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LOGARITHMS. 89
If the deducted sum, b, exceeds the interest due at the first
period of time, the amount a will become smaller than the prin-
cipal/, and in time the whole principal will be used up. This
will be when
:
100 b (r n — 1)
fix
This transposes to
:s to
y
100 b
100 b
log. -
—py
100 3
100 3 — py
" - log- r
Example.
A principal of $5000 is invested at 4% per year, but at the
end of each year #600 is withdrawn. How long will it take to
use the whole principal ?
100 x 600
loS- 100 X 600 — 5000 X 4
log.
log. 1.04
6O000
900— 20000
log. 1.04
log. 1.50
log. 1.04
0.176091
0.017033
n = 10.3 years.
Paying a Debt by Instalments.
This same formula applies also in this case; for instance:
A man uses $1500 every year toward paying a debt of $10,000,
and b% interest per year. How long will it take to pay it?
100 x 1500
l0S- 100 x 1500 — 10000 x 5
log. 1.05
150000
ioJ- 1000O0
log. 1.05
log- 1.5
log. 1.05
0.176091
0.021189
8.3 years.
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