[ 2 7 * ] 
joint lives of 40/.'*) fubtradted from twice 132, (the 
value of a fingle life of 40) that is, 16.58 years 
purchale. And this fubtradted from 25 (the perpe- 
tuity) gives 8.42, which multiplied by 40 gives 
3 36.8 /. the value of the given eftate, were it certainly 
to be enjoyed after the extinction of the longed; of 
two lives both 40 ; that is, whether one or other of 
them failed laft. But that A’s life in particular 
fhould fail laft rather than B’s, is an even chance. 
The true value of the reverfion, therefore, is 4 the 
lad: value, or 168.4/. 
In like manner. The fecond queftion is the fame 
with the queftion. “ What is the prefent value of 
* { 40 /. per arm. for ever, to be entered upon after the 
<£ extinction of two joint lives both 40 ; that is, 
“ whenever either of them fhall fail, provided the 
“ firft that fails fhould happen to be A’s life in par- 
“ ticular?” And the anfwer is found by fubtra&ing 
the prefent value of the two joint lives from the per- 
petuity, and multiplying the remainder by 4, or the 
chance that A in particular fhall die firft 5 and this will 
give the required value, 303 /. 
In fhort, it appears in both thefe cafes, that, ac- 
cording to the firft method of folution, we are to 
fubtradt from the perpetuity the value of one of the 
fingle lives, when, in the former cafe, the value of 
* The value of the two joint lives is here given on M. de 
Moivre’s hypothecs of an equal decrement of life; and it has 
been calculated by a rule in Mr. Simpfon’s treatife on the Doc* 
trine of Annuities and Reverfions, p. 16. M. de Moivre’s rules, 
in the fecond and third problems of his treatife on annuities, 
give the values of joint lives fo much lefs than the truth, 
that they ought never to be ufed. 
the 
