Questions: Completing a few rows of an amortization table Hawraa To help buy her new condominium, Lucy is taking out a 247,000 mortgage loan for 30 years at 3.5% annual interest. Her monthly payment for this loan is 1109.14. Fill in all the blanks in the amortization schedule for the loan. Assume that each month is 1/12 of a year. Round your answers to the nearest cent. Payment number Interest payment Principal payment New loan balance ------------ 1 2 246,221.42 ... ... ... ... 150 509.21 599.93 173,985.19 151

Solution Steps

To fill in the blanks in the amortization schedule, we need to calculate the interest payment, principal payment, and new loan balance for each specified payment number. The interest payment for a given month is calculated by multiplying the remaining loan balance by the monthly interest rate. The principal payment is the difference between the total monthly payment and the interest payment. The new loan balance is the previous balance minus the principal payment.

The monthly interest rate is calculated as follows: \[ \text{monthly interest rate} = \frac{0.035}{12} = 0.002916666666666667 \]

For payment number 1, the calculations are:

• Remaining loan balance: \( \$247,000 \)
• Interest payment: \[ \text{Interest payment}_1 = 247000 \times 0.002916666666666667 \approx 720.25 \]
• Principal payment: \[ \text{Principal payment}_1 = 1109.14 - 720.25 \approx 388.89 \]
• New loan balance: \[ \text{New balance}_1 = 247000 - 388.89 \approx 246611.11 \]

For payment number 2, using the new balance from payment 1:

• Remaining loan balance: \( \$246611.11 \)
• Interest payment: \[ \text{Interest payment}_2 = 246611.11 \times 0.002916666666666667 \approx 719.06 \]
• Principal payment: \[ \text{Principal payment}_2 = 1109.14 - 719.06 \approx 390.08 \]
• New loan balance: \[ \text{New balance}_2 = 246611.11 - 390.08 \approx 246221.03 \]

For payment number 151, using the given balance from payment 150:

• Remaining loan balance: \( \$173985.19 \)
• Interest payment: \[ \text{Interest payment}_{151} = 173985.19 \times 0.002916666666666667 \approx 507.21 \]
• Principal payment: \[ \text{Principal payment}_{151} = 1109.14 - 507.21 \approx 601.93 \]
• New loan balance: \[ \text{New balance}_{151} = 173985.19 - 601.93 \approx 173383.26 \]

Final Answer