PRACTICAL RULES AND EXAMPLES. 
221 
N m _! + R m+ „+ n. M MU — N„ 1+ „_ 1 R, 
Tlie annual premium to assure £l and a return of all the premiums 
paid will be 
M m 
Suppose an assurance of £T to be provided for by payments at the 
beginning of each year, the premiums being diminished at the end of 
every successive year by the nth part of the first premium, so that after 
n payments they shall altogether cease, the first premium will be 
1 
71 
PRACTICAL RULES AND EXAMPLES, 
To find the value of an annuity on single and joint lives; 
Find in the table the present value of £l per annum at the given 
age and rate per cent, and multiply by the annuity whose value is 
required. 
Example. What is the present value of an annuity of £70 on a life 
aged 36, according to the Carlisle rate of mortality, when 6 per cent 
interest is allowed ? 
In Table 21, under 6 per cent opposite the age 36, we find 12.465 
which, multiplied by . . . . . 70 
gives 872.550= 
£872 11 
When the annuity is payable half-yearly, add .25 to the number of 
years’ purchase in the table; when payable quarterly, add .375. 
In the above example, if the annuity be payable half-yearly, the value 
will be 12.715x70 = 896.05 = 890 1 0; if payable quarterly, the 
value will be 12.840 x 70=898.80 = £898 16 0. 
Example. What is the present value of an annuity of £40 payable 
during the joint existence of two lives aged 35 and 40? (Northamp 
ton 3 per cent.) 
In Table 8, look for younger age 35, and opposite to 40 j ^ 0134 
we have 
which, multiplied by 
40 
gives 448.536= 
£448 10 9