INCREASING AND DECREASING ASSURANCES. 
207 
M m+B =M 60 = 23*7.3317 
N m+n _ i: =N 59 = 3728.068 
R m = R 40 = 11054.01 
14782.08 
20 
w.M m+n = 4746.634 
N m _,=:N 39 = 17659.528 
R„ l+n =R C0 = 2802.281 
25208.443 
14782.08 
10426.36~)3382.152 ( .3243 
3127908 
40 
254244 12.972=£12 19 5 
208527 
45717 
41705 
"4012 
3128 
.884 
269. If p be the annual premium to insure £a and a return of the 
premiums, the assurance is for a+p in the first instance, and an increase 
of £p each year during life: we have therefore by Art. 266, 
a. M m + p. R m 
« • M m -1- p. R m ”p. N m _ t , 
by transposing, P(N m _ 1 -RJ = a.M„ 1 , 
£a'and a return of all the annual premiums. 
Required the annual premium for the assurance of ¿£100, to he paid 
on the death of a person aged 40, with a return of all the premiums 
paid on the policy. (Northampton 3 per cent.) 
N M _ 1 =N 8B = 17659.528 M 40 “ 599.9792 
R m =R 40 = 11054.01 
100 
6605.52 ) 59997.92 (9.083=^9 1 8 
5944968 
54824 
52844 
1980 
270. Suppose n payments, the first whereof is £l paid immediately, 
and the remaining payments each diminished by the ?ith part of £l 
to be paid at the end of each successive year, we shall then have for 
the present value, £l the sum paid down to he added to the present 
n