Annual effective rate from the continuous rate

Statement

An investment yields $7\%$ with continuous compounding. What is the equivalent annual effective rate (annual compounding)?

Solution

Equate the amounts of $1\ \text{€}$ after one year: $1+i = e^{0{.}07}$. $i = e^{0{.}07} - 1 \approx 1{.}072508 - 1 = \boxed{7{.}25\%}.$