36 university of colorado studies 



§ 2. The Mortality Table 



In this country premiums are computed on the basis of the American 

 Experience MortaHty Table (see p. 37). The table begins, not with 

 birth, but with the age of ten, for two reasons. First, the law of infant 

 death-rate is unknown, and, secondly, it is illegal in most states (Colorado 

 included) to insure children under that age. It was found necessary 

 to pass this law on account of the large number of children who were 

 put to death for the insurance money. 



The fact that out of 81,822 men, age 35, 732 died, is no proof, theo- 

 retically, that 732 will die out of the next 81,822 of the same age. Experi- 

 ence shows, however, that the number will be astonishingly close to this. 

 You will see later that in the computations based on this table, the 

 theoretical net premiums are increased by the so-called loading to allow 

 for an unexpected excess in mortahty. As a matter of fact, the above 

 table is very consen^ative, and the death-rate is not so high as there 

 indicated. Especially during the first five or six years, before the influ- 

 ence of the selection by the prehminary medical examination has dis- 

 appeared, the actual mortahty is a rather small percentage of the tabular 

 mortahty rate. 



§ 3. The Net Single Premium 



To begin with, it will be shown, by a typical example, how hfe insur- 

 ance premiums are computed. The solution is outhned for the age 35, 

 but it will be apparent that the method is perfectly general and can be 

 employed to find the premium at any other age. For the sake of illus- 

 tration, the pohcy is supposed for $1,000; of course, a pohcy for $5,000 

 would cost five times as much, one for $10,000 would cost ten times as 

 much. So that the method about to be given (which is, at bottom, the 

 one actually employed in the construction of the tables for the insurance 

 companies) serves to determine the premium at any age and for any 

 amount. 



Let us suppose that a hfe-insurance company is organized, consisting 

 of 81,822 persons each 35 years of age and each insured for $1,000 

 payable at death. For convenience we take the figures 81,822 as our 

 total membership that being the number of persons still hving at age as 

 given in the mortahty table of § 2. It is also for convenience — to make 



