. In the absence of restrictions it is obvious th^t insurance com- panies would suffer from an unfavorable selec- tion of risks. Tlie unhealthy and the weak would seek the benefits of insurance, while the strong and healthy would make comparatively little use of it. Under such conditions the mortality of the members of an insurance company could not safe- ly be inferred from the mortality of the general population. To avoid such unfavorable selection, insurance companies endeavor to limit their operations to persons of average expectation of life, and to bar out those below the average. In the beginning, therefore, insured lives are a selected class, and might be expected to show a death-rate considerably below the average for the general pnpvilation. It is commonly claimed, however, that through the tendency of the strong- er to surrender their insurance readily and of the weaker to keep theirs up as long as possible,
