C 490 ] 
The annuity fecured by land mult necefiarily be of 
greater value than the above ; becaufe, altho’ the an- 
nuitant dies before the payment becomes due, yet his 
heirs are to receive a part thereof; the annuitant, 
therefore, in this cafe, hath not only the probability 
of receiving the firft payment, but he hath alfo an 
expectation upon part of the probability -jg-, which, in 
the firft cafe, was wholly againft him. Now it may 
be efteemed an equal chance (fuppofing him to die 
in the firft year) whether that deceafe happens before 
the expiration of half that year, or after it ; and if 
it happens before, he is to receive lefs than half the 
annual payment; but if after it, more. 
The annuitant may, therefore, be fuppofed to have 
an equal chance, if he fails of receiving the whole 
firft payment, yet of receiving half thereof; and, 
confequently, half of the probability, which was 
before totally againft him, will (in this cafe) be fa- 
vourable to him; and his expectation of receiving 
either the whole, or at lcaft half of the firft payment, 
will be H + fr- 
ill like manner, fince the probability of his dying, 
in the fecond year, is, alfo, fg- ; we may (by arguing 
in the fame manner) prove, that one half thereof will 
(in this cafe) become favourable to him ; and, confe- 
quently, that -jJ + T V will be the probability of his 
receiving the whole, or at lcaft half, of the fecond pay- 
ment. 
It appears, therefore, that, for every year which he 
hath the poffibility of living, he will (in this cafe) 
have the probability ( 7 V or) half of fg- in his favour, 
more than he had in the former cufe ; and therefore, 
if the prefent worths of the conftant fum 7l /. (fup- 
pofed 
2 
