Time to double with quarterly compounding

Statement

In how many years does a capital double at $4\%$ per year with quarterly compounding?

Solution

$(1{.}01)^{4t}=2\Rightarrow 4t=\dfrac{\ln 2}{\ln 1{.}01}=\dfrac{0{.}693147}{0{.}009950}=69{.}66$. $t=\frac{69{.}66}{4}\approx\boxed{17{.}42\ \text{years}}.$