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.)

We can solve this problem in several steps. First, we calculate the discounted price Janice will pay for the car, then add the additional fees, and finally determine the monthly loan payment using the loan amortization formula.

### Step 1: Calculate the price after discount
The original MSRP is $33,500, and the discount is 20%.

\[
\text{Discounted Price} = 33,500 \times (1 - 0.20) = 33,500 \times 0.80 = 26,800
\]

### Step 2: Add tax and license fees
The additional fees total $1,885. Therefore, the total cost of the car is:

\[
\text{Total Cost} = 26,800 + 1,885 = 28,685
\]

### Step 3: Loan Amortization Formula
To calculate the monthly payment, we use the loan amortization formula:

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

where:
- $M$ is the monthly payment,
- $P$ is the principal loan amount, which is $28,685,
- $r$ is the monthly interest rate, which is the annual rate divided by 12: $ \frac{5.75\%}{12} = \frac{0.0575}{12} \approx 0.0047917$,
- $n$ is the total number of payments, which is $3 \, \text{years} \times 12 \, \text{months/year} = 36 \, \text{months}$.

Now, let's calculate $M$.Janice's monthly payment is approximately **$869.41**.

Would you like further clarification on any part of the calculation?

Here are 5 related questions you might find useful:
1. What happens if the interest rate changes?
2. How would the monthly payment change if the loan period was extended?
3. What is the total interest paid over the 3-year loan?
4. How can you calculate the remaining balance after one year of payments?
5. What is the difference between compounding monthly vs. annually?

**Tip:** When comparing loans, always consider both the interest rate and the loan term to understand the total cost over time.

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.)

Learn how to calculate the monthly payment for a 3-year car loan with a 5.75% annual interest rate, compounded monthly. This problem involves calculating a 20% discount off the MSRP, adding fees, and using the loan amortization formula. Suitable for college or advanced high school students.

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