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