Question

How long will it take $200 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places. 6%, 13%, 19%, 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*200)=200*(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*200)=200*(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*200)=200*(1.19)^n

2=(1.19)^n

Taking log on both sides;

log 2=n*log (1.19)

n=log 2/log (1.19)

=3.98 years(Approx)

d.(2*200)=200*(2)^n

2=(2)^n

Taking log on both sides;

log 2=n*log 2

n=log 2/log 2

=1 year(Approx)