Compound interest compounded monthly

Statement

We invest $2000\ \text{€}$ at a nominal annual rate of $6\%$ compounded monthly for $3$ years. What is the accumulated value?

Solution

The periodic rate is $\dfrac{0{.}06}{12} = 0{.}005$ and the number of periods is $n = 3\cdot 12 = 36$. $M = 2000\left(1 + \frac{0{.}06}{12}\right)^{36} = 2000\cdot 1{.}005^{36} \approx \boxed{2393{.}36\ \text{€}}.$