Years to triple an investment

Statement

Mr Avari invests two hundred thousand euros in shares yielding $13\%$ interest per year. Determine in how many years he manages to triple his investment.

Solution

Tripling means reaching $600000$ euros: $200000\cdot 1.13^{\,n}=600000\iff 1.13^{\,n}=3.$ Taking logarithms: $n=\frac{\ln 3}{\ln 1.13}\approx\frac{1.0986}{0.1222}\approx 8.99.$ So about $9$ years are needed (by the 9th year the investment has tripled).

$\boxed{n=\dfrac{\ln 3}{\ln 1.13}\approx 8.99\ \Rightarrow\ 9\ \text{years}}$