Paula is considering the purchase of a new car. She has narrowed her search to two cars that are equally appealing to her. Car A costs $28,000, and Car B costs $28,300. The manufacturer of Car A is offering 0% financing for 48 months with zero down, while the manufacturer of Car B is offering a rebate of $2000 at the time of purchase plus financing at the rate of 3%/year compounded monthly over 48 months with zero down. If Paula has decided to buy the car with the lower net cost to her, which car should she purchase? (Round numerical values to the nearest cent.)


To determine which car has the lower net cost to Paula, we need to compute the total cost for both Car A and Car B, factoring in the financing options and any rebates. Let's break down the problem step by step.

### Car A:
- **Cost:** $28,000
- **Financing:** 0% financing over 48 months

Since there is no interest on the financing for Car A, Paula would only pay the car's price divided evenly over 48 months. The total cost of Car A would simply be the initial cost of $28,000.

### Car B:
- **Cost:** $28,300
- **Rebate:** $2000, reducing the cost to:
  
  \[
  28,300 - 2000 = 26,300
  \]

- **Financing rate:** 3% per year, compounded monthly.
- **Loan term:** 48 months

Now, we need to calculate the total cost of Car B using the monthly payment formula for a loan:

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

Where:
- $ M $ is the monthly payment,
- $ P $ is the loan principal, which is $26,300,
- $ r $ is the monthly interest rate (annual rate of 3%, so $ r = \frac{0.03}{12} = 0.0025 $),
- $ n $ is the number of monthly payments (48 months).

Let’s calculate the monthly payment $ M $, and then determine the total cost over the loan term.For **Car B**:
- The monthly payment is approximately **$582.13**.
- The total cost over 48 months is approximately **$27,942.37**.

### Conclusion:
- **Car A** has a total cost of $28,000.
- **Car B** has a total cost of $27,942.37.

Since Car B has a slightly lower net cost, Paula should choose **Car B**.

Would you like further details or explanations on any part of this solution?

Here are five related questions to extend your understanding:
1. What factors influence the total cost of a loan?
2. How would the comparison change if the interest rate for Car B were higher, say 5%?
3. What if Car A offered a rebate instead of 0% financing—how would you compare costs?
4. How would early repayment of the loan for Car B affect the total interest paid?
5. What are other benefits and risks of choosing financing options with interest rates?

**Tip:** When comparing financing offers, always account for both the principal reduction (like a rebate) and the interest accumulated over time.

Paula is considering the purchase of a new car. She has narrowed her search to two cars that are equally appealing to her. Car A costs $28,000, and Car B costs $28,300. The manufacturer of Car A is offering 0% financing for 48 months with zero down, while the manufacturer of Car B is offering a rebate of $2000 at the time of purchase plus financing at the rate of 3%/year compounded monthly over 48 months with zero down. If Paula has decided to buy the car with the lower net cost to her, which car should she purchase? (Round numerical values to the nearest cent.)

Compare the total cost of purchasing a car with 0% financing versus 3% interest compounded monthly with a rebate. Learn how to calculate monthly payments and determine which financing option offers the lower total cost. This problem includes key financial concepts like loan payment formulas and compound interest, suitable for Grades 10-12.

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