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to determine the regular payment​ amount, rounded to the nearest dollar. The price of a home is ​$207 comma 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 7​%. Complete parts​ (a) through​ (e) below.
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Part 1
a. Find the required down payment.

To solve this problem, we'll break it down step by step. First, let's find the required down payment.

### Step 1: Calculate the Down Payment
The down payment is typically a percentage of the total price of the home. Here, the bank requires a 20% down payment.

Given:
- Price of the home $ P = \$207,000 $
- Down payment percentage = 20%

The formula to calculate the down payment is:

\[
\text{Down Payment} = \text{Price of the Home} \times \left(\frac{\text{Down Payment Percentage}}{100}\right)
\]

Substituting the values:

\[
\text{Down Payment} = 207,000 \times \left(\frac{20}{100}\right) = 207,000 \times 0.20
\]

\[
\text{Down Payment} = \$41,400
\]

### Final Answer
The required down payment is **\$41,400**.

Would you like to proceed to the next part of the problem, or do you have any questions about this step? 

Here are five follow-up questions related to this step:

1. How would the down payment change if the percentage required was 15% instead of 20%?
2. What is the loan amount after making the down payment?
3. How does the down payment affect the monthly mortgage payments?
4. If the home price was $250,000, what would be the down payment at 20%?
5. Can you calculate the total initial cost of the down payment plus the three points?

**Tip:** Always double-check your percentage calculations, especially when dealing with large financial amounts.

Learn how to calculate the required down payment for a $207,000 home mortgage. This problem involves understanding percentages and mortgage calculations. Suitable for adults learning about home financing.

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