Answer
$\$1,100.76$
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}\\
&=1000e^{4.8\% \cdot 2}\\
&=1000e^{0.048\cdot 2}\\
&=1000e^{0.096}\\
&\approx 1100.76
\end{align*}
Thus, the valule of the investment after $2$ years is approximately $\$1,100.76$
