Question

5-13 TIME FOR A LUMP SUM TO DOUBLE How long will it take $300 to double if it earns the following rates? Compounding occurs once a year.

a. 6%

b. 13%

c. 21%

d. 100%

Answer 1

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*300)=300*(1.06)^n

2=(1.06)^n

Taking log on both sides;

log 2=n*log (1.06)

n=log 2/log (1.06)

=11.9 years(Approx).

b.(2*300)=300*(1.13)^n

2=(1.13)^n

Taking log on both sides;

log 2=n*log (1.13)

n=log 2/log (1.13)

=5.67 years(Approx).

c.(2*300)=300*(1.21)^n

2=(1.21)^n

Taking log on both sides;

log 2=n*log (1.21)

n=log 2/log (1.21)

=3.64 years(Approx).

d.(2*300)=300*(2)^n

2=(2)^n

Taking log on both sides;

log 2=n*log (2)

n=log 2/log (2)

=1 year