Time to triple with monthly compounding

Statement

In how many years does a capital triple at a nominal rate of $9\%$ compounded monthly?

Solution

The periodic rate is $\dfrac{0{.}09}{12} = 0{.}0075$. From $(1{.}0075)^{12n} = 3$: $12n = \frac{\ln 3}{\ln 1{.}0075} = \frac{1{.}098612}{0{.}007472} \approx 147{.}0 \ \Rightarrow\ n = \frac{147{.}0}{12} \approx \boxed{12{.}25\ \text{years}}.$