Answer to Question #216740 in Financial Math for Kelly

Question

The balance in an account grew from $5,032 to $12,145 in 15 years, when interest was compounded quarterly. What was the interest rate? 

Answer 1

Solution:

Given, $P=\$ \ 5032, A=\$\ 12145, t=15\ years=60\ quarters$

Let rate of interest per annum be $r\%$ compounded annually.

Then, $A=P(1+\dfrac{r}{400})^{60}$

$\Rightarrow 12145=5032(1+\dfrac{r}{400})^{60} \\ \Rightarrow 2.413553=(1+\dfrac{r}{400})^{60} \\ \Rightarrow 1.014793=1+\dfrac{r}{400} \\ \Rightarrow \dfrac{r}{400}=0.014793 \\ \Rightarrow r=5.9172$

Thus, the rate of interest is 5.9172% per annum compounded annually.