USE AND CONSTRUCTION OF TABLES. 
.0585 No. in column S at age 95 
.2998 ,, N ,, 94 
.3583 
.8589 
1.211 
S 
N 
94 
93 
93 
The construction of columns M and R are somewhat too intricate to 
he explained verbally ; an example for the Carlisle 4 per cent is given 
in Art. 192. 
Table VII. shows the number of years’ purchase which should be 
given for an annuity according to the Northampton table of mortality 
at the various rates per cent; the values given in the table being mul 
tiplied by any annuity will show the value of that annuity. 
Example. The value of an annuity of £40, during the existence of 
a life aged 45, at 4 per cent, is thus found : opposite to age 45, under 
column 4 per cent, is 12.2835, which multiplied by 40, gives 491.340, 
the value required. 
The values in this table are obtained by means of D and N columns, 
such as are given in Table VI., the number in column N being divided 
by the number in column D to find the value of the annuity. As an 
example,—the value of £l per annum, at 3 per cent, on a life aged 
29, is found by dividing 32376.615, the number in column N at that 
age, by 1892.585, the number in column D, which gives 17.1070 
the value of the annuity. 
Table VIII. shows, in a similar manner, the value of an annuity 
payable until the failure of the joint existence of two lives, and is con 
structed in a similar manner from columns D and N in Table XXXIII. 
Table IX. shows the present value, according to the Northampton 
table, of ¿£1 to be received at the end of the year in which the existence 
of a life shall fail: thus, at 5 per cent, at the age of 40, the present 
value of a reversion of £l is .38871, this, multiplied by 100, gives 
38.871, the value of ¿Pi00 to be secured at the end of the year in 
which a life aged 40 shall fail. 
The Table is constructed by subtracting the present value of ¿£l due 
at the end of one year from unity, and multiplying the difference by the 
value of the annuity given in Table VII., increased by unity, and sub 
tracting the result thus obtained from unity: thus, to find the value at 
5 per cent on a life aged 40, we find in Table IV., Part I., the present 
value of £l due at the end of one year, at 5 percent, is .952381,which, 
taken from unity, leaves .047619, and the value of the annuity in Table 
VII., at the age of 40, under column 5 per cent, increased by unity, is 
12.837 : then, .047619 X 12.837—.61129, which, taken from unity, 
leaves .38871, the value in the Table. 
Tables XI. to XVIII. are similar to Table VI. 
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