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 calculate the amount owed after 5 years on a loan of \( \$12,450 \) at an interest rate of \( 4.56\% \), compounded quarterly, we use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount owed after time \( t \) - \( P \) is the principal amount (\$12,450) - \( r \) is the annual interest rate (4.56% = 0.0456) - \( n \) is the number of times that interest is compounded per year (4 for quarterly) - \( t \) is the time the money is invested or borrowed (5 years) Plugging in the values: \[ A = 12450 \left(1 + \frac{0.0456}{4}\right)^{4 \times 5} \] Calculating it step by step: 1. Calculate \( \frac{0.0456}{4} = 0.0114 \) 2. Add 1: \( 1 + 0.0114 = 1.0114 \) 3. Calculate \( 4 \times 5 = 20 \) 4. Raise it to the power of 20: \( (1.0114)^{20} \approx 1.2523 \) 5. Now multiply by the principal: \( A \approx 12450 \times 1.2523 \approx 15517.73 \) Rounding to the nearest dollar: \[ A \approx 15518 \] Thus, the amount owed after 5 years is \( \boxed{15518} \).