Marta takes a loan of \( \$ 12,450 \) at an interest rate of \( 4.56 \% \), compounded quarterly. Assuming no payments are made, find the amount owed after 5 years. Round to the nearest dollar. Type your numerical answer below.

To find the amount owed after 5 years with the given loan details, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after \( n \) years, including interest. - \( P \) is the principal amount (the initial loan amount, which is \( 12,450 \)). - \( r \) is the annual interest rate (decimal) (4.56% becomes \( 0.0456 \)). - \( n \) is the number of times that interest is compounded per year (quarterly means \( 4 \)). - \( t \) is the time the money is invested for in years (5 years). Substituting the values into the formula: \[ A = 12450 \left(1 + \frac{0.0456}{4}\right)^{4 \times 5} \] Calculating further: \[ A = 12450 \left(1 + 0.0114\right)^{20} \] \[ A = 12450 \left(1.0114\right)^{20} \] Calculating \( (1.0114)^{20} \): \[ (1.0114)^{20} \approx 1.2686 \] Now, we calculate \( A \): \[ A \approx 12450 \times 1.2686 \approx 15851.67 \] Rounding to the nearest dollar, the amount owed after 5 years is approximately \( \$15,852 \).