Questions: Complete the first two months of the amortization schedule for a fixed-rate mortgage. Complete parts (a) through (h). a: 0 Mortgage, 144,500; Interest rate, 4.5%; Term of loan, 15 years Fill out the amortization schedule and round all values to the nearest cent. (Do not round until the final answer. Then round to the nearest cent as needed.) Payment Number Total Payment Interest Payment Principal Payment Balance of Principal --- --- --- --- --- 1 (a) 1105.42 (b) (c) (d)

Solution Steps

To complete the amortization schedule for the first two months, we need to calculate the monthly payment, interest payment, principal payment, and remaining balance. The monthly payment can be calculated using the formula for an annuity. The interest payment for each month is calculated by multiplying the remaining balance by the monthly interest rate. The principal payment is the difference between the total payment and the interest payment. The remaining balance is updated by subtracting the principal payment from the previous balance.

The monthly payment \( M \) for a fixed-rate mortgage can be calculated using the formula:

\[ M = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1} \]

where:

• \( P = 144500 \) (principal)
• \( r = \frac{0.045}{12} = 0.00375 \) (monthly interest rate)
• \( n = 15 \times 12 = 180 \) (total number of payments)

Substituting the values, we find:

\[ M \approx 1105.4153 \]

For the first month:

• Interest payment \( I_1 \) is calculated as:

\[ I_1 = \text{Balance} \cdot r = 144500 \cdot 0.00375 \approx 541.875 \]

• Principal payment \( P_1 \) is:

\[ P_1 = M - I_1 \approx 1105.4153 - 541.875 \approx 563.5403 \]

• Remaining balance after the first payment is:

\[ \text{Balance}_1 = \text{Balance} - P_1 \approx 144500 - 563.5403 \approx 143370.8061 \]

For the second month:

• Interest payment \( I_2 \) is calculated as:

\[ I_2 = \text{Balance}_1 \cdot r \approx 143370.8061 \cdot 0.00375 \approx 539.7617 \]

• Principal payment \( P_2 \) is:

\[ P_2 = M - I_2 \approx 1105.4153 - 539.7617 \approx 565.6536 \]

• Remaining balance after the second payment is:

\[ \text{Balance}_2 = \text{Balance}_1 - P_2 \approx 143370.8061 - 565.6536 \approx 142805.1525 \]

Final Answer