Years to reach a target capital

Statement

How many years are needed for $8000\ \text{€}$ to become $20\,000\ \text{€}$ at $7\%$ compounded annually?

Solution

From $8000\,(1{.}07)^{n} = 20\,000$ it follows $1{.}07^{n} = 2{.}5$. $n = \frac{\ln 2{.}5}{\ln 1{.}07} = \frac{0{.}916291}{0{.}067659} \approx \boxed{13{.}54\ \text{years}}.$