Answer
$12.246 \%$
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
Here we have:
$t= 6$
$\text{Compounded annually } \to n = 1$
Since the investment is to be doubled $ \hspace{20pt} \therefore A = 2P$
$2P = P\left(1+\dfrac{r}{1} \right)^{1 \times 6}$
$2P = P (1+r)^6$
Divide both sides by $P$
$2 = (1+r)^6$
$(1+r) = \sqrt[6]{2}$
$r = \sqrt[6]{2}-1$
$r \approx 0.12246$
$r = \boxed{12.246 \%}$
