Answer
$\$565.16$
Work Step by Step
Recall:
Continuous Compounding Formula:
$$A=Pe^{rt}$$
where
$A$ = future value of the investment
$P$ = principal or amount invested
$r$ = interest rate per year
$t$ = time in years
Thus, the future value of a $\$500$ investment compounded continuously earning an annual interest rate of $4.9\%$ after $2.5$ years is:
\begin{align*}
A&=500\left(e^{4.9\% \cdot 2.5}\right)\\
A&=500\left(e^{0.049 \cdot 2.5}\right)\\
A&=500\left(e^{0.1225}\right)\\
A&\approx 565.16
\end{align*}
The value of the investment after $2.5$ years is around $\$565.16$.
