TIME FOR A LUMP SUM TO DOUBLE
How long will it take $500 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.
3%.
year(s)
10%.
year(s)
17%.
year(s)
100%.
year(s)
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
a.
(2*500)=500*(1.03)^n
2=(1.03)^n
Taking log on both sides;
log 2=n*log (1.03)
n=log 2/log (1.03)
=23.45 years(Approx).
b.
(2*500)=500*(1.1)^n
2=(1.1)^n
Taking log on both sides;
log 2=n*log (1.1)
n=log 2/log (1.1)
=7.27 years(Approx).
c.
(2*500)=500*(1.17)^n
2=(1.17)^n
Taking lo0g on both sides;
log 2=n*log (1.17)
n=log 2/log (1.17)
=4.41 years(Approx).
d.
(2*500)=500*(2)^n
2=(2)^n
Taking log on both sides;
log 2=n*log (2)
n=log 2/log (2)
=1 year.
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