Questions: Use PMT = P(r/n) / [1 - (1 + r/n)^(-n t)] to determine the regular payment amount, rounded to the nearest dollar. The price of a home is 174,000. 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 7.5%. Complete parts (a) through (e) below. a. Find the required down payment.

Use PMT = P(r/n) / [1 - (1 + r/n)^(-n t)] to determine the regular payment amount, rounded to the nearest dollar. The price of a home is 174,000. 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 7.5%. Complete parts (a) through (e) below. a. Find the required down payment.
Transcript text: Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $\$ 174,000$. 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 $7.5 \%$. Complete parts (a) through (e) below. a. Find the required down payment. $\square$
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Solution

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Solution Steps

To solve this problem, we need to follow these steps:

  1. Calculate the required down payment, which is 20% of the home's price.
  2. Calculate the loan amount by subtracting the down payment from the home's price.
  3. Use the given formula to determine the regular payment amount (PMT).

Let's start with part (a) and calculate the required down payment.

Solution Approach
  1. Calculate the down payment as 20% of the home's price.
Step 1: Calculate the Down Payment

The down payment is calculated as a percentage of the price of the home. Given that the down payment is 20%, we can calculate it as follows:

\[ \text{Down Payment} = 0.20 \times \$174,000 \]

Step 2: Perform the Multiplication

Now, we perform the multiplication to find the down payment:

\[ \text{Down Payment} = 0.20 \times 174,000 = 34,800 \]

Final Answer

The required down payment is:

\[ \boxed{\$34,800} \]

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