Accumulated value with annual compound interest

Statement

We invest $5000\ \text{€}$ at $4\%$ per year with annual compound interest. What is the accumulated value after $6$ years? How much compound interest is earned?

Solution

The accumulated value follows $M = C\,(1+i)^n$. $M = 5000\cdot 1{.}04^{6} = 5000\cdot 1{.}265319 \approx \boxed{6326{.}60\ \text{€}}.$ Compound interest: $I = M - C \approx 6326{.}60 - 5000 = \boxed{1326{.}60\ \text{€}}$.