Suppose \( \$ 1800 \) is borrowed for four years at an interest rate of \( 3 \% \) per year, compounded continuously. Find the total amount owed, assuming no payments are made until the end. Round to the nearest cent.

To find the total amount owed when borrowing money at a continuously compounded interest rate, you can use the formula: \[ A = Pe^{rt} \] Where: - \( A \) is the amount of money accumulated after n 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 or borrowed for, in years. - \( e \) is the base of the natural logarithm, approximately equal to 2.71828. Given: - \( P = 1800 \) - \( r = 0.03 \) - \( t = 4 \) Plugging in these values: \[ A = 1800 \cdot e^{0.03 \cdot 4} \] \[ A = 1800 \cdot e^{0.12} \] Now, calculating \( e^{0.12} \): \[ e^{0.12} \approx 1.1275 \] Now substitute this value back into the formula: \[ A \approx 1800 \cdot 1.1275 \approx 2030.50 \] Thus, the total amount owed after four years, rounded to the nearest cent, is approximately **\$2030.50**.