Question

A financial analyst tells you that investing in stocks will allow you to double your money in 7 years. What annual rate of return is the analyst assuming you can earn?

Answer 1

Answer on Question #62850 Economics / Finance

A financial analyst tells you that investing in stocks will allow you to double your money in 7 years. What annual rate of return is the analyst assuming you can earn?

Solution:

Assuming returns are reinvested, due to the effect of compounding, the relationship between a rate of return $r$, and a return $R$ over a period of length $t$ is:

$$1 + R = (1 + r)^t$$

Considering a period of $t = 7$ years, we have the value of return $R = 1$ (or 100%).

Let's substitute the values of $t$ and $R$ to the equality above and solve the equation for $r$.

$$\begin{array}{l} 1 + 1 = (1 + r)^7 \\ 2 = (1 + r)^7 \\ \sqrt[7]{2} = 1 + r \\ \sqrt[7]{2} - 1 = r \\ r \approx 0.1041 \\ \end{array}$$

Answer: The analyst assuming that you can earn 0.1041 (or 10.41%) annual rate of return.

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