332 VALUATION, DEPRECIATION AND THE RATE-BASE
The amount of $1 for 30 years at 15 per cent is found to be
$66.211772.
Then 9.357621 X 66.211772 = $619.58,
which is the amount of $1 at 15 per cent in 46 years.
While occasion may rarely arise when it is necessary to know
the amount of $1 at these high rates of interest for a long term
of years this section of the table is valuable for other purposes.
It can be used to determine the present value of $1 due at a
future date; the amount of an annuity of $1, and also the present
value of an annuity of $1.
The method of use for these purposes is explained in connection
with the respective tables which follow.
To Illustrate. — What is the present value of a mine yielding
$10,000 net per annum whose estimated life is ro years and
which, owing to the hazards of the enterprise, should yield a net
return of 20 per cent per annum?
From Table 22 it is found that $1 at 20 per cent compound
interest will amount to $6.191736 in 10 years.
According to formula (23) in the explanation of Table 26 the
amount of an annuity of $1 for ro years will be
61917301
oe = $25.95868.
And by formula (25) in the explanation of Table 27 the present
value of an annuity of $1 for 10 years
25.05868
ant = $4.192149.
Consequently the value of the mine equipped to produce the
net annual amount of $10,000:
10,000 X 4.192149 = $41,921.49.