Use PMT equals StartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis Over left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndFraction to determine the regular payment​ amount, rounded to the nearest dollar. The price of a home is ​$119,000. 

The bank requires a​ 20% down payment and three points at the time of closing. The cost of the home is financed with a​ 30-year fixed-rate mortgage at 8.5%

a. Find the required down payment.

b. Find the amount of the mortgage.

c. How much must be paid for the three points at​ closing? (Round to the nearest dollar as​ needed.)

d. Find the monthly payment​ (excluding escrowed taxes and​ insurance).(Round to the nearest dollar as​ needed.)

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**.

---

### 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**.

---

### 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**.

---

### 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?

---

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.

Use PMT equals StartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis Over left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndFraction to determine the regular payment​ amount, rounded to the nearest dollar. The price of a home is ​$119,000. The bank requires a​ 20% down payment and three points at the time of closing. The cost of the home is financed with a​ 30-year fixed-rate mortgage at 8.5%. a. Find the required down payment. b. Find the amount of the mortgage. c. How much must be paid for the three points at​ closing? (Round to the nearest dollar as​ needed.) d. Find the monthly payment​ (excluding escrowed taxes and​ insurance).(Round to the nearest dollar as​ needed.)

Learn how to calculate the down payment, mortgage amount, points at closing, and monthly payment for a $119,000 home with a 30-year fixed-rate mortgage at 8.5% interest. Includes step-by-step guidance on using the PMT formula and solving percentage calculations.

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