4- 
TEMPORARY ANNUITIES. 
123 
multiplied by the present value of £l due 22 years [hence, multiplied 
by the living at 1G. 
What is the present value of an annuity of £45 5 0 payable during 
the joint lives of two males aged 30 and 35, by the Chester Rate of 
Mortality Table, when the interest of money is 3 per cent ? 
Table 23, ^0.35 = 13.544 =£45 5s. =£45.25 
45.25 
67720 
27088 
67720 
r 54176 
612.86600 =£612 17 4. 
What is the present value of an annuity of £50 payable during the 
joint existence of a male aged 30 and a female aged 40, Chester Rate 
of mortality, 5 per cent ? 
Table 23, a 30 , 40 = 11.109 
50 
"555.45 = £555 9 0. 
What is the annuity that may be purchased for £800 on the joint 
lives of two females aged 45 and 50, Chester 3 per cent ? 
Table 23, a 45 . 50 = 11.5 4 9 
Art. 120. - 8 - 00 - = 69.261 = £69 5 3 
11.549 
DEFERRED AND TEMPORARY ANNUITIES, 
133. Let the value of an annuity deferred n years on a life aged m i 
and then to continue during the remainder of life, be denoted by a ( ^ , 
then the present value of the first payment of the annuity, which is to be 
received at the end of («+ 1) years provided the life shall continue to 
exist until that time, is found by multiplying the present value of ¿£1 
due at the end of (n+1) years by the chance of the life surviving that 
period ; and the present value of any other of the payments is found by 
multiplying the present value of £l due in the number of years that 
must lapse from the present time, until the payment becomes due, by 
the chance the life has at present of surviving that term. 
„ An+n+l r" +l + l m +n+Z rn+ ~~^ L+n+* r " +3 4 - ^nt+n+4 r 1 + & C> 
«(»o Ti - Tm