194 
LIFE ASSURANCES. 
of the year immediately after the payment of the premium is £83 6 9, 
and that at the end of the year just before the next payment becomes 
due, the value is reduced to £68 9 6, owing to the risk the office has 
incurred during the interval between the two periods. 
If the value of the policy were required when the policy has been in 
force 5 years and 7 months, we must find the diminution in the value 
at the end of the year, and multiply it by that portion of the year which 
has lapsed since the payment of the premium, and subtract the result 
from the value at the beginning of the year, thus : 
83 6 9 
68 9 6 
14 17 3 
83 6 9 
8 13 5 
74 13 4 value at the end of 5 years 7 months. 
7 
12)104 0 9 
8 13 5 
INCREASING AND DECREASING SCALES OF PREMIUMS. 
257. Suppose the annual premium to increase or decrease a certain 
sum every t years, and at the end of v intervals of t years each, the 
premium to continue constant during the remainder of life. What 
annual premium should be required during the first t years P 
Let the annual premium required, 
q— the increase or decrease per £l every t years. 
p(l“h®m)db Q 4'#(m) 4" 4” ) 
v 1<-1 12<-1 13<-1 1d<-1 7 
by transposition and division, 
14"®m 
By substitution in the first equation, 
from which we obtain 
+ q (N m+< ! +N, 
4“ —x 4* •••••• • 4“ 
Example. What annual premium should be required during the 
first 5 years to insure ¿£100 on a life aged 31, the annual premium to 
increase 4s. every 5 years, and remain constant at the end of 20 years? 
(Carlisle 4 per cent.)