190 
LIFE ASSURANCES. 
246. To find the principal. 
If payable at the end of the year, 
¿+2? (1 + i) 
a — s. ——- , from which 
1-Kl + O 
l-p(I-H) 
y = a. ■ 
'i+p (1+0 * 
241. If payable until death, 
1 -p 
s = a.- . 
i + p 
248. To find (0 the rate of interest. 
If payable at the end of the year, 
i+ ®(l + 0 
a ~ 5 -i-Ki+0’ 
By transposition, 
a—ap—api—si+sp+spi. 
i{s+p(s-j-a)}=a—p(s+a), 
. « — p (s+a) 
S+p (5+«) 
249. If the annuity be payable until death, 
i+p 
a=s. , 
1 -P 
a—ap=is+sp, 
. _ a—p{s + a) 
250. To find the annual premium, 
i+p (1+0 
a — ap~ api=si+sp+spi, 
p {j(l + 0 + a(l+0} = a ”"^> 
a — si 
V 
(s+a) (1+0 ' 
251. If the annuity be payable until death, 
i+p 
a=s. , 
1 ~P 
’.a—ap—is + sp, 
p (s+a)=a—ts,