40 



UNIVERSITY OF COLORADO STUDIES 



of this calculation, but shall content myself with a statement of the 

 principles involved and the result obtained. The net single premium 

 of $370.55 is worth more than 20 premiums of $18.53 each, although 



^^—^ = 18.53. The reasons for this are easily seen. Suppose two 



men, A and B, each 35 years of age, take out pohcies for $1,000; A 

 paying in 20 premiums and B in a single premium. Let us compare the 

 accumulations on these pohcies after the expiration of twenty years. 

 Suppose the company charges A (erroneously) the net sum of $18.53 

 per year. His first $18.53 would therefore be invested for 20 years, 

 the last $18. 53 for only i year. The second $18. 53 would be invested 

 19 years, the next to last $18. 53 for only 2 years. Thus on the average 

 the company has the use of A's $370.55 for loj years. It has the use 

 of B's net single premium of $370. 55 for 20 years, however. Clearly, then, 

 on account of the difference in interest accumulations, $18.53 P^^^ V^^^ 

 for 20 years is not equivalent to $370 . 55 paid in a lump sum, in advance. 



Moreover, some of those whose pohcies are on the 20-pay plan will 

 die before the expiration of the 20 years, and a certain number of pre- 

 miums will thus be lost to the company; and this loss, as well as the one 

 mentioned above, must be counterbalanced by an extra charge to the 

 survivors. 



Calculations based on these two principles show that a single payment 

 of $370.55 is equivalent to a promise, made by a man 35 years of age, to 

 pay $27 per year for 20 years. Thus the net value of a 20-pay Ufe pohcy 

 at age 35 is $27 (in round numbers). 



In the second column of Table III I give the net annual premiums, 

 at five-year intervals, for the ages 25 to 40. In the third column are 

 given the gross premiums, ' for the same ages. 



TABLE III 



These gross premiums, differing slightly with the variotis companies, are necessarily only approximate. 



