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} (A)/(P)=(1+r)^t \\ \ln(A)/(P)=t\ln(1+r) \\ \ln(1+r)=(1)/(t)\ln(A)/(P) \\ 1+r=e^{(1)/(t)\ln(A)/(P)} \\ r=e^{(1)/(t)\ln(A)/(P)}-1 \end{gathered}`

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

`r=e^{(1)/(7)\ln(38700)/(5000)}-1\approx0.3396=33.96\%`