136
LIFE ANNUITIES.
=14.3812
« 50 =13.0950
27.4762
«45.50 = 9.823
log 17.6532 = 1.2468234
log. ¿ 4 ._] 0 g. / 35 +log r 10 - 1.8004510 as in last example.
— 1.9105034 do.
0.9577778 = 9.0736
50
log l M — log l i0
453. 680 = £453 13'7.'
151. To find the value of a temporary annuity on any number of
lives.
Rule. Find the value of the annuity for the whole term of life, and
of the annuity deferred as many years as the temporary annuity is to
continue ; the difference between them will he the value of the tempo
rary annuity. (Art. 137.)
Example. What is the present value of an annuity of £50 for the
next 10 years, depending on the existence of the joint lives or of the
survivor of two males aged 35 and 40 ? (Chester 3 per cent.)
= 16.9758
= 15.6537
«35
«40
32.. 6295
« 35 ,40 = 12.2160
20.4135
By the last example hut one the value off ^
the deferred annuity is J *
8.4685
50
423.425 =£423 8 6.
DEFERRED TEMPORARY ANNUITIES.
152. Suppose A entitled to an annuity to he entered upon at the
expiration of d years, and then to continue during the existence of a
life now aged m, and B to enter upon a similar annuity at the expiration
of d -j- n years, the difference between the two will be the value of an
annuity to be entered upon at the expiration of d years, and then to
continue n years, subject to the existence of a life now aged m, viz,:
Its value is r d . « m+i