The premium must always be fixed in advance. The calculations for determining the premiums on different kinds of insurance policies are many and complex, but all conform to a few general principles. The three factors assumed are an average mortality table, a rate of interest (or yield on investments), and an expense rate in proportion to the premiums or outstanding insurance. Insurance on the reserve plan is often called "scientific insurance" because, upon the basis of these assumptions resulting from experience, it makes exact mathematical calculations of the premiums and reserves needed for insurance of any particular kind in respect to age of insured, number of payments, method of paying the beneficiary, and any other conditions. The premium thus fixed is, however, only a maximum, and usually is reduced as the result of conditions more favorable than those assumed. § 11. #The mortality table.# When large numbers of men are taken as a group, a certain proportion of those at each age may be expected to die. A mortality table starts with a group of persons, as 100,000, at a given age, as 10 years, and shows the number who die and the number who survive at each year of age until all are dead. The table most widely used in the United States is the American Experience Table of Mortality, constructed by Sheppard Homans in 1868. The figures of this table, at different years, are given below: Age Number Living Deaths each year Death rate per 1,000 10 100,000 749 7.49 20 92,637 723 7.80 30 84,441 720 8.43 35 81,822 732 8.95 40 78,106 765 9.79 50 69,804 962 13.78 60 57,917 1,546 26.69 70 38,569 2,391 61.99 80 14,474 2,091 144.47 90 847 385 454.54 95 3 3 1,000.00 The actual number of deaths of any group of insured will not correspond exactly with the figures of any mortality table. But this is not an essential defect of a table so long as the figures of the table are approximately correct and are at least as great in the earlier years as the actual mortality. For any excess of premium thus collected but increases the safety of the insurance and reduces later payments. In fact the mortality in nearly all companies in the United States is much below the figures of the American Experience Table, partly because of the influence of medical selection on the recently insured and partly because of the decided improvement in longevity since the table was constructed.