234 
LIFE ASSURANCES. 
For the annual premium, 
*77 738 
"= .01132=annual premium for assurance of £l for 7 years, 
300 
3.396 = £3 7 11 do. l £300. 
6866.398 
ASSURANCE ON ONE LIFE AGAINST ANOTHER. 
To find the single premium to secure a sum payable on the death of 
A, provided he die before B : 
First, find the present value of an assurance of £l on the two joint 
lives, then find by the tables the value of an annuity of £1 on two joint 
lives, one a year younger than A, the other of the age of B, and divide 
it by the probability of a life one year younger than A living one year; 
add the result to the present value of the assurance of £l on the joint 
lives. 
Then subtract the value of an annuity of £1 on the two joint lives, 
one the age of A, the other one year younger than B, divided by the 
chance of a life one year younger than B living one year. 
The difference divided by two will be the value of an assurance of £1 
on the death of A, provided he die before B. 
The annual premium is found by dividing the single premium by the 
value of an annuity of £l on the joint lives of A and B increased by 
unity. 
Example, What single and annual premium should be charged to 
insure £500 on the death of a person aged 38, provided another aged 
43, survive him? (Northampton 3 per cent.) 
10.6349 value of annuity at 38.43, 
♦ 
10.7170= do. 
37.43, 
10.7438= do. 
38.43. 
.029126 
Table 5, age 37, 1.019810 
Table 5, age 42, 
1.022910 
9436.11 
0717.01 
8347.01 
29126 
1019810 
1022910 
2913 
71387 
71604 
1747 
1020 
4092 
87 
713 
307 
12 
10.92930 
82 
2 
10.98995 
.33887 
11.6349)150.120(12.903=£12 18 
.66113 
116349 
ann. prem. 
10.92930 
33771 
11.59043 
23270 
10.98995 
10501 
2).60048 
10471 
.30024 
.30 
005 
150,120“ 
:£150 2 5 single premium.