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 of $3600 with an interest rate of 6% compounded continuously, we can use the formula for continuous compounding: \[ A = P e^{rt} \] Where: - \( A \) is the amount owed after \( t \) years, - \( P \) is the principal amount (initial loan amount), - \( r \) is the annual interest rate (in decimal form), - \( t \) is the time in years. Given: - \( P = \$3600 \), - \( r = 6\% = 0.06 \), - \( t = 4 \) years. Substitute the values into the formula: \[ A = 3600 e^{0.06 \times 4} \] Now, we can calculate the amount owed after four years. Calculate the value by following steps: - step0: Calculate: \(3600e^{0.06\times 4}\) - step1: Multiply the numbers: \(3600e^{0.24}\) - step2: Convert the expressions: \(3600e^{\frac{6}{25}}\) - step3: Rewrite the expression: \(3600\sqrt[25]{e^{6}}\) The amount owed after four years on a loan of $3600 with an interest rate of 6% compounded continuously is approximately $4576.50.