Jenna bought a new car for $29,000. She paid a 10% down payment and financed the remaining balance for 48 months with an APR of 4.5%. Determine the monthly payment that Jenna pays.

To determine Jenna's monthly payment, we need to break the problem into a few steps. We'll use the formula for monthly payments on a loan:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the loan principal (amount financed after the down payment)
- $ r $ is the monthly interest rate (APR divided by 12)
- $ n $ is the total number of payments (loan term in months)

### Step 1: Calculate the down payment
Jenna made a 10% down payment on a $29,000 car.

\[
\text{Down payment} = 29,000 \times 0.10 = 2,900
\]

### Step 2: Determine the amount financed (principal)
The remaining balance that is financed is:

\[
P = 29,000 - 2,900 = 26,100
\]

### Step 3: Determine the monthly interest rate
The APR is 4.5%, so the monthly interest rate is:

\[
r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

### Step 4: Determine the number of months
Jenna is financing the car for 48 months, so:

\[
n = 48
\]

### Step 5: Calculate the monthly payment
Now, we can plug the values into the monthly payment formula:

\[
M = \frac{26,100 \cdot 0.00375(1 + 0.00375)^{48}}{(1 + 0.00375)^{48} - 1}
\]

Let me calculate this for you.Jenna's monthly payment is approximately **$595.17**.

Would you like further details or have any questions about this calculation?

Here are 5 related questions to expand your understanding:
1. How would the monthly payment change if the loan term were extended to 60 months?
2. What is the total amount Jenna will pay over the 48 months?
3. How much interest will Jenna pay over the life of the loan?
4. How does changing the APR to 5.5% affect the monthly payment?
5. What happens to the monthly payment if Jenna makes a larger down payment?

**Tip:** Increasing your down payment reduces the principal financed, which can significantly lower your monthly payments and the total interest paid.

Learn how to calculate the monthly payment for a car loan with a down payment and an APR of 4.5%. This problem involves key financial concepts, including interest rates and loan amortization, and uses the monthly payment formula. Suitable for students in Grades 10-12.

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