38 UNIVERSITY OF COLORADO STUDIES 



the problem as simple as possible — that we assume that each member 

 of our company will maintain his membership during his entire hfetime, 

 and that no new members will be added after the date of organization. 



The 81,822 members of our company will all die within the next 61 

 years, making a total ultimately to be paid of $81,822,000. This enor- 

 mous sum is to come entirely from the premiums that are to be paid by 

 the members and the interest which these premiums will earn. The 

 problem is to determine how large a premium each member must pay 

 in order to create a fund sufficient for this purpose. 



It is not known how long any particular member of our company 

 will live. The amount that each member should pay, therefore, cannot 

 be determined by means of a computation based on a single life. But 

 if it is not known how long any one individual will live, it is known how 

 long certain groups of members will live. For example, the mortahty 

 table shows at age 35 that 732 members will live only i year, 746, 2 years; 

 812 will live 10 years to age 45; 1,143, 20 years to age 55; and that 3 

 will hve 61 years to age 96. The computations must therefore be based 

 upon the aggregate number of lives, the length of time the members 

 will live as a body, as shown in case of these several groups. Although 

 it is customary to pay immediately upon proof of death, it is here assumed, 

 for the sake of simphcity, that payment is made at the end of the year in 

 which the deaths occur. 



Since 732 die the first year, the company will have to pay out $732,000 

 at the end of the year. It is not necessary, however, to have the full 

 sum on hand at the beginning of the year. The present worth of $732,- 

 000 is $707,258.40; that is to say, if one invests $707,258.40 at 3I per 

 cent, interest, it will amount to $732,000 in one year. Similarly, since 

 737 die during the second year, the additional liability of the company 

 at the end of the second year is $737,000. Now, if $694,693.18 is 

 invested at 3J per cent, for two years, it will accumulate to $737,000 — 

 the amount of the second year's death claims. 



The following table shows how this method is applied up to the end 

 of the mortality table. In the third column the present values of the 

 losses (shown in the second column) are given. The fourth column 

 contains the formula by means of which the third column is computed. 



