232 
LIFE ASSURANCES. " 
For the annual premium we have 
.02913= . 140G3—.02913=. 11150=annualprem. for ¿£l; 
7.1108 
therefore . 11150 X 400=44.600=£44 12 0=annual prem. required. 
Example. Required the single and annual premium for the insur 
ance of ¿£400 on the death of the survivor of three lives aged 38, 45, 
and 64. (Northampton 3 per cent.) 
15.2975=value of ¿£l per annum on a life aged 38, Table 7, 
13.6920= do. do. do. 45, 
8.6115= do. 
6.1108= do. 
43.7118 
do. do. 64, 
by last example on three joint lives 
aged 38, 45, and 64. 
m a nor _ J va l ue °f £l per annum on two joint lives aged 38 and 45, 
10.4026 | Tables, 
7.3152= do. do. do. 38 and 64, 
7.0536= do. do. do. 45 and 64, 
24.7714 
43.7118 — 24. 7714=18.9404=value of £l per annum on the sur 
vivor of three lives aged 38, 45, and 64 (page 222) 
1—(19.9404 X .029126) = !— .58077=.41923=single prem.for £l 
.41923 x400=167.692=£l67 13 lOszsinglepremium required. 
For the annual premium we have 
— .02913=.05015— .02913=.02102=ann. prem. for £l, 
19.9404 1 ’ 
.02102X400 = 8.408=i£8 8 2= annual premium required. 
TEMPORARY ASSURANCES. 
Find the present value of £l at the end of the term subject to the 
existence of the life or lives, subtract it from unity, and multiply the 
difference by the present value of £l due at the end of one year; from 
the result subtract the present value of ¿£l per annum on the life or 
lives for the term, multiplied by the difference between unity and the 
present value of £l due at the end of a year. 
Or, When the assurance is on a single life, divide the difference be 
tween the numbers in column M at the present age, and at the age which 
he would attain on surviving the term of assurance by the number in 
column D at the present age. 
To find the annual premium: 
Find the present value of the expectation of receiving ¿£l at the end 
of the terra, subject to the existence of the lives; subtract it from unity,