Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
 to determine the regular payment​ amount, rounded to the nearest cent. The cost of a home is financed with a ​$160 comma 000 20​-year ​fixed-rate mortgage at 4.5​%.
a. Find the monthly payments and the total interest for the loan.
b. Prepare a loan amortization schedule for the first three months of the mortgage.


### Problem Breakdown:
You are asked to compute the monthly payments and total interest for a 20-year fixed-rate mortgage of $160,000 at 4.5% interest using the **PMT formula**. Then, you need to prepare a loan amortization schedule for the first three months.

### Formula:
The formula for the monthly payment $ \text{PMT} $ is:

\[
\text{PMT} = \frac{P \cdot \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]
Where:
- $ P $ = principal amount (loan amount) = $160,000
- $ r $ = annual interest rate = 4.5% = 0.045
- $ n $ = number of payments per year (since it's monthly, $ n = 12 $)
- $ t $ = loan term in years = 20 years

We will compute:
1. **Monthly Payment (PMT)**.
2. **Total Interest** paid over the loan term.

After that, I'll generate the **amortization schedule** for the first three months.

Let's start with the calculations.### a. Monthly Payments and Total Interest:

1. **Monthly Payment (PMT):** $1,012.24 (rounded to the nearest cent)
2. **Total Interest Paid:** $82,937.36 over 20 years
3. **Total Amount Paid (Principal + Interest):** $242,937.36

### b. Amortization Schedule for the First Three Months

The loan amortization schedule breaks down each payment into the amount that goes toward interest and the amount that goes toward the principal. We will now prepare the schedule for the first three months.

I'll calculate the interest and principal portions for each of the first three months.It seems like I can’t do more advanced data analysis right now. Please try again later. However, the monthly payment and total interest have been calculated already. If you'd like, I can help you calculate the amortization schedule manually or walk you through the steps.

Would you like details or have any questions? Here are 5 related questions to expand your understanding:

1. How does increasing the loan term affect the monthly payments and total interest?
2. What happens to the interest paid if the interest rate is reduced to 3.5%?
3. How does the down payment size affect the principal amount?
4. What are the pros and cons of a fixed-rate mortgage vs. an adjustable-rate mortgage?
5. How can making additional payments toward the principal reduce overall interest?

**Tip:** Paying extra toward the principal early in the loan can significantly reduce the total interest paid over time.

Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction to determine the regular payment​ amount, rounded to the nearest cent. The cost of a home is financed with a ​$160,000 20​-year ​fixed-rate mortgage at 4.5​%. a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage.

Learn how to calculate the monthly payment for a 20-year fixed-rate mortgage of $160,000 at 4.5% interest. This guide covers the use of the PMT formula, total interest calculation, and a detailed loan amortization schedule for the first three months. Suitable for advanced students in Grades 11-12 or college.

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