A certain loan program offers an interest rate of \( 6 \% \), compounded continuously. Assuming no payments are made, how much would be owed after four years on a loan of \( \$ 3600 \) ? Do not round any intermediate computations, and round your answer to the nearest cent. If necessary, refer to the list of financial formulas.

To calculate the amount owed after four years on a loan compounded continuously at an interest rate of \( 6\% \), we can use the formula: \[ A = Pe^{rt} \] where: - \( A \) is the amount owed after time \( t \), - \( P \) is the principal amount (initial loan), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years, - \( e \) is Euler's number (approximately \( 2.71828 \)). Plugging in the values: - \( P = 3600 \) - \( r = 0.06 \) (which is \( 6\% \)) - \( t = 4 \) We calculate: \[ A = 3600 \times e^{0.06 \times 4} \] \[ A = 3600 \times e^{0.24} \] \[ A \approx 3600 \times 1.271828 \] \[ A \approx 4578.77 \] Thus, the amount owed after four years would be approximately \( \$ 4578.77 \).