Questions: b. How much interest is paid in the first month of the loan? How much is paid toward the principal in the first month of the loan? c. How much interest is paid in the last month of the loan? How much is paid toward the principal in the last month of the loan? (Round to the nearest cent as needed.)

Solution Steps

To solve the problem, we need to calculate the interest and principal paid in the first and last months of the loan. The interest for each month can be calculated using the formula: Interest = (Previous Balance) * (Monthly Interest Rate). The principal is then the difference between the total payment and the interest. For the last month, we need to ensure the balance reaches zero.

For the first month, the interest paid is calculated as follows: \[ \text{Interest}_{\text{Month 1}} = 9100 \times 0.0075 = 68.25 \] The principal paid in the first month is then: \[ \text{Principal}_{\text{Month 1}} = 115.28 - 68.25 = 47.03 \]

For the last month, the balance before the payment is \( 113.45 \). The interest paid in the last month is: \[ \text{Interest}_{\text{Month 120}} = 113.45 \times 0.0075 \approx 0.8509 \] The principal paid in the last month is: \[ \text{Principal}_{\text{Month 120}} = 113.45 - 0.8509 \approx 112.5991 \]

Final Answer