Answer
$25.99\%$
Work Step by Step
According to the Compound Interest Formula, where $P$ is the principal, the amount deposited, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded annually, $t$ is the number of years, $A$ is the amount the investor gets back after $t$ years:
$A=P\cdot(1+\frac{r}{n})^{n\cdot t}$
The investment is compounded annually hence $n=1$.
Thus, the formula above becomes
$A=P\cdot(1+\frac{r}{1})^{1\cdot t}\\ A=P\cdot(1+r)^{t}$
The given situation has
$t=3$ years
$A=2P$ since the investment doubles after $3$ years.
Using the formula above gives:
\begin{align*}
2\cdot P&=P\cdot(1+r)^3\\
2&=(1+r)^3\\
\sqrt[3]{2}&=\sqrt[3]{(1+r)^3}\\
\sqrt[3]{2}&=1+r\\
\sqrt[3]{2}-1&=r\end{align*}
Use a calculator to obtain:
$r=\sqrt[3] 2-1\\
r=1.2599210499-1\\
r=0.2599210499\\
r\approx25.99\%$
