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Let's work through the problem step by step. Here's what we need to do:

### Problem Breakdown:
- The price of the home is **$166,000**.
- The bank requires a **20% down payment** and **three points** at closing.
- The home is financed with a **30-year fixed-rate mortgage** at an interest rate of **8.5%**.
- We are asked to calculate parts (a) through (e).

#### Let's address each part:

### a) **Find the required down payment:**
The down payment is **20%** of the total home price.

\[
\text{Down Payment} = \text{Price of Home} \times 0.20
\]
\[
\text{Down Payment} = 166,000 \times 0.20 = 33,200
\]

So, the down payment is **$33,200**.

---

### b) **Find the amount of the mortgage:**
The mortgage amount is the remaining balance after subtracting the down payment from the price of the home.

\[
\text{Mortgage Amount} = \text{Price of Home} - \text{Down Payment}
\]
\[
\text{Mortgage Amount} = 166,000 - 33,200 = 132,800
\]

So, the mortgage amount is **$132,800**.

---

### c) **How much must be paid for the three points at closing?**
A point is **1%** of the mortgage amount, and you're required to pay for **three points**.

\[
\text{Cost of Three Points} = \text{Mortgage Amount} \times \left(\frac{3}{100}\right)
\]
\[
\text{Cost of Three Points} = 132,800 \times 0.03 = 3,984
\]

So, the amount paid for the three points is **$3,984**.

---

### d) **Find the monthly payment (excluding escrowed taxes and insurance):**
We are provided the formula for the monthly payment:

\[
\text{PMT} = \frac{P \times \frac{r}{n}}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]
Where:
- $ P = 132,800 $ (mortgage amount)
- $ r = 8.5\% = 0.085 $ (annual interest rate)
- $ n = 12 $ (monthly payments)
- $ t = 30 $ (number of years)

We can now plug in the values to calculate the monthly payment.

### e) **Find the total cost of interest over 30 years:**
The total interest paid is the total of all payments over 30 years minus the mortgage amount.

---

Let me calculate the monthly payment and total interest for you.### d) **Monthly Payment:**
The monthly payment, excluding taxes and insurance, is approximately **$1,021.12**.

---

### e) **Total Cost of Interest Over 30 Years:**
The total interest paid over the 30-year period is approximately **$234,802.16**.

---

Would you like more details on any of these steps? Here are some related questions for further exploration:

1. How does increasing the down payment affect the monthly payments?
2. What would happen if the interest rate were reduced by 1%?
3. How is the total cost of interest affected by shorter loan durations (e.g., 15 years)?
4. How do the three points at closing impact the overall mortgage cost?
5. What is the impact of making extra payments on the mortgage balance?

**Tip:** Making extra payments on your mortgage, especially early on, can significantly reduce the total interest paid over the life of the loan.

The price of a home is $166,000. The bank requires a 20% down payment and three points at closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Complete parts (a) through (e) below.

Learn how to calculate the down payment, mortgage amount, points at closing, and monthly payment for a home priced at $166,000 with a 20% down payment and an 8.5% interest rate. The mortgage is a 30-year fixed-rate loan, and we calculate the total interest paid over 30 years.

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