An initial amount of \( \$ 3600 \) is invested in an account at an interest rate of \( 5 \% \) per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after four years. Do not round any intermediate computations, and round your answer to the nearest cent.

To find the amount in the account after four years with continuous compounding, you can use the formula: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after \( t \) years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( t \) is the time the money is invested for in years. - \( e \) is the base of the natural logarithm, approximately equal to \( 2.71828 \). Given: - \( P = 3600 \) - \( r = 0.05 \) - \( t = 4 \) Now, substituting the values into the formula: \[ A = 3600 \cdot e^{0.05 \cdot 4} \] \[ A = 3600 \cdot e^{0.20} \] Calculating \( e^{0.20} \): \[ e^{0.20} \approx 1.2214 \] Now plug it back into the equation: \[ A \approx 3600 \cdot 1.2214 \approx 4396.04 \] Thus, the amount in the account after four years would be approximately **$4396.04**.