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%6 LOGARITHMS.
Solution
:
„ _ 39 X 1.02 X (10232 — 1)
1.02 — 1
_ 39 X 1.02 X 0.8845
0.02
a = 1759.27
Thus, by paying the money in advance semi-annually, he
will gain (1759.27 — 1724.77) = $34.50.
If a principal denoted by p is invested at a given rate of
compound interest, and successive smaller or larger equal pay-
ments denoted by b are made at the end of each period of time
so that they will commence to draw interest at the beginning of
the following period at the same rate as the principal, the
formula will be :
a = p x r« + *>-*>
r — 1
but for logarithmic calculations it is more convenient to denote
the rate of interest by y % and the formula will read :
a = p X
a = p X r n -\
b (r n — 1)
+ y
100
100 b (r n -1)
ay–py X rR
100
ay
rn — 100
+ 100 £
py -f 100 b
, ay + 1003
cog.
P y + 100 b
log.
log. r
a y -f 100 b
P y + 100 b
Note.—Using these formulas it must be understood that
n represents the number of periods of time that the principal is
invested, and that this first period is considered to be the period
at the end of which the first payment, b, is made.
Example.
A man has ^50 in a savings bank and he also puts in #25
every month, which goes on interest every 6 months ; the bank
pays 4% interest, computed semi-annually. How much money
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