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84 LOGARITHMS.
Example.
A bill of $500 is due in 3 years. How much cash is it worth
if 3% compound interest should be deducted.
Log. p = log. a — n X log. r
Log.p = 2.698970 — 3 X 0.012837
Log.p = 2.698970 — 0.038511
Log.p = 2.660459
p = $457.57 = Cash payment.
Note.— Such examples may be checked to prevent miscal-
culations, by multiplying the result (the cash payment), by the
tabular number given for corresponding number of years and
percentage of interest in table on page 23 ; if calculations are
correct, the product will be equal to the original bill. For in-
stance, 457.57 X 1.092727 = 499.99909339 = $500.00. Thus, the
calculation in the example is correct.
Sinking Funds and Savings.
If a sum of money denoted by b, set apart or saved dur-
ing each period of time, is put at compound interest at the end
of each period," the amount will be
:
a = b at the end of the first period.
a = b -f- br at the end of the second period.
a = b + br + br2
at the end of the third period.
At the end of n periods the last term in this geometrical
series is br n —
1
and the first term is b, while the ratio is r.
The sum of the series is the amount which according to the
rules for geometrical progression (see page 69) will be
:
r(br Q - 1
)
— b
a = —-
r— 1
b(r" —1)
r— 1
Example.
At the end of his first year’s business a man sets apart
$1200 for a sinking fund, which he invests at 4% per year. At
the end of each succeeding year he sets apart $1200 which is
invested at the same rate. What is the value of the sinking
fund after 7 years of business ?
Solution
:
a = 1200 X (1.047 — 1)
1.04 — 1
1200 X 0.31593
a = -
a =
0.04
a = $9477.90
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