141. We have just supposed n + 1 annual payments to be made to 
secure the deferred annuity: if we suppose only n payments we shall 
have 
l-f^cm) : l :: a 
(m) • 
1“ l+« (m ). 
N. 
N, 
or 
D„ 
: i:: 
N. 
D,„ * N m _ v - N. 
Examples. 
1. Required the present value of an annuity of £30, to he entered 
upon at the expiration of nine years, and then to continue during the life 
of an individual aged 36. (Carlisle 4 per cent.) 
14.1046