DEFERRED TEMPORARY ANNUITIES. 
137 
By Davies’s formulae— 
hi m-\-d+n *“ 
d: dt - ” k • 
The present value of £l paid down, and of an annuity of ¿61 for 
d years, subject to the existence of a life aged m, is (Art. 139) 
N m _; — N OT+ct 
d~ 
153. If the total number of payments be d, the first of which is paid 
down, the present value will be 
, N m —__ D m -f N m — N m+(i _i N m _! 
+ D m " D m ~ D m 
154. To find the annual premium necessary to secure an annuity for 
ii years, to be entered upon at the expiration of d years, we must divide 
the present value of the deferred annuity by unity added to the present 
value of an annuity for d years, which gives 
(Art. 139) 
-h* m-\-d ~~~ hlm-f-rf-j-n * h; 
D m N m _j—N m+ii N m _!— 
155. When the total number of annual payments is d, w r e divide the 
present value of the deferred annuity by unity added to the present 
value of an annuity for d — 1 years, which gives 
hIm-4-i? D,„ ,n-\-d A 
D,„ Nm+rt-l N m ^_, 
Example. Required the single premium to secure an annuity of ¿650 
for 7 years, to be entered upon at the expiration of 9 years, subject to 
the existence of a life now aged 40. (Carlisle 4 per cent.) 
#(401 >— 
19 
'40 
#49 = 
7 + 9=16 
4458x .702587x 13.15312 
5075 
— 8.11769 
0 (40) 
lia 
/ r la 
6 50« ' 
110 
#56 — 
4000 x.533908 X 10.96607 
5075 
— 4.61467 
3.50302 
50 
£175 3 0 175.1510 
Also, 
N 40+9 —N 40+9+7 _N 49 -N 56 _8580.9492-4878.0207_3702.9285 ; 
D 40 D 40 , “ 1057.0669 ~~ 1057.0669 
3.50302 
50 
175.1510 =£175 3 0