Question

How long will it take a given sum of money to increase 4 times it's present value when compounded half yearly at 7% rate of interest?

Answer 1

20.149 years

calculation:

$A=P(1+\cfrac{r}{n})^{nt}$

A=4P

 r=0.07

 n=2

t is time taken

$4P=P(1+\cfrac{0.07}{2})^{2t}$

$\cfrac{4P}{P}=\cfrac{P}{P}(1+0.035)^{2t}$

$4=(1.035)^{2t}$

$4=(1.035^2)^t$

$t=\cfrac{log 4}{log 1.035^2}$

$t=20.14879168$