Suppose that you decide to buy a car for ​$25 comma 63525,635​, including taxes and license fees. You saved $ 6000$6000 for a down payment and can get a threethree​-year car loan at 7.447.44​%. Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFractionPMT=
P
r
n
1−1+
r
n−nt to find the monthly payment and the total interest for the loan.
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Part 1
The monthly payment is ​$enter your response here.
​(Round to the nearest cent as​ needed.)

To calculate the monthly payment for the car loan, we can use the formula:

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

### Given:
- **Car Price (P)**: $25,635
- **Down Payment**: $6,000
- **Loan Amount**: $ P - \text{Down Payment} = 25,635 - 6,000 = 19,635 $
- **Annual Interest Rate (r)**: 7.44% or 0.0744
- **Loan Term (t)**: 3 years
- **Number of Payments per Year (n)**: 12 (monthly)

### Calculating Variables:
1. **Loan Amount (P)**: $ 19,635 $
2. **Monthly Interest Rate**: $ \frac{r}{n} = \frac{0.0744}{12} = 0.0062 $
3. **Total Number of Payments**: $ nt = 12 \times 3 = 36 $

### Plugging Values into the Formula:
\[
PMT = \frac{19,635 \left(0.0062\right)}{1 - \left(1 + 0.0062\right)^{-36}}
\]

### Calculating:
1. Calculate the denominator:
   \[
   1 + 0.0062 = 1.0062
   \]
   \[
   (1.0062)^{-36} \approx 0.8358
   \]
   \[
   1 - 0.8358 \approx 0.1642
   \]

2. Calculate the monthly payment:
   \[
   PMT = \frac{19,635 \times 0.0062}{0.1642} \approx \frac{121.763}{0.1642} \approx 741.03
   \]

### Monthly Payment:
\[
PMT \approx 741.03
\]

### Total Payment and Interest:
1. **Total Payment over 3 Years**:
   \[
   \text{Total Payment} = PMT \times 36 = 741.03 \times 36 \approx 26,676.08
   \]

2. **Total Interest**:
   \[
   \text{Total Interest} = \text{Total Payment} - \text{Loan Amount} = 26,676.08 - 19,635 \approx 7,041.08
   \]

### Summary:
- **Monthly Payment**: $741.03
- **Total Interest**: $7,041.08

Would you like any more details or have any questions? Here are some related questions you might consider:

1. How would the monthly payment change with a different interest rate?
2. What would the impact of a larger down payment be on the total interest paid?
3. How does the loan term affect monthly payments and total interest?
4. What other costs should be considered when budgeting for a car purchase?
5. How can I improve my credit score to get a better loan rate? 

**Tip**: Always compare loan offers from different lenders to find the best interest rate and terms.

Suppose that you decide to buy a car for $25,635, including taxes and license fees. You saved $6,000 for a down payment and can get a three-year car loan at 7.44%. Use PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] to find the monthly payment and the total interest for the loan.

Discover how to calculate the monthly payment and total interest for a car loan of $25,635 with a $6,000 down payment and a 7.44% interest rate over three years. This guide includes detailed calculations and financial concepts, suitable for Grades 10-12.

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