Doubling with continuous compounding

Statement

With continuous compounding at $4\%$, in how many years does the capital double?

Solution

From $C\,e^{0{.}04 t} = 2C$ it follows $e^{0{.}04 t} = 2$, so $0{.}04 t = \ln 2$. $t = \frac{\ln 2}{0{.}04} = \frac{0{.}693147}{0{.}04} \approx \boxed{17{.}33\ \text{years}}.$