A car dealer offered an end-of-year clearance that was 20% off the MSRP of $33,500. Janice Ng agrees to that price plus additional tax and license fees of $1,885. If she obtains a 3-year loan at an annual interest rate of 5.75% compounded monthly, what is her monthly payment (in dollars)? (Round your answer to the nearest cent.)

To determine Janice Ng's monthly car payment, we need to break the problem into a few steps:

1. **Calculate the sale price after the discount:**
   The original MSRP (Manufacturer's Suggested Retail Price) is $33,500, and the dealer offers a 20% discount. Let's first calculate the sale price.

   \[
   \text{Discount amount} = 0.20 \times 33,500 = 6,700
   \]
   \[
   \text{Sale price} = 33,500 - 6,700 = 26,800
   \]

2. **Add the tax and license fees:**
   Janice will also have to pay additional fees of $1,885.

   \[
   \text{Total amount to be financed} = 26,800 + 1,885 = 28,685
   \]

3. **Set up the loan details:**
   - Loan amount: $28,685
   - Loan term: 3 years (36 months)
   - Annual interest rate: 5.75%, compounded monthly
   - Monthly interest rate: $\frac{5.75}{12} = 0.47917\%$ or $0.0047917$ in decimal form

4. **Use the formula for the monthly payment on an amortized loan:**

   \[
   M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
   \]

   Where:
   - $M$ = monthly payment
   - $P$ = loan principal ($28,685)
   - $r$ = monthly interest rate (0.0047917)
   - $n$ = number of payments (36 months)

Now let's calculate the monthly payment.Janice Ng's monthly payment on the 3-year loan would be approximately **$869.41**.

Would you like more details on how the formula works or have any other questions?

Here are 5 related questions for further exploration:
1. How much total interest will Janice pay over the life of the loan?
2. What would her monthly payment be if the interest rate were 4.5% instead of 5.75%?
3. How would her payment change if she chose a 5-year loan instead of 3 years?
4. What is the difference in total cost between paying cash versus taking the loan?
5. How does the monthly compounding affect the total amount paid compared to annual compounding?

**Tip:** When considering loans, always pay attention to both the interest rate and the loan term to understand the total cost.

A car dealer offered an end-of-year clearance that was 20% off the MSRP of $33,500. Janice Ng agrees to that price plus additional tax and license fees of $1,885. If she obtains a 3-year loan at an annual interest rate of 5.75% compounded monthly, what is her monthly payment (in dollars)? (Round your answer to the nearest cent.)

Find the monthly payment for Janice Ng's car loan after a 20% discount off the MSRP of $33,500 and additional fees of $1,885. Learn how to apply the loan amortization formula with an annual interest rate of 5.75% compounded monthly. Suitable for Grades 11-12 students.

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