[ 2 74 ] 
In the pra&ice of aflufances on the furvivorfhip 
of one life beyond another, there is frequent occafion 
for making fuch affurances, for a term of years only. 
The method of determining the value in fuch cafes 
I have not feen any where defcribed. Perhaps, there- 
fore, a brief account of it here may be of fome 
ufe. 
By reafoning in the fame manner with Mr. Simpfon, 
p. 322, Seledt Exercifes, it will appear, that the value 
of any given fum S affured, for n years on a given 
life A, provided in that time another given life B 
fhould furvive A, is ~x- — - + Scc.fcon- 
tinued to n terms) 4 ^ X ^.4-^4 ( con - 
tinued likewife to n terms) r denoting i /. increafed 
by its interefl for one year ; and a and b , the numbers 
in the table of obfervations alive at the ages of A 
and B, divided by the quotient arifing from dividing 
the fum of the differences in the table from thefe 
value required. But 1 , 
n 2r zr 1 2r 3 
, n — r n — r «■— ' • I * 
petuity ; and f \~ 
2 nr 2 u r 2 >i l r 
, &c. is half the per 
— 2I 
n — 2 ^ n — 2 
2 nr 1 2 nr z 2 » 2 r x 
n — 7 n — 7 n — T) . . .... 
; r— r-, &<*. is halt the value of the joint 
2 nr 3 2 nr 2 nr* 
lives fuhtra&ed from half the fum of the values of the two fino-Ie 
lives ; that is, half the value of the long.-ft of the two lives by 
problem IV. of M. de Moivre’s Treatife on Life Annuities. 
A fimilar demonftration may be ealily applied to the folution of 
the other queftion. 
The beft rules for finding, in all cafes, the values of reverfions 
depending cn furvivorfhips, are Mr. Simpfon’s, in his Sele£t 
Kxercifes, p. 297, &c. 
ages 
O 
