TEMPORARY ASSURANCES. 
233 
and divide the difference by the difference increased by the value of £l 
per annum for the term on the given lives; from the quotient take the 
difference between unity and the present value of <£1 due at the end of 
one year. 
When there is only one life 
Divide the difference between the numbers in column M at the present 
age, and at the age which the party would attain on surviving the term 
of the assurance, by the difference between the numbers in column N 
at ages respectively one year younger than taken for column M. 
Example 1. What is the present value of an assurance of £200 
for seven years on a life aged 36 ? (Northampton 3 per cent.) 
Table 1, living at 36—3935, living at 43=3404, 
Table 4, Part 1, the present value of £l due 7 years = .813092 
do. do. 1 year =.970874 
3404 
“ «865057 = expectation of life surviving seven years, 
.865057 X .813092=: .703371=value of expectation of receiving £l 
at the end of the term, 
1- .703351 = .296649, 
.296649X .970874=.2880087, 
By Table 7, the value of £l per annum on a life aged 36=15.7288 
do. do. 43=14.1626 
15.7288—(14.1626x .70337l) = 15.7288—9.9616=5.7672= 
value of temporary annuity for seven years, 
. 2880087 - (. 029126 x 5.7672) =. 2880087- . 167975= • 120034 = 
single premium for assurance of £l, 
. 120034 X 200=24.0068=£24 0 2=single premium required. 
•296649 _ .296649 
.296649 + 5.7672 6.0638 
.02913= 
.04892 — .02913= .0l979=annual prem. for assurance of £l, 
.01979x200 —3.958= £3 19 2 do. £200. 
Example 2, Required the single and annual premium for an assur 
ance of £300 for 6 years on a life aged 36. (Carlisle 4 per cent.) 
Number in col. M at 36= 454.802 
do. 42= 377.064 
do. in col. D at 36 = 1293.150 
Number in col. N at 35 = 21797.041 
do. 41 = 14930.643 
6866.398 
454.802—377.064 77.738 
1293.150 “ 1293.150 
. 06012=single premium for assur- 
ance of £l, 
• 06012 x300= IS.036 = £18 0 9 single premium for £300.