Continuous rate to grow by sixty percent

Statement

At what nominal rate with continuous compounding does an investment increase by $60\%$ in $4$ years?

Solution

From $C\,e^{4r} = 1{.}6\,C$ it follows $e^{4r} = 1{.}6$, so $4r = \ln 1{.}6$. $r = \frac{\ln 1{.}6}{4} \approx \frac{0{.}470004}{4} = \boxed{11{.}75\%}.$