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88 LOGARITHMS.
Example.
A man calculates that if he had $1800 he would start
in business. He has only $120, but is earning $15 a week and
figures that he can save half of his weekly earnings. He puts
his money in a savings bank, where it goes on interest every
six months, at the rate of 4% a year. How many years will it
take him to save the required amount? (Note.—$7.50 a week
= 26 X ny
2 = $195 in six months, and 4% per year = 2% per
six months, or per period of time).
Solution by formula
:
7 a y + 100 b
log.
n = jjz + 100 b
log.
log. r
1800X2 + 100X195
120 X 2 + 100 X 195
log.
log. 1.02
3600 + 19500
240 + 19500
log. 1.02
_ log. 1.1702 0.0683
8 periods of time (nearly).
log. 1.02 0.0086 \ 31
One period = 6 months ; 8 periods = 4 years ; therefore,
under these conditions it takes four years to save this amount
of money.
If a certain sum of money is withdrawn instead of added,
at the end of each period of time, the formula on page 86 will
change to
:
100 £ (r n — 1)
a = p X rn
y
Every letter denotes the same value as it had in the formula
on page 86, except that b represents the sum withdrawn instead
of the sum added.
Example.
A man has $5000 invested at b% interest compounded an-
nually, but at the end of each year he withdraws $200. How
much money has he left after six years ?
Solution:
a = 1.056
X 5000 — 100 X 200 X(1.056 — 1)
a =1.34 X 5000
a = 6700 — 1360
a = $5340 = Amount.
100 X 200 X 0.34
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