Time to grow to 2.5 times

Statement

In how many years does a capital become $2{.}5$ times its initial value at $6\%$ per year with semiannual compounding?

Solution

$(1{.}03)^{2t}=2{.}5\Rightarrow 2t=\dfrac{\ln 2{.}5}{\ln 1{.}03}=\dfrac{0{.}916291}{0{.}029559}=31{.}00$. $t=\frac{31{.}00}{2}\approx\boxed{15{.}50\ \text{years}}.$