ANNUITIES. 



certainty, thai is, it must be. multipl'ii d 

 f>y the probability that the given life will 



sun-ive one year, or supposing -to ex- 

 press this probability, it will be X 



lUx" 



The values of annuities on the joint conti- 

 nuance of two lives are found by reason- 

 ing in a similar manner; and such values, 

 both for single and joint lives, are given 

 in the following tables. 



TABLK DI. 



Shewing the value of an annuity of 11. 

 on a single life, at every age, acconing 

 to the probabilities of the duration of 

 life ut Northampton, reckoning intertst 

 at 5 per cent, per annum. 



The values in this and the following- 

 tables suppose the payments to be math: 

 yearly, and to begin at the end of a year ; 

 but if all the payments are to be lull 

 yearly payments, and to be made at the 

 end of every half year from the time of 

 purchase, the value will be increased 

 about one-fifth of a year's purchase. 



The above table is formed from the pro- 

 babilities of life, as deduced from the re- 

 gister of mortality at Northampton for 46 

 years, from 1735 to 1780 ; and as it gives 

 the mean values of lives between the 

 highest and lowest, it is better adapted 

 for general use than any other extant. It 

 has of late years been generally adopted 

 for calculating the rates of assurance on 

 lives, and is well suited to this purpose ; 

 but it is by no means a proper table for 

 individuals or societies to grant life annui- 

 ties from ; for having been formed from a 

 register comprehending persons of all 

 ages and conditions, it cannot give a cor- 

 rect representation of the duration and 

 value of such lives as usually form a body 

 of annuitants, such persons being gene- 

 rally a selection of the best lives from the 

 common mass, the interest of every per- 

 son who purchases an annuity on any life 

 requiring that he should take care that it 

 is a good life. The best table for regula- 

 ting the grant of life annuities is that 

 formed from the table of mortality pub- 

 lished by Mr. D. Parcieux, from the lists 

 of the French tontines, but even this ta- 

 ble gives the values of the advanced ages 

 considerably too low. 



