EXPLANATION OF TABLES IN PART I. 
Table IV. is constructed by dividing unity by the corresponding num 
ber in Table III : thus, to find the number corresponding to the present 
value of £l to be received at the end of 16 years at 5 per cent com 
pound interest, we find in Table III., under column 5 per cent opposite 
1 
to 16 years, 2.18287459 ; then 
= .45811152, the present 
2.18287459 
value given in Table IV. 
By the assistance of this table we may find the present value of any 
sum by multiplying the present value of £l by the sum, the present 
value of which is required. 
Example. To find the present value of £120 to be received at the 
end of 9 years, allowing 5 per cent compound interest, we find under 
5 per cent opposite to 9 years 
.64460892 
which multiplied by 120 
gives 77.353 =£77 7 1, the present value required. 
Table V. is constructed by subtracting unity from the corresponding 
number in Table III, and then dividing by the annual interest of <£l. 
Example. The amount of £l per annum in 15 years at 5 per cent 
compound interest is thus found; opposite to 15 years in Table III., 
under column 5 per cent, we find 2.07892818, which diminished by 
unity gives 1.07892818; this divided by .05 gives 21.578564, which 
is the number found in Table V. 
This table enables us to find the amount of any annuity by multiply 
ing the amount in the table by the annuity of which it is required to 
find the amount. 
Example. A has to pay B £30 per annum for a lease for 20 years, 
but proposes in lieu thereof to pay him a fixed sum at the expiration of 
that term; what sum should be received so as to allow him 5 per cent 
interest ? 
In Table V., opposite to 20 years in column 5 per cent we have 
33.065954 
which multiplied by 30 
gives 991.979=£991 19 7 the sum to be received. 
Table VI. is constructed by subtracting the number in Table IV. from 
unity, and dividing by the annual interest of ¿£1. 
In Table IV., under 5 per cent opposite to 11 years we find .58467929, 
which subtracted from unity leaves .41532071; this divided by .05, 
gives 8,306414, the present value of £l per annum for 11 years at 
5 per cent. 
To find the present value of any annuity we multiply the value given 
in the table corresponding to the sum and rate by the annuity of which 
the present value is required. 
Example. The present value of an annuity of i 50 for 18 years at 
nun 
the 
• 12£ 
may 
M 
annuit 
Exc 
which 
be pure 
Tabi 
Table 
are acc