Question

company abc saw their eps grow from $10.00 per share to $46.00 per share during the past 12 years. what is the annual rate of growth over this period? a 13.56% b 14.21% c 16.18% d 18.66%

Explanation:

Step1: Recall the compound - growth formula

The formula for compound growth is $FV = PV(1 + r)^{n}$, where $FV$ is the future value, $PV$ is the present value, $r$ is the annual growth rate, and $n$ is the number of years. We need to solve for $r$.

Given that $PV=\$10.00$, $FV = \$46.00$, and $n = 12$ years.

First, we can rewrite the formula to solve for $(1 + r)$:
$\frac{FV}{PV}=(1 + r)^{n}$

Substitute the given values:
$\frac{46}{10}=(1 + r)^{12}$
$4.6=(1 + r)^{12}$

Step2: Take the 12 - th root of both sides

To solve for $(1 + r)$, we take the 12 - th root of both sides. The 12 - th root of a number $x$ can be written as $x^{\frac{1}{12}}$. So,
$1 + r=4.6^{\frac{1}{12}}$

Calculate $4.6^{\frac{1}{12}}$:
We know that $a^{\frac{1}{n}}=\sqrt[n]{a}$. Using a calculator, $4.6^{\frac{1}{12}}\approx4.6^{0.08333}\approx1.1356$

Step3: Solve for $r$

Subtract 1 from both sides to find $r$:
$r=1.1356 - 1=0.1356$
Convert to a percentage: $r = 0.1356\times100\%=13.56\%$

Answer:

A 13.56%