INCREASING AND DECREASING ANNUITIES. 201 
13 
Required the present value of an annuity on a life aged 30, com 
mencing at £40 and increasing £5 each year until death. (Northamp 
ton 3 per cent.) 
(a—p) N m +pS m _ (40—5)N 30 +5.S 30 
Dm D 30 
N 30 = 30570.053 
53 
“91710159 
15285027 
1069951.86 
S 30 = 446138.7 
5 
2230693^5 
1069951.9 
D 30 — 1806.562)3300645.4 (1827.031 = 
1806562 ¿£1827 0 8 
,14940834 
’14452496 
488338 
361312 
127026 
126459 
567 
542 
25~ 
Required the present value of an annuity on a life aged 70, com 
mencing at £200, and decreasing £5 each year until death. (North 
ampton 3 per cent.) 
(a+P) N m -p.S m _ 205N 7 q— 5.S 70 
D m “ D 70 
N 70 = 1047.824 
502 
2095648 
52391 
214803.9 
S 70 — 6264.30 
5 
31321.50 
31321.5 
D 70 = 155.598) 183482.4(1179.209=£l 179 4 2 
155598 
27884 4 
123246 
108919] 
14327 
14003 
324 
311