Suppose that you decide to buy a car for 

​$31 comma 63531,635​, 

including taxes and license fees. You saved 

$ 9000$9000 

for a down payment and can get a 

threethree​-year 

car loan at 

7.527.52​%. 

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 EndEndFractionPMT=Prn1−1+rn−nt 

to find the monthly payment and the total interest for the loan.

Question content area bottom

Part 1

The monthly payment is 

​$enter your response here.

​(Round to the nearest cent as​ needed.)

We can solve this problem using the **PMT formula** for finding the monthly payment on a loan:

\[
PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

Where:
- $ P $ is the loan principal (the amount you need to borrow),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the number of payments per year (monthly payments means $ n = 12 $),
- $ t $ is the loan term in years.

### Step 1: Identify the values:
- **Car price**: $31,635
- **Down payment**: $9,000
- **Loan principal**: $ P = 31,635 - 9,000 = 22,635 $
- **Annual interest rate**: $ r = 7.52\% = 0.0752 $
- **Loan term**: $ t = 3 $ years
- **Number of payments per year**: $ n = 12 $

### Step 2: Substitute the values into the formula:
\[
PMT = \frac{22,635 \left( \frac{0.0752}{12} \right)}{1 - \left(1 + \frac{0.0752}{12}\right)^{-12 \times 3}}
\]

I will now calculate the monthly payment using this formula.The monthly payment for the car loan is approximately **$704.30**.

Would you like to see the total interest paid over the loan period, or do you have any other questions?

Here are 5 follow-up questions for further exploration:
1. How can you calculate the total amount paid over the loan term?
2. How do different loan terms (e.g., 4 or 5 years) affect the monthly payment?
3. What would be the monthly payment if the down payment increased?
4. How does the interest rate affect the overall loan cost?
5. Can you calculate the loan's amortization schedule?

**Tip**: Making extra payments towards the loan principal can significantly reduce the total interest paid over the loan's duration.

Suppose that you decide to buy a car for $31,635, including taxes and license fees. You saved $9,000 for a down payment and can get a three-year car loan at 7.52%. Use the PMT formula to find the monthly payment and the total interest for the loan.

Find the monthly payment for a car loan of $22,635 over three years at an interest rate of 7.52%. Use the PMT formula to calculate the monthly installment and total interest. Learn key loan calculation concepts, including interest rates and annuity formulas, suitable for Grades 10-12.

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