Answer
$8\%$
Work Step by Step
Given $$ P= 15000;\ \ A= 17500;\ \ t= 2; \ r= ?$$ Set in the given values into the equation and solve for the interest rate $ r$. $$\begin{aligned}
P(1+r)^t&= A\\
15000(1+r)^2&=17500\\
(1+r)^2&= \frac{17500}{15000}\\
(1+r)^2&=1.1666667\\
1+r&= \pm\sqrt{1.1666667}\\
r&=\sqrt{1.1666667}-1\\
r& \approx 0.080= 8.0\%
\end{aligned}$$ We took only the positive value, since r must be positive for the money to grow.
The required interest rate is about $8\%$.
