124
LIFE ANNUITIES.
at any ages of the same difference as that for which the various products
have been found may be obtained by dividing the sum of the products
above the ages, by the products opposite to them.
129. If, previous to calculating the values of annuities on joint lives,
calculations have been made of the values on single lives, the products
opposite each age in the D column for the single lives will form part of
the operation in finding the products for the joint lives.
130. When one life is a male and the other a female, and the rate of
mortality distinguishes the sexes, the number of living at the age of the
male must be taken from the table of mortality amongst males, and the
living at the age of the female from the table of mortality amongst
females.
Or, when there is no difference of sex, but it is thought proper to
use different rates of mortality for the two lives, the number of living at
the age of each of the individuals must be taken, in forming the products,
from the corresponding rate of mortality.
131. The following calculation of the value of an annuity during the
joint existence of a male aged 85 and a female aged 90, will illustrate
what has been said, and show the methods by which the values in
Table 23 were calculated (Chester 5 per cent) :
r m xtoo xtT= • 00760049 x 23 X 126 = 22.03782
r" x4o Xl ai - .00798471 X 30x158= 37.84753
?' 98 x4a X/ 93 =. 00838395 x 37 x190= 58.93918
r 97 X l a7 Xl 92 = .00880315 x 44x221= 85,60183
r 96 X/ 9C X/ 9l =.00924331 x 51 x252= 118.79502
323.22138"
r M X/95 x4o=.00970547 X 68x283= 186.77208
r 9 ‘ x4* x/ C9 — .01019074 x 92X313= 293.45255
» 93 X4a x/ U8 =.01070028x 116x343= 425.7426
r 92 x4* X4?=-01123530x146x384= 629.8959
r 01 X 4i X4e=.01179706x176x436= 905.2590
2764.3435
r 90 x4o X 4;= -01238691 X205 X 510 = 1295.0517.
^00.95 —
°85.90 —
323.22138
186.77208
2764.3435
1295.0517
1.731
132. The principle laid down for calculating annuities on two joint
lives applies to finding the values on any number of joint lives: if the
values were calculated on three lives when the differences of the ages
are 5 and 1, the number in the D column opposite the ages 16, 21, and
22, would be equal to the product of the number of living at 21 and 22