DEFERRED ASSURANCES. 
171 
To find the single premium. 
208. (1) Multiply the present value of £l due at the end of one more 
than the number of years for which the insurance is deferred, by the 
chance of the life or lives surviving the number of years deferred, and 
subtract from this the product found by multiplying the value of a 
deferred annuity for the same term, by the difference between unity and 
the present value of £l due at the end of a year. 
209. (2) Divide the number in column M opposite the age the life 
will attain when the assurance commences, by the number in column 
D opposite the present age. 
210. (3) Find the value of an assurance for the whole period of exist 
ence on lives as many years older than the given lives as the assurance 
is deferred, multiply it by the present value of £l due the number of 
years deferred and by the probability of the lives surviving that period. 
211. To find the annual premium. 
When the premium is payable only during the term the assurance 
is deferred, the divisor is the same as for a temporary assurance; but 
if the premium be payable during the whole term of life, the divisor is 
the value of the annuity on the life increased by unity. 
212. By Davies’s Tables. 
When the premium is payable during the term of deferment, divide 
the number in column M opposite the present age increased by the 
number of years deferred, by the difference between the number in 
column N opposite the age one year younger than the present, and the 
number in the same column opposite the present age increased by one 
less than the number of years the insurance is deferred. 
When the premium is payable during the whole term of life, divide 
the same quantity by the number in column N opposite the age one 
year younger than the present. 
Example. What single and annual premium should be paid to 
secure the payment of £400 on the death of a person aged 48, provided 
that event take place after the expiration of 7 years? (Carlisle 4 per 
cent.) 
r t+l p m>t —{\—r)a inC) =/%. 7 -(l-r)a ( 48 ) , 
p v 
r B p w .7~r'Xr 1 p iS ' 7 =. 
(1 - r)a m ^ =. 
or thus : 
961538 X.68462= 
038462x7.7359: 
;. 658288 See Ex. 1. Temp. Ass ces - 
:. 297537 do. 
.360751 
400 
A 55 x400: 
144.3004 =¿£144 6 
.759918x4073X.526938 
= .36075X400: 
4521 
: 144.300. 
X 400 
To find the annual premium payable until the 
144. 3000 
1 ~"r 7 piB.f+-(lç iB ) 
144.300 
5.9986 
=24.056=^24 
F 
assurance commences. 
1. (Ex. 5, page 169.)