Answer
$25.992 \%$
Work Step by Step
Recall:
$A = P \left(1+\dfrac{r}{n} \right)^{n t}$
where
$P:$ The principal amount
$r:$ Annual interest rate
$n:$ Number of compoundings per year
$t:$ Number of years
$A:$ Amount after $t$ years
The given problem has:
$t= 3$
$\text{compounded annually } \to n = 1$
Since the investment is to be doubled $ \hspace{20pt} \therefore A = 2P$
Using the formula above gives:
$2P = P\left(1+\dfrac{r}{1} \right)^{1 \times 3}$
$2P = P (1+r)^3$
Dividing both sides by $P$
$2 = (1+r)^3$
$(1+r) = \sqrt[3]{2}$
$r = \sqrt[3]{2}-1$
$r \approx 0.25992$
$r \approx \boxed{ 25.992 \%}$