254 ESSAY ON PROBABILITIES. 



45 years hence is small, compared with that of a sum 

 now due, or receivable soon. This last consideration 

 works as follows: When^a percentage comes to be added 

 to the whole present value or to the premium deducible 

 from it, for the security' of the office, that percentage 

 being made upon a much larger sum than the present 

 value just mentioned, a very trifling deduction from 

 the whole additional sum will cover a very serious 

 mistake in the mortality of the older years. For ex- 

 ample, in the Northampton tables, the chance of 

 40 living to 85 is about T / (T , and the present value of 

 11. due in 45 years is about 5*. at 3 per cent. From 

 this it follows that 100/., to be paid if a person aged 40 

 dies after 85, cannot be worth so much as 1'25/. But 

 the present value of the whole insurance is 53*8/. ; and 

 if this be the real value, and 10 per cent, be added for 

 security, then 5'38/. is added; so that if T25/. were 

 considered as added solely for the chances after 85 years, 

 it follows that we might consider ourselves as having 

 allowed for not being able to calculate the chances on 

 old lives within one half, and as having added 8 per 

 cent, to the whole present value besides. Thus, it ap- 

 pears that our comparatively little knowledge of old 

 life, though not unimportant, yet can be made to be of 

 less importance than might have been expected by 

 one who has not considered the matter. Of course, 

 the preceding reasoning must be considered only as 

 addressed to a person to whom, for any thing he sees 

 to the contrary, it is of as much consequence to know 

 the entire law of mortality in the insurance of young 

 lives as of old ones. 



There is one use of the table of old lives, by which 

 an insurance office might make its existence very pro- 

 blematical, to use a gentle term ; namely, by inverting 

 the order of security, and selling guaranteed* benefits, 

 which are to increase with the age of the party, and to 

 be accumulated solely out of his premiums. To take 



* This, of course, does not apply to divisions of profit gained, but to 

 contracts for sums to be accumulated after the date of the engagement. 



