Question

24

At a growth (interest) rate of 9 percent annually, how long will it take for a sum to double? To triple? Use Appendix A for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answers to 2 decimal places.)
  

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value($2x)
P=present value($x say)
r=rate of interest
n=time period.

2x=x*(1.09)^n

2=(1.09)^n

Taking log on both sides;

log 2=n*log (1.09)

n=log 2/log (1.09)

=8.04 years(Approx).

b.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).