INCREASING AND DECREASING ASSURANCES. 
205 
■N»n—1 N'/n+M — 1 
commencing at ¿£'1000, and diminishing <£20 each year until death. 
(Northampton 3 per cent.) 
(a+p)M w — 1020 M 60 —20,R 60 
Urn -Deo 
M 60 = 237.3317 
0201 
2373317 
47466 
242078,3 
56045.6 
11«,= 2802.281 
20 
56045.62 
D 60 =345.916) 186032.7(537.798 =£537 16 0= single 
1729580 premium 
130747~ 
103775 
26972 
24214 
- 2758 
2421 
337 
311 
26 
N M = 3728.068) 186032.7(49.900=£49 18 0 = annual prem. 
1491227 
369100 
335525 
33575 
33552 
23~ 
267. Required the annual premium to secure a sum at the end of n 
years, should a life now aged m live so long, or the return of all the 
premiums in case he should die before that time. 
Suppose £l the sum to be secured, and p the annual premium re 
quired; the risk in addition to that of paying the £1, will be an assur 
ance for ii years, commencing at £p and increasing £p each year, the 
annual premium for which (Art. 266,) added to the annual premium 
to secure £l will he 
V (R M —R,, 1+ n—M m+K ) + D w +n. 
N —N * 
x ' VI —1 Wl+7*—1 
and by the conditions this expression must be equal to ¡p, viz., 
V (R;,i R m + n —^*M m+n ) -f" U m 4-n ___