Earnings growth rate

Statement

A company’s earnings per share go from $4{,}00\ \text{€}$ to $7{,}00\ \text{€}$ in $5$ years. What is the annual compound growth rate?

Solution

From $4{.}00\,(1+i)^{5} = 7{.}00$ we get $(1+i)^{5} = \dfrac{7}{4} = 1{.}75$. $i = 1{.}75^{1/5} - 1 \approx 1{.}11843 - 1 = \boxed{11{.}84\%}.$