Doubling time of a capital

Statement

In how many years does a capital invested at $5\%$ per year with compound interest double?

Solution

From $C\,(1{.}05)^{n} = 2C$ it follows $1{.}05^{n} = 2$. Taking logarithms: $n = \frac{\ln 2}{\ln 1{.}05} = \frac{0{.}693147}{0{.}048790} \approx \boxed{14{.}21\ \text{years}}.$