VALUATION OF LIFE POLICIES.' 
193 
Or, Take the difference between the premium which would be 
required at the present age and the premium charged in the policy, 
multiply it by unity added to the value of the annuity at the present 
age of the life in the policy. 
Or, Increase by unity the value of an annuity of £l at the present 
age, and divide the sum by unity added to the present value of an 
annuity of £l at the age when the policy was effected, subtract the 
quotient from unity, and multiply the“difference by the sum assured. 
This rule applies only when the annual premium has been calcu 
lated at the same rate per cent, and by the same table of mortality as 
are used in valuing the policy. 
Example. What is the value of a policy which was effected 5 years 
ago at the Equitable Insurance Office for ¿£500, on a life then aged 55, 
at an annual premium of ¿£26 11 3, supposing the premium just due 
and not paid, and that the value is to be calculated at the same rate as 
the premiums charged at that office, viz., by the Northampton, 3 per 
cent. ? 
s. A m+n ~ 500 [ 1 - (1—r) (1 + a 60 ) } = 500(1 - . 0291262 x 10.7774) = 
500 X.686096 = 343.048 
+ = 26.5625x10.7774 286.273 
56.775 = 
¿£56 15 6, the value required. 
Or thus ;—The annual premium at 60 is £6.3661 per cent (Table 9 3 ) 
p m +n=p*0= 6.3661 X 5=31.8305 
p m =p № =26.5625 
(Pm+n—Pm) (l + «,»+„) = 5.2680X 10.7774 =£56.774= 56 15 6. 
Or thus : 
l-)-ff„ 
: 1 ■ 
10. 7774 
= 1-.88703=. 11297 
1 +a m 12.15 
.11297 X 500=56.485=£56 9 9. 
This value differs a little from the values found before, owing to the 
annual premium charged on the policy not being exactly correct ac 
cording to the Northampton Table. 
255. Suppose the premium, instead of being just due and not paid, to 
have been just paid, we must in that case add the amount of the pre 
mium to the value just found, to obtain the value. 
£56 15 6+ ¿£26 11 3=£83 6 9. 
Let us now find what will be the value of the same policy just before 
the premium becomes due, when it has been in force another year; that 
is, when it has been in force 6 years. 
By Table 9, 
A 6i x 500=. 694382 x 500=347. 191 
Pm(l + «ai) = 26.5625x 10.4929 =278.716 
68.475 = i £68 9 6. 
256. From these examples it appears that the value at the beginning 
o