*Untitled - Notepad File Edit Format View Help 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 follow these steps: 1. **Calculate the interest for the first 40 days:** The formula for ordinary interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{360} \] For the first 40 days: \[ \text{Interest} = 12,000 \times 0.07 \times \frac{40}{360} = 12,000 \times 0.07 \times 0.1111 \approx 12,000 \times 0.007 = 84.00 \] Total amount after 40 days = Principal + Interest = \( 12,000 + 84 = 12,084 \). 2. **Deduct the first payment of $1,500:** \[ 12,084 - 1,500 = 10,584 \] 3. **Calculate the interest for the next 60 days (from $10,584):** \[ \text{Interest} = 10,584 \times 0.07 \times \frac{60}{360} \approx 10,584 \times 0.07 \times 0.1667 \approx 10,584 \times 0.01167 \approx 123.55 \] Total amount after next 60 days = Principal + Interest = \( 10,584 + 123.55 = 10,707.55 \). 4. **Deduct the second payment of $2,000:** \[ 10,707.55 - 2,000 = 8,707.55 \] 5. **Calculate the interest for the final 60 days (from $8,707.55):** \[ \text{Interest} = 8,707.55 \times 0.07 \times \frac{60}{360} \approx 8,707.55 \times 0.07 \times 0.1667 \approx 8,707.55 \times 0.01167 \approx 101.80 \] Total amount due at the end = Principal + Interest = \( 8,707.55 + 101.80 \approx 8,809.35 \). So, the final amount due on the loan after 160 days is approximately **$8,809.35**.