20 BUSINESS OF LIFE INSURANCE

age 10 were to set forth, paying the annual premium alleged to be correct for that age. Assume that interest is earned precisely as expected and that the mortality is just as per the American Experience Table. The premiums are received the first year in advance from 100,000 youths. They are improved at interest for one year; $749,000 in death claims, because of the deaths of 749 of the group, must be paid at the end of the year. The 99,251 survivors pay their second premiums. The fund is again improved at interest for one year, and the 746 deaths which take place that year are paid for. The process is continued until the survivors have reached 95, during which year of age the last of them pass away. If the premiums have been correctly computed, and if the assumptions as to interest and mortality have been exactly realised, there will be just money enough on hand at the end of the year of age, 95, to pay the last claims and nothing left.

This test of adequacy applies to all kinds of premiums and, whether the actuary's processes are easy to understand or difficult, they are, in computing premiums, directed toward bringing out results which will stand this test. If the premiums asked by any company or society are not such that, when worked out in connection with a large group and precisely on the assumptions according to which they are supposed to