Rate to triple with quarterly compounding

Statement

What annual rate makes a capital triple in $8$ years with quarterly compounding?

Solution

$\left(1+\dfrac{i}{4}\right)^{32}=3\Rightarrow 1+\dfrac{i}{4}=3^{1/32}=e^{\frac{\ln 3}{32}}=e^{0{.}034332}=1{.}034928$. $\frac{i}{4}=0{.}034928\Rightarrow i\approx\boxed{13{.}97\%}.$