Maturity value with semiannual compounding

Statement

Ms Vaccari invests $3000\ \text{€}$ at $6\%$ per year with semiannual compounding. What is the value after $3$ years?

Solution

With $m=2$ periods per year, $M=C\left(1+\dfrac{i}{m}\right)^{mt}$. $M=3000\,(1+0{.}03)^{6}=3000\cdot 1{.}194052\approx\boxed{3582{.}16\ \text{€}}.$