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