Continuous compounding

Statement

We invest $1000\ \text{€}$ at a rate of $5\%$ per year with continuous compounding for $4$ years. What is the accumulated value?

Solution

With continuous compounding $M = C\,e^{rt}$. $M = 1000\,e^{0{.}05\cdot 4} = 1000\,e^{0{.}2} \approx 1000\cdot 1{.}22140 = \boxed{1221{.}40\ \text{€}}.$