172 
LIFE ASSURANCES. 
To find the annual premium payable during the whole terra of life. 
By Davies’s method— 
M m+< _ M 55 _ 248.22116 
D m D 48 688.0125 
-.= 144. 300=£144 6 0 single prern. 
To find the annual premium. 
! y 4on 
9921.4104-5193.9145 
¿£24.056 =¿£24 1 1, the annual pre- 
mium payable during the term the assurance is deferred. 
¿£I0.008=£10 0 2 = 
the annual premium payable during the whole term of life. 
SURVIVORSHIP ASSURANCES. 
213. To determine the present value of £l to be received at the end 
of the year wherein a life aged m may fail, provided that life be sur 
vived by another aged m x . 
By Art. 118, the probability of this event happening in the nth 
year is 
mil»—1 Pm\, n ) '—2 Ohm, mi), n—1 P(m,m{),n Pm,n 
-\rp m 9 n—l xp mj>n ) 
and 
Cp(m, mj), n—l P(m iWj),« Pm, n X pmi, n — l -f P m,n—i XPmy.n) 
is the present value of the assurance. 
By Art. 181, 2>” Pirn.md.n) is the present value of an 
assurance payable on the failure of the joint existence of the lives 
(A m , mi ), and 
2 ? ’Pm, n X Pm x , 
^m-f-1 • ^f ^ 
c 
and since 
¿m+l 1 -, 
——, we have 
m 
a m+1, mi 
J.r n .p m>n Xp, 
— -j~r (l+o mTl , m .) ; 
and