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82 LOGARITHMS.
Compound Interest by Logarithms.
When the interest, at the end of each period of time, is
added to the principal the amount will increase at a constant
rate ; and this rate will be the amount of one dollar invested
for one period of the time. For instance : If the periods of time
be one year each, then $30 in 3 years at 5 % compound interest
will be :
#30 X 1.05 = #31.50 at the end of first year.
#31.50 X 1.05 = $33,075 at the end of second year.
$33,075 X 1.05 = $34.73 at the end of third year.
This calculation may be written
:
#30 X 1.05 X 1.05 X 1.05 = #34.73
which also may be written
#30 X (1.05)3 = $34.73.
Thus, compound interest is a form of geometrical progres-
sion, and may be calculated by the following formulas :
a –
=p X. rn
Log. a -= 71 X log. r + log. p
p-
Log. p
71
’
a
= t^t
= log. a —
_ log.a-
7i X log. r
- log- P
Log. r
log.
_ log. a -
r
- log. p
71
p = Principal invested.
n r= The number of periods of time.
a = The amount due after n periods of time.
r — The amount of $1 invested one period of time.
Note.—The quantity r is always obtained by the rule :
Divide the rate of interest per period of time by 100, and
add 1 to the quotient.
Example.
What is the amount of $816 invested 6 years at A.% com-
pound interest?
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