Let’s break down and solve the problem step-by-step using the PMT formula and other calculations related to mortgage payments.

Given Information:

• Price of the home (P): $119,000
• Down payment percentage: 20%
• Mortgage rate (r): 8.5% annually (or 0.085)
• Term of the loan: 30 years
• Number of payments per year (n): 12 (monthly payments)
• Three points: 3% of the mortgage amount.

We'll now calculate each part:

a. Find the required down payment.

The down payment is calculated as 20% of the home price: $\text{Down payment} = 0.20 \times 119,000 = 23,800$ So, the down payment is $23,800.

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b. Find the amount of the mortgage.

The mortgage amount is the total cost of the home minus the down payment: $\text{Mortgage amount} = 119,000 - 23,800 = 95,200$ So, the mortgage amount is $95,200.

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c. How much must be paid for the three points at closing?

Three points are 3% of the mortgage amount: $\text{Points cost} = 0.03 \times 95,200 = 2,856$ So, the amount to be paid for the three points at closing is $2,856.

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d. Find the monthly payment (excluding escrowed taxes and insurance).

We use the PMT formula for the monthly mortgage payment:

$\text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}}$ Where:

• $P = 95,200$ (mortgage amount)
• $r = 0.085$ (annual interest rate)
• $n = 12$ (number of monthly payments in a year)
• $t = 30$ (loan term in years)

Substitute the values into the formula: $\text{PMT} = \frac{95,200 \left( \frac{0.085}{12} \right)}{1 - \left( 1 + \frac{0.085}{12} \right)^{-12 \times 30}}$ Now, I'll calculate the monthly payment.The monthly mortgage payment, excluding escrowed taxes and insurance, is $732.

Summary of results:

1. Down payment: $23,800
2. Mortgage amount: $95,200
3. Three points at closing: $2,856
4. Monthly payment: $732

Would you like more details or have any questions?

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Here are five related questions for further exploration:

1. How would the monthly payment change if the interest rate increased to 9%?
2. What would be the total interest paid over the 30-year loan term?
3. How does the size of the down payment affect the monthly mortgage payment?
4. What is the impact of making extra payments on a mortgage?
5. How do mortgage points affect the overall cost of the loan?

Tip: A larger down payment can significantly reduce both the amount of the loan and the monthly payments.