Compound Annual Growth Rate

If you were offered $15,000 fifteen years from now in return for an investment of $5,000 currently, what annual rate of interest would you earn if you took the offer?

Solutions

Expert Solution

Here,

Begining Value = $15,000

Ending Value = $5,000

Number of years = 15

The terms used in the formula

BV - Begining Value

EV - Ending Value

n - Number of years

$ \begin{align*}\rm\text{Compound Annual Growth Rate} &= \left ( \frac{EV}{BV} \right )^{\frac{1}{n}}-1\\ &= \left ( \frac{\$15,000}{\$5,000} \right )^{\frac{1}{15}}-1\\ &= 1.075989 – 1\\ &= 0.075989 \rm\text{ or } 7.60\%\end{align*} $

The compounded annual growth rate is 7.60%

Annual rate of interest is 7.60%

Vinay answered 2 years ago

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