DEFERRED ASSURANCES. 215 
The single premium for an assurance for n years on the longest of two 
lives aged m and m x is 
A 
(m, m\) 
-^-(mi) r " A ^ 
ni nl 
the annual premium is 
(w, mj) 
nl 
An+n 
An 
Ci+n 
Anj / 
jr B +a ( 
Anj + tt 
^1+” \ 
^mi 
An 
'i y 
An+n . AnjHf-r 
+ 
v m v m j 
, mj) 
«1 
or, 
+ 
I I 'm4-ti , Ani+n bm-\-n \ „ . . 
! 7 i 7 "J * “7 1 ^ ^(m) ”1" ^(w, w^) 
4n+n ^ 
— (1-r). 
DEFERRED ASSURANCES. 
The single premium for air assurance on a life aged m, to be entered 
upon at the expiration of n years is 
¿C) = r . -J±-r"— (1 —r) . 
In 
r 7* • Cl m .|- n , 
nt]’ ! ( 
^m+n n t 
C. ■ 
m+n 5 
or 
M 
m-\-n 
D m ’ 
D m+n -(l-r)N„ 
D„, 
the annual premium for the same payable n years at the commencement 
of each year is 
iyr •: 
TVX m _(. w ■ 
,5 
l (m) 
Bln 
L 
1-f-r». +«„ 
I'm. 
(1 O hi,„_[_ n _i 
or ; 
N m _! N,n-|-n-I 
the annual premium for the whole term of life is 
l oo 
1 + a m ’ 
N ’ 
Dm+l— (1 -Q 
l^m-1 
The single premium for an assurance on two joint lives aged[m and 
s 
-n. 
m ( , to commence at the end of n years is 
A 
(rn, mi) 
r i-m+n ' 4n t +n ÇY ¡.^ im + n , *”»!+” „,11 
l m ¿rn l> 
^ * ^m+n» mj+n 9 
or 
An+W n A 
‘ • ¿Im+ii, mi+n 9 
I'm ^mi 
the annual premium for the same payable n years at the commence 
raent of each year is