Answer
$0.08=8\%$
Work Step by Step
We will determine $r$ by solving the system of equations:
$$\begin{cases}
P(1+r)^t&=2500\\
P(1+r)^{t+2}&=2916.
\end{cases}$$
Divide the second equation by the first, side by side:
$$\begin{align*}
\dfrac{P(1+r)^{t+2}}{P(1+r)^t}&=\dfrac{2916}{2500}\\
(1+r)^2&=1.1664.
\end{align*}$$
Solve for $r$:
$$\begin{align*}
1+r&=\pm\sqrt{1.1664}=\pm 1.08\\
1+r&=1.08\text{ or }1+r=-1.08\\
r&=0.08\text{ or }r=-2.08.
\end{align*}$$
Because the rate must be positive, the only solution is $r=0.08=8\%$.
