for the Valuation of Life-annuities . 115 
fn and the Northampton table of obfervations. There- 
fore, intereft fuppofed at 4 per cent. 
25x0,04 
1,01 
* 15)769=9,072 
1,01 
= 9,199 
The different values, given by thefe theorems, of life* 
annuities payable yearly, half-yearly, and quarterly, fup* 
pofe nothing to be due to an annuitant for that year, 
half-year, or quarter, in which he fliali happen to die. 
If, on the contrary, he is to be entitled to fuch part of the 
annuity as fhall be proportioned to the time which fhall 
happen to intervene between his death and the time 
when the payment immediately preceding his death be- 
came due; or in other words, if the annuity is an annuity 
V 
fecured by land, — muft be added to the firft theorem in 
order to obtain the value of luch an annuity payable 
yearly. And in like manner, — muft be added to the 
fecond theorem to obtain the value of the fame annuity 
payable half-yearly : and ~ to the third theorem, to ob- 
tain its value payable quarterly. 
The value, therefore, in the firft example, of an annuity 
payable yearly on a life aged 36 being 1 3,829 ; its value, 
if fecured by land, or to be enjoyed to the laft moment of 
Q ^ 
life. 
