Question

How long will it take $300 to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

1. 5%.

   ?year(s)

2. 10%.

   ?year(s)

3. 18%.

   ?year(s)

4. 100%.

   ?year(s)

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*(1.05)^n

2=(1.05)^n

Taking log on both sides;

log 2=n*log (1.05)

n=log 2/log (1.05)

=14.21 years(Approx).

b.

(2*300)=300*(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*300)=300*(1.18)^n

2=(1.18)^n

Taking log on both sides;

log 2=n*log (1.18)

n=log 2/log (1.18)

=4.19 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.