USE AND CONSTRUCTION OF TABLES.
XXIX
Table XIX. is similar to Table VII.
Table XXL is similar to Table VIII.
Table XXII. is similar to Table IX.
Table XXIII. is similar to Table VIII.
Table XXIV. is constructed from the Carlisle in a similar manner to
Table V. from the Northampton.
Table XXVI. is formed from Table XL. in the following manner :—
to the number in column D at the ages of A and B add the number in
column N at ages one year younger than A, and the age of B; from the
sum subtract the number in column N at the age of A and one year
younger than A, and divide the difference by double the number in
column D, at the age of A and B.
Example. To find the probability of a life aged 10, dying before
a life aged 60 :
To the number at the ages of 10 and 60 in column D, viz., 23533180
Add the number in column N at ages 9 and 60, viz., . 308095739
331629519
From the sum subtract the number in column N, ages 10
and 59 327354967
leaves 4274552
which, divided by 47067560, gives .0908, the required probability.
Column D in Table XXVII. is found by multiplying the number in
column D at the older age in Table XI. by the number of living at the
younger age: thus, to find the number in column D at the ages of 10
and 15, we multiply 4043.730, the number in column D at age 15, by
6460, the number living at the age of 15 according to the Carlisle mor
tality in Table I., which gives 26122497.6, the number in column D
at the ages of 10 and 15, under difference of age 5 years.
Column N is formed from column D in precisely the same manner
as in Table VI.
Tables XXVIII. to XXXIII. are formed in a similar manner.
Tables XXXVI. to XXXVIII. show the single and annual pre
miums for different assurances on two lives, the construction being
somewhat too intricate to be explained here.
Table XXXIX. shows the value of a policy of £100 according to
the Northampton rate of mortality after it has been in force any num
ber of years, the original premium being assumed to have been charged
according to the same table of mortality and rate of interest; it is
constructed in the following manner: divide the value of the annuity
increased by unity at the age when the policy is valued by the value of
the annuity increased by unity at the age when the assurance was
effected, subtract the quotient from unity, and multiply by 100. Or,
To the annual premium for assuring £1 at the age when the policy
was taken out, add .029126, and add the same quantity to the annual