Answer
$13.9$ years
Work Step by Step
The formula for compound interest wit $ n $ compoundings per year is given by : $ A= P(1+\dfrac{r}{n} )^{nt}$
Plug in the given data.
$8000=4000 (1+\dfrac{0.05}{4} )^{4t}$
or, $2=(1.0125)^{4t}$
Take the log of each side.
$ t= \dfrac{\ln 2}{4 \ln 1.0125} \approx 13.9$ years
