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