Answer
$r\approx9.54$%
Work Step by Step
Consider the given formula for the interest rate $r$ that will allow principal $P$ to grow into the amount $A$ over two years.
$$r=\sqrt{\frac AP}-1$$
You are willing to invest 10,000 dollars in order to make a profit of 2,000 dollars. This means we want 12,000 dollars in the account after two years.
Substitute the values into the formula:
$r=\sqrt{\frac AP}-1$
$r=\sqrt{\frac{12000}{10000}}-1$
$r=\frac{\sqrt{30}-5}{5}$
Use a calculator to solve this.
$\frac{\sqrt{30}-5}{5} \approx 0.095445$
$r \approx 9.54$%
