Answer
$3.7\%$
Work Step by Step
Given $$ P= 2000;\ \ A= 2150;\ \ t= 2; \ r= ?$$ Set in the given values into the equation and solve for the interest rate, $ r$. $$\begin{aligned}
P(1+r)^t&= A\\
2000(1+r)^2&=2150\\
(1+r)^2&= \frac{2150}{2000}\\
(1+r)^2&=1.075\\
1+r&= \pm\sqrt{1.075}\\
r&=\sqrt{1.075}-1\\
r& = 0.0368= 3.7\%
\end{aligned}$$ We took only the positive value, since r must be positive for the money to grow.
The required interest rate is about $3.7\%$.
