A certain loan program offers an interest rate compounded continuously. Assuming no payments are made, how much would be owed after 6 years on a \( \$ 3800 \) loan? Round to the nearest cent.

To find the amount owed after 6 years on a loan with continuously compounded interest, 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 loan) which is \( \$ 3800 \). - \( r \) is the annual interest rate (in decimal form). - \( t \) is the time in years. - \( e \) is Euler's number (approximately 2.71828). Since you didn't specify the interest rate, let's say it’s 5% (0.05 in decimal form) for this example. Plugging in the values: \[ A = 3800 \times e^{0.05 \times 6} \approx 3800 \times e^{0.3} \] Calculating \( e^{0.3} \) gives approximately \( 1.34986 \): \[ A \approx 3800 \times 1.34986 \approx 5129.68 \] Thus, after 6 years, you would owe approximately \( \$ 5129.68 \). If your interest rate differs, just substitute it into the formula as needed!