Answer
$\$291.91$
Work Step by Step
Recall:
The formula for interest that compounds continuously is:
$$A=Pe^{rt}$$
where
$P$ = principal amount invested
$r$ = annual interest rate
$t$ = time in years
Using the given values and the formula above gives:
\begin{align*}
A&=Pe^{rt}\\
&=250e^{6.2\% \cdot 2.5}\\
&=250e^{0.062\cdot 2.5}\\
&=250e^{0.155}\\
&\approx 291.91
\end{align*}
Thus, the valule of the investment after $2.5$ years is approximately $\$291.91$
