Maturity value with continuous compounding

Statement

$5000\ \text{€}$ are invested at $7\%$ per year with continuous compounding. Maturity value after $10$ years?

Solution

With continuous compounding $M=C\,e^{rt}$. $M=5000\,e^{0{.}07\cdot 10}=5000\,e^{0{.}7}=5000\cdot 2{.}013753\approx\boxed{10068{.}76\ \text{€}}.$