Question

How long will it take $400 to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places. 6%. year(s) 15%. year(s) 20%. year(s) 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*400)=400*(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*400)=400*(1.15)^n

2=(1.15)^n

Taking log on both sides;

log 2=n*log (1.15)

n=log 2/log (1.15)

=4.96 years(Approx)

c.(2*400)=400*(1.2)^n

2=(1.2)^n

Taking log on both sides;

log 2=n*log (1.2)

n=log 2/log (1.2)

=3.80 years(Approx)

d.(2*400)=400*(2)^n

2=(2)^n

Taking log on both sides;

log 2=n*log (2)

n=log 2/log (2)

=1 year