734 ^^^^ POPULAR SCIENCE MONTHLY. 



Age 94 living, 21 x '52027= contributions $10 92 



Balance 8 52 



Death-claims , 



Balance 



Age 95 living, 3 x 5202'7= contributions, 



Balance 



Death-claims . 



One important element, however, the investment of money at in- 

 terest, has been omitted in the above illustration, and will be intro- 

 duced now. It has already been stated that premiums are payable at 

 the beginning, while death-claims are due at the end, of the same year. 

 To bring these different amounts and dates to a common basis we 

 must determine the 2)i*esent value of each, at the age at which the in- 

 surance begins. Knowing, from the table, the amounts of the contri- 

 butions and the number of deaths and the time at which they become 

 due, it is to be ascertained what amount of money deposited at the 

 beginning of the period, improved at compound interest, would be 

 equivalent to the total of these sums. 



The present value of |1 at the beginning of the year, at 4| per 

 cent, interest, is $0'95G9 ; that is to say, |0*9569 invested at 4^ per 

 cent, interest will amount to $1 at the end of the year. The present 

 value of %l for two years is 10-9157, for three years $0-8763 ; or these 

 amounts, improved at 4^ per cent, compound interest, will become $1 

 by the end of these years. 



Applying this principle to the class of 847 persons under considera- 

 tion, and assuming each contribution and each death-claim to be $1, 

 we need only multiply these by the present value corresponding to 

 each year, bearing in mind that the living pay in advance, while the 

 death-claims are due at the end of the year : 



Age. Living^. Deaths. 



90... 847 X $1 =$847 00 385 x -9569 = $368 41 



91 4G2 X -9569= 442 10 246 x '9157 = 225 26 



92 216 X -9157= 197 79 137 x -8763 = 120 05 



93 79 X -8763= 69 23 58 x "8386 = 48 64 



94 21 X -8386= 17 61 18 x "8025 = 14 44 



95 3x -8025= 2 41 3 x '7679 = 2 30 



$1,576 14 $779 10 



The above calculation shows the present value of the 1,G28 contri- 

 butions, at %\ each, to be $1,570.14, and the present value of the 847 

 death-claims to be $779.10 ; therefore, to meet these latter, the con- 

 tributions need only be, instead of one dollar, yVtW? ^^ ^"^ dollar, or 

 $0*49432 (49 + cents). The item of interest has reduced the premium 

 to $0-49432, when, without it, it would have been $0-52027. 



