486 PHILOSOPHICAL TRANSACTIONS. [aKNO J 692-3. 



560 to 7, or 80 to 1 , that he does not die in a year ; because, out of 567 living 

 of 25 years of age, there die no more than 7 in a year, leaving 560 of 26 years 

 old. 



So likewise, for the odds that any person does not die before he attain any 

 proposed age ; take the number of the remaining persons of the age proposed, 

 and divide it by the difference between it and the number of those of the age 

 of the party proposed ; and that shows the odds there is between the chances 

 of the party's living or dying. As for instance, what is the odds that a man of 

 40 lives 7 years ? take the number of persons of 47 years, which in the table is 

 377j and subtract it from the number of persons of 40 years, which is 445, and 

 the difference is 68 ; which shows that the persons dying in that 7 years, are 68, 

 and that it is 377 to 68, or 54^ to 1, that a man of 40 lives 7 years. And the 

 like for any other number of years. 



Use III. But if it be inquired at what number of years it is an even lay that 

 a person of any age shall die, this table readily performs it ; for if the number of 

 persons living of the age proposed be divided in two, it will be found by the table 

 at what year the said number is reduced to half by mortality ; and that is the 

 age, to which it is an even wager, that a person of the age proposed shall arrive 

 before he die. As for instance, a person of 30 years of age is proposed ; the 

 number of that age is 531, the half of which is 265, which number I find to 

 be between 57 and 58 years ; so that a man of 30 may reasonably expect to 

 live between 27 and 28 years. 



Use IV. By what has been said, the price of insurance on lives ought to be 

 regulated, and the difference is discovered between the price of insuring the life 

 of a man of 20 and 50, for instance : it being 100 to 1 that a man of 20 dies 

 not in a year, and only 38 to 1 for a man of 50 years of age. 



Use V. On this depends the valuation of annuities on lives ; for it is plain 

 that the purchaser ought to pay for only such a part of the value of the 

 annuity, as he has chances that he is living ; and this ought to be computed 

 yearly, and the sum of all those yearly values being added together, will 

 amount to the value of the annuity for the life of the person proposed. Now 

 the present value of money payable after a term of years, at any given rate of 

 interest, either may be had from tables already computed, or almost as compen- 

 diously, by the table of logarithms ; for the arithmetical complement of the 

 logarithm of unity and its yearly interest (that is, of 1,06 for 6 per Cent, being 

 9,974694) being multiplied by the number of years proposed, gives the present 

 value of one pound payable after the end of so many years. Then, by the 

 foregoing proposition, it will be, as the number of persons living after that term 

 of years, is to the number dead ; so are the odds that any one person is alive 



