Answer
$6.1\%$
Work Step by Step
$$\begin{aligned}
P(1+r)^t&= A\\
800(1+r)^2&=900 && \text{Let }P=800\text{ and }t=2.\\
(1+r)^2&= \frac{900}{800}\\
(1+r)^2&=\frac{9}{8} && \text {Take the square root of both sides.}\\
1+r&= \pm\sqrt{\frac{9}{8}}\\
r&=\pm\frac{3}{\sqrt{8}}-1\\
r&=\frac{3}{2\sqrt{2}}-1 \\
r& = 0.061= 6.1\%
\end{aligned}$$ We took only the positive value since $r$ must be positive for the money to grow.
The required interest rate is about $6.1\%$.
