https://file.aiquickdraw.com/mathbot/file/1727361105639mvqpt6cz.jpg

Let's go through the details in the image.

### Problem Information:
- Mortgage amount: $288,500
- Term: 15 years
- Annual interest rate: 5.1%

### Part (a) - Find the monthly payment on this mortgage:
To calculate the monthly payment, we use the following mortgage formula:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal = \$288,500
- $ r $ = monthly interest rate = $\frac{5.1\%}{12} = 0.00425$
- $ n $ = total number of payments = 15 years × 12 months/year = 180 months

### Part (b) - First two rows of the amortization schedule:
- **Interest Payment (1st Payment)** is given as \$1,227.
- **Principal Payment (1st Payment)** can be found by subtracting the interest payment from the total monthly payment.
  
I’ll calculate the monthly payment and the first two rows of the amortization schedule. Let's start.The monthly payment for the mortgage is approximately **$2,296.50**.

### Part (b) - First two rows of the amortization schedule:
- The interest payment for the first month is given as **$1,227**.
- The principal payment for the first month is the total payment minus the interest payment:
  \[
  \text{Principal Payment} = 2296.50 - 1227
  \]
- The balance of the loan after the first payment will be the initial balance minus the principal payment.

Let's calculate the first and second rows of the amortization schedule.Here are the calculations for the first two rows of the amortization schedule:

1. **First Payment**:
   - Interest Payment: **$1,227** (given)
   - Principal Payment: **$1,069.50**
   - Balance of Loan after Payment: **$287,430.50**

2. **Second Payment**:
   - Interest Payment: **$1,221.58**
   - Principal Payment: **$1,074.92**
   - Balance of Loan after Payment: **$286,355.59**

Let me know if you'd like further details or additional questions. Here are five related questions:

1. How does changing the interest rate affect the monthly payment?
2. What would the monthly payment be if the loan term was 30 years instead of 15?
3. How do you calculate the total interest paid over the loan term?
4. What impact does paying extra towards the principal each month have on the loan?
5. How does an adjustable-rate mortgage differ from a fixed-rate mortgage?

**Tip**: Regularly check how extra payments toward the principal can significantly reduce the total interest and the loan term.

Suppose you take out a $288,500 mortgage for 15 years at 5.1% interest. (a) Find the monthly payment on this mortgage. (b) Fill out the first two rows of the amortization schedule below. Round your answers to the nearest dollar.

Learn how to calculate the monthly payment for a $288,500 mortgage with a 15-year term at 5.1% interest. This problem also walks through the first two rows of an amortization schedule, showing the interest, principal payments, and the remaining loan balance.

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