\begin{tabular}{l} Question \( 9 \quad 0 / 3 \) pts \( 5 \leftrightarrows 99 \) (i) Details \\ You deposit \( \$ 3000 \) in an account earning \( 4 \% \) interest \\ compounded continuously. How much will you have in \\ the account in 10 years? \\ \( \$ \) \\ Question Help: \( \square \) Video \\ Submit Question \\ \hline\end{tabular}

To find the future value of your investment with continuous compounding, you can use the formula \( A = Pe^{rt} \), where \( A \) is the amount of money accumulated after n years, including interest. Here, \( P \) is the principal amount (\$3000), \( r \) is the annual interest rate (0.04), and \( t \) is the time the money is invested for (10 years). Plugging in the numbers gives you \( A = 3000 \times e^{0.04 \times 10} \). When you perform the calculation, you'll find that you'll have approximately \$8,202.10 in your account after 10 years. It's amazing how money can grow when you let it sit and earn compound interest! Speaking of compounding, did you know that the concept dates back centuries? Mathematicians like Jacob Bernoulli studied compound interest as early as the 17th century. The exponential function \( e \) itself was introduced in the context of calculus around that time, making it a fascinating blend of finance and mathematics!