How long will it take $800 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.
8%.
year(s)
12%.
year(s)
19%.
year(s)
100%.
year(s)
We use the formula:
A=P(1+r/100)^n
where
A=future value($1600)
P=present value
r=rate of interest
n=time period.
1.
1600=800(1.08)^n
(1600/800)=1.08^n
2=1.08^n
Taking log on both sides;
log 2=n*log 1.08
Hence n=log 2/log 1.08
which is equal to
=9.01 years(Approx)
2.
1600=800(1.12)^n
(1600/800)=1.12^n
2=1.12^n
Taking log on both sides;
log 2=n*log 1.12
Hence n=log 2/log 1.12
which is equal to
=6.12 years(Approx)
3.
1600=800(1.19)^n
(1600/800)=1.19^n
2=1.19^n
Taking log on both sides;
log 2=n*log 1.19
Hence n=log 2/log 1.19
which is equal to
=3.98 years(Approx)
d.
1600=800(1.2)^n
(1600/800)=1.2^n
2=1.2^n
Taking log on both sides;
log 2=n*log 1.2
Hence n=log 2/log 1.2
which is equal to
=1 year.
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