Question

Sometimes we need to find out long it will take money to grow to some particular amount. For example, if a company’s sales are growing at 9% per year, how long will it take sales to triple? If you want the investment to quadruple in 8 years, what interest rate must it earn?

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value($3x)
P=present value($x say)
r=rate of interest
n=time period.

3x=x*(1.09)^n

3=(1.09)^n

Taking log on both sides;

log 3=n*log (1.09)

n=log 3/log (1.09)

=12.75 years(Approx).

b.We use the formula:
A=P(1+r/100)^n
where
A=future value($4x)
P=present value($x say)
r=rate of interest
n=time period.

4x=x*(1+r/100)^8

(4)^(1/8)=(1+r/100)

(1+r/100)=1.1892

r=1.1892-1

=18.92%(Approx).