Question

Invested $5,000 seven years ago and that this investment is worth $38,700 today. What was annual rate of return if compounds annually?

Answer 1

For an initial amount P invested at an annually compounded interest rate r, after t year the total amount is given by:

$A=P(1+r)^t$

Then we have:

$\begin{gathered} \frac{A}{P}=(1+r)^t \\ \ln\frac{A}{P}=t\ln(1+r) \\ \ln(1+r)=\frac{1}{t}\ln\frac{A}{P} \\ 1+r=e^{\frac{1}{t}\ln\frac{A}{P}} \\ r=e^{\frac{1}{t}\ln\frac{A}{P}}-1 \end{gathered}$

Therefore, for P - $5,000, A = $38,700 and t = 7 years, we have:

$r=e^{\frac{1}{7}\ln\frac{38700}{5000}}-1\approx0.3396=33.96\%$