Answer
$\approx\$11,843.27$
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 $\$6000$ investment compounded continuously earning an annual interest rate of $6.8\%$ after $10$ years is:
\begin{align*}
A&=6000\left(e^{6.8\% \cdot 10}\right)\\
A&=6000\left(e^{0.068 \cdot 10}\right)\\
A&=6000\left(e^{0.68}\right)\\
A&\approx 11,843.27
\end{align*}
The value of the investment after $10$ years is around $\$11,843.27$.
