218 ESSAY ON PROBABILITIES. 1 



The premium demanded by an office is that charged 

 by their tables at the age which the party will attain at 

 his next birthday ; thus if a person desire to insure his 

 life the day after he attains 31 years complete, he will 

 be required to pay the same as if he had deferred 

 completing the insurance till the day before his thirty- 

 second birthday. This is, one party with another, a 

 gain of half a year to the office. Thus, the North- 

 ampton table at 3 per cent, giving 16*7 and l6'5 as 

 the values of annuities at the above-mentioned ages, all 

 parties who have passed 31 years at their last birth day 

 are considered as having lives worth 16*5, whereas they 

 are worth, one with another, l6'6. The tables are not 

 sufficiently accurate to make the effect worth caring for. 



A party having made an insurance, and paid one or 

 more premiums, the instrument by which the right to 

 receive the stipulated sum at death on payment of a 

 stipulated premium is conveyed, is called a policy of 

 insurance. The value of this policy is then easily 

 determined ; at least what we may call its office value, 

 supposing the tables of the office to be perfectly correct. 

 A person aged thirty insures for 100/., for which he pays, 

 say 31. ; he continues to pay this premium until the 

 age of fifty, at which time, if he had began to insure, 

 the annual premium would have been, say 51. Suppose 

 that the holder of the policy wishes to sell his interest 

 just before he would otherwise have had to pay another 

 premium, it is plain that he then offers for an in- 

 surance on the life of 50, a better bargain than the 

 office would offer, since the buyer of the policy (who 

 pays all future premiums) will acquire, in consider- 

 ation of an annuity due of 31. upon the life of A, that 

 which the office would not sell for less than an annuity 

 due of 51. upon the same life. The difference, or an 

 annuity due of 2/. upon the same life, is the value of 

 the policy. 



RULE. To find the present value of a policy of insur- 

 ance, at the moment before a premium becomes due, sub- 

 tract the premium which is to be paid from the premium 



