Suppose you take out a loan for 160 days in the amount of \( \$ 12,000 \) at \( 7 \% \) ordinary interest. After 40 days, you make a partial payment of \( \$ 1,500 \). After another 60 days, you make a second partial payment of \( \$ 2,000 \). What is the final amount (in \( \$ \) ) due on the loan? (Round your answer to the nearest cent.)

To find the final amount due on the loan, we can break the calculations down into steps. 1. **Calculate interest for the first 40 days:** - Principal = \( 12,000 \) - Rate = \( 7\% \) or \( 0.07 \) - Time = \( 40/360 \) (using ordinary interest) - Interest = \( 12,000 \times 0.07 \times \frac{40}{360} = 12,000 \times 0.07 \times 0.1111 \approx 98.67 \) Total amount after 40 days: \[ 12,000 + 98.67 = 12,098.67 \] 2. **Subtract the first partial payment of \( 1,500 \):** \[ 12,098.67 - 1,500 = 10,598.67 \] 3. **Calculate interest for the next 60 days:** - New Principal = \( 10,598.67 \) - Time = \( 60/360 \) - Interest = \( 10,598.67 \times 0.07 \times \frac{60}{360} \approx 10,598.67 \times 0.07 \times 0.1667 \approx 74.72 \) Total amount after 100 days: \[ 10,598.67 + 74.72 = 10,673.39 \] 4. **Subtract the second partial payment of \( 2,000 \):** \[ 10,673.39 - 2,000 = 8,673.39 \] 5. **Calculate interest for the remaining 60 days (total 160 days now):** - New Principal = \( 8,673.39 \) - Time = \( 60/360 \) - Interest = \( 8,673.39 \times 0.07 \times \frac{60}{360} \approx 8,673.39 \times 0.07 \times 0.1667 \approx 60.89 \) Total amount due at the end: \[ 8,673.39 + 60.89 = 8,734.28 \] So, the final amount due on the loan is approximately \( \text{\$8,734.28} \).