4:30 LIFE INSUKANCE ACTUARIES 1 TABLE continued. AGE. Living. Dying. Chances out of 1,000 of dying in one year. Natural premium to insure $1,000 for one year. 71... 38,510 2,351 70'16 6746 72... 81,159 2,362 75-80 72 89 73. 28,797 2,358 81-88 78 78 74. 26,439 2,339 88-47 85 07 75. 24,100 2,303 95-56 91 89 76. 21,797 2,249 103-18 99 21 77. 19,548 2,179 111-47 107 18 78. 17,369 2.092 120-44 115 81 79. 15,277 1,987 130-06 125 06 80. 13,290 1,866 140-41 135 01 81. 11,424 1,730 151-44 145 61 82. 9,694 1,582 163-19 156 92 83. 8,112 1,427 175-91 169 15 84. 6,685 1,263 189-68 182 88 85. 5,417 1,111 205-10 197 21 86. 4,306 953 222-48 213 92 87. 8,348 811 242-23 232 92 88. 2,537 673 265-27 25507 89. 1,864 545 292-3S 231 14 90. 1,319 427 323-73 811 28 91. 892 822 360-99 847 10 92. 570 231 405-26 889 68 93. 339 155 457-23 439 64 94. 184 95 516-30 496 45 95. . 89 52 534-27 561 80 96. . 37 24 648-65 623 70 97. . 13 9 692-31 665 63 98. . 4 3 750-00 721 15 99. . 1 1 1000-00 96JL 54 It is assumed for the sake of simplicity, both in calculation and practice, that insurable lives of the same age, counting always either from the nearest birthday or the next succeeding birthday, are of the same risk. This assump- tion of course cannot accord with the actual facts, but it accords sufficiently well with our attainable knowledge of the facts ; and to at- tempt a distinct classification on other grounds than age would in some measure defeat the very end of life insurance. The only excep- tion made in practice, to any considerable ex- tent, is, that when individuals are admitted not fairly up to the average standard of health, either an arbitrary extra premium is charged, or the premium is arbitrarily charged which belongs to a more or less advanced age. The natural premiums above given are supposed to be payable at the beginning of the year, and the death claims to be settled at the end of it. Hence the value of the risk, or chance of dying out of a thousand, is discounted a year, and, for the sake of safety, at the low interest of 4 per cent. The policies being all equal, if the deaths should occur out of the persons insured at each age precisely according to the table, and there were no working expenses, and ex- actly 4 per cent, should be realized on the premiums, these natural premiums would ex- actly settle all the death claims at the end of the year, and there would be nothing left. But supposing the policies unequal, and paid for according to amount as well as age, if the assumed interest is realized, any one of three probable events, in the absence of the other two, may make the natural premiums insuffi- cient. The number of deaths may exceed the tabular expectation ; they may not be distrib- uted among the ages according to the tabular expectation ; or the average death claim may exceed the average policy. To guard against these adverse contingencies, as well as to pro- vide for the working expenses, besides the precaution of assuming a rate of interest in all the calculations below that which is expected, it is deemed necessary to add to the net natu- ral premiums, as well as to the artificial ones into which they are commuted, what is called a " loading." It is plain that, if we can rely upon the deaths in a very numerous company being distributed among the ages very nearly according to the above table, and upon bad risks being excluded by the medical officers to such an extent that the aggregate mortality shall much oftener fall below than above that expected, with a proper addition for the ex- penses and the contingencies above named, a mutual insurance company, including all ages and considerable difference in amount of policy, can be safely founded on these natural pre- miums for one year. At the end of the year, if the contracts to pay the ascending scale of premiums extended for many years or for life, there would be nothing bat a stipulation with- out penalty to prevent sound lives from dis- continuing their policies, while the impaired lives would be pretty sure to continue. Here is a moral hazard too great to be incurred in the present state of society. A company so organized would inevitably become bankrupt, unless at the start it exacted of every policy holder, as security for the continuance of the payments, a deposit, to be forfeited in case of discontinuance, sufficient to make the company whole against the loss of its best life. Other objections to an ascending scale of premiums will readily occur. The impracticability of founding a permanent company on the natural ascending scale of premiums led to commu- ting them at the start into single premiums, OP equal annual premiums, payable for a limited number of years or during the whole term of the policy. This was very naturally done by Mr. Simpson and Dr. Price, because in the old unscientific system which they supplanted the payments were equal. The improvement was to make them different for different ages of entry, allowing them still to remain, as before, equal for the successive years of the same age of entry. Thus was at once solved the problem of securing against discontinuance, by the for- feiture of the early excess of the level premi- ums. The security, unfortunately, became too ample as the policy proceeded, even to the ex- tent of keeping it in force after the cessation of the insurable interest. Time had to reveal this defect, which might have been foreseen at first, but was not ; and it will probably take a good deal of time to remove it. Nothing can contrib- ute more to this desirable end than thorough- ly to popularize the method of commuting the net natural ascending into the net equal an- nual premium. Though algebra is very con- venient in this process, it is an entire mistake that it cannot be perfectly understood without
