To solve the given problems, let’s break them down step by step.

Step 1: Calculate the Down Payment

The down payment is 20% of the list price: $\text{Down Payment} = 565,000 \times 0.20 = 113,000$

Step 2: Monthly Payment Calculation

You are financing the remaining amount after the down payment:

$\text{Loan Amount} = 565,000 - 113,000 = 452,000$

For a 15-year mortgage with a 3.2% annual interest rate, we use the formula for the monthly mortgage payment:

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

Where:

• $P$ = Loan Amount = 452,000
• $r$ = Monthly Interest Rate = $\frac{3.2\%}{12} = 0.0026667$
• $n$ = Total Number of Payments = $15 \cdot 12 = 180$

Substitute the values:

$M = 452,000 \cdot \frac{0.0026667(1+0.0026667)^{180}}{(1+0.0026667)^{180} - 1}$

Using a calculator:

$M \approx 452,000 \cdot 0.006958 = 3,145.92$

So, the monthly payment is approximately $3,145.92.

Step 3: Total Payment Over 15 Years

The total payment is the monthly payment multiplied by the total number of payments:

$\text{Total Payment} = M \cdot n = 3,145.92 \cdot 180 \approx 566,265.60$

Summary of Results:

1. Down Payment: $113,000
2. Monthly Payment: $3,145.92
3. Total Payment Over 15 Years: $566,265.60

Let me know if you’d like a detailed explanation of any step or further calculations.

Questions to Explore Further:

1. How does the down payment affect the total interest paid over 15 years?
2. What would the monthly payment be if the interest rate increased to 4%?
3. How much total interest is paid over the life of the loan?
4. What would the monthly payment be for a 30-year loan instead of 15 years?
5. How does paying extra toward the principal each month affect the total loan cost?

Tip: When financing a house, using a mortgage calculator can help visualize the impact of different interest rates and loan durations.