[ 4^9 1 
be 36, all but one are favourable, in the fir ft year, 
to any individual ; and, confequently, it is 3 5 to 1 , 
that he receives one payment of the annuity, by living 
till it becomes due 5 that is, the probability of his 
receiving it, is yg, and. that of his not receiving it, y'g-. 
Again j fince, by fuppofition, there dies but one 
perfon in the firft year, and one in the fecond ; there 
are but two chances, in the 36, againft his receiving 
the fecond payment, by living till it becomes due ; 
and, confequently, -fg- will be the probability of his 
receiving that alfo - } the probability of his dying in 
that year being yg-, as before. 
In like manner it may be proved, that the proba- 
bility of his receiving the third, fourth, fifth, &c. 
payment, will be yg-, -^g-, yg-, &c. and therefore, if 
the annual payments were each 1 /. and if the in- 
tereft of money was not to be confidered, we might 
conceive thefe feveral probabilities, as the prefent 
worths of the feveral payments, and the fum of them 
would be the value of an annuity of the firft kind. 
But fince the intereft of money necefiarily enters 
the procefs, and fince the payments become due at 
the end of the firft, fecond, third, &c. year ; there- 
fore the firft of thefe payments muft be difcounted 
for one year, the fecond for two years, the third for 
three years, &c. and the fum of their prefent worths 
will be the value of an annuity of the firft kind, to 
continue during the life of a perfon, who may pofiibly 
live 3 6 years j and this fum may be found by an eafy 
and well-known procefs (from the common tables of 
compound intereft and annuities), which need not be 
inferted here. 
Q^qq 
The 
