Rate to double in twelve years

Statement

At what annual rate does a capital double in $12$ years with annual compounding?

Solution

From $C\,(1+i)^{12}=2C$ we get $(1+i)^{12}=2$, so $1+i=2^{1/12}$. $1+i=e^{\frac{\ln 2}{12}}=e^{0{.}057762}=1{.}059463\Rightarrow i\approx\boxed{5{.}95\%}.$