Question

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.

1. 3%.

   year(s)

2. 10%.

   year(s)

3. 17%.

   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*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.