An amount of \( \$ 37,000 \) is borrowed for 10 years at \( 6.5 \% \) interest, compounded annually. Assuming that no payments are made, find the amount owed after 10 years. Use the calculator provided and round your answer to the nearest dollar.

To find the amount owed after 10 years with an initial borrowing of \( \$ 37,000 \) at a compound interest rate of \( 6.5\% \), we will use the formula for compound interest: \[ A = P(1 + r)^t \] 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 number of years the money is invested or borrowed. Plugging in the values: - \( P = 37,000 \) - \( r = 0.065 \) - \( t = 10 \) Calculating, \[ A = 37000(1 + 0.065)^{10} \] \[ A = 37000(1.065)^{10} \] Now, calculate \( (1.065)^{10} \): \[ (1.065)^{10} \approx 1.7137 \] Now multiply by \( 37000 \): \[ A \approx 37000 \times 1.7137 \approx 68608.90 \] Rounding to the nearest dollar, the amount owed after 10 years is approximately \( \$ 68,609 \).