211 
DEFERRED ANNUITIES. 
The value of an annuity to be entered upon at the expiration of n 
years, and continued until the failure of the existence of a life now aged 
m, is 
Hm) 
N / 
“m+n „ 
-jj—> or ——- r". a m+n 
The annual premium payable in n payments, the first to be made 
immediately, is 
L 
N. 
ni-\-n 
"»■+» 
L 
r . a 
m-\-n 
, !m+n „ lm+-n „ 
^ ^ "h I • ? • Cl m \ n 
'm 'm 
The single premium for an annuity on two joint lives aged m and m u 
to be entered upon at the expiration of n years is 
„ ^m+n lm\+n _ 
(m, wij) i * j ? * -n, m\j-n 5 
In in 
L 
which, divided by 
1 - 
i,-fn 
,r n + a m>m — 
'm i v. 
lin+ n l’m\ t n 
.a 
>77-4-77, m^+n J 
will give the annual premium. 
The single premium for an annuity to be entered upon at the expir 
ation of n years, and then to continue until the death of the last sur 
vivor is 
a (m) + ct (m 1 ') a (m, mi) • 
In ]n 1?! 
DEFERRED TEMPORARY ANNUITIES. 
¡The single premium for an annuity to be entered upon at the expira 
tion of d years, and then to continue n years, subject to the existence of 
a life now aged m, is 
l'm+d * f • Orn -•-/! I, 
m+d ^oi+d+it • ^ • ^m+d+n -^m+d+n 
, or 
N„ 
lmei D„. 
The annual premium payable d years at the beginning of each year, is 
■^«7+d ~~ 
N N ’ 
ly m-l ^m+d—l 
or it may be found by dividing the single premium by 
lm+d ,i , lm + d j 
—j ' T a m —— r d .a m+d . 
I'm 
p 2 
i-