VALUATION OF POLICIES
191
Examples.
Required the sum that should he given for an annuity of ¿£50 payable
at the end of each year during the existence of a life, supposing the
purchaser to make 5 per cent interest, and to secure his capital by
effecting an assurance on the life at the rate of £2 8 per cent.
1—p (1 + 0
s—a-—-———■—rr =50.
i+p (1+0
.9748'
1-.024x1.05
50
,0752
.05+. 024x1.05
48.74
= 50x
-.0252
.0752
.05.+.0252
=648.138=£648 2 9.
What annuity payable at the end of each year during the existence of
a given life should be given for £648 2 9, so as to allow the purchaser
5 per cent interest, and the premium for securing his capital by an
assurance, supposing the rate £2 8 0 per cent ?
¿ + p(l + i) .05+.024X 1.05
a— s.
i —p (i +o
648.138
.024x1.05
.0752
648 - 138x 'i 5 - + olf =648 - 138x iiii= £50 -
Required the sum that should be given for an annuity of £50 during
the existence of a given life payable until the day of death, supposing
the purchaser to make 5 per cent interest, and to secure his capital by
effecting an assurance on the life at the rate of £2 8 0 per cent.
1 -P.
if-p
48.88_
.074 “
: 50 X •
1 —.024
:50X
.976
.05+ .024 .074
: 660. 541=¿£660 10 10.
Required the annuity on a given life payable until the day of decease,
that should be allowed for £660 10 10, supposing the purchaser to
obtain 5 per cent, and to secure his capital by an assurance at the rate
of £2 8 0 per cent.
a—s.
i+p _
L ~P ~
:660.541X
48.88
.976
.05+ .024
1 —.024
= ¿£50.
: 660.541X
.074
7976
VALUATION OF LIFE POLICIES.
252. When a policy has been in existence a certain number of years,
it frequently happens that the party possessing it is desirous of dis
posing of his right therein, either to the office in which the assurance
was effected, or to private individuals ; the method of determining the
values of policies will therefore be shown.
Let a sum s have been assured by an individual at the time he was