Question

Assume that it takes 11.5 years for $1,000 to accumulate to $3,000 if you earn 10% per year. What will happen to the length of time needed for $1,000 to accumulate to $3,000 if the interest rate increases?

Increase

Stay the same

Decrease

Impossible to determine

Answer 1

Let interest rate be 15%

Hence

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

3000=1000*(1.15)^n

(3000/1000)=(1.15)^n

Taking log on both sides;

log 3=n*log (1.15)

n=log 3/log (1.15)

=7.86 years(Approx)

Hence length of time decreases as interest rate increases.