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The problem describes a scenario where Christina buys a car for $26,000, makes a 20% down payment, and finances the remaining balance for 48 months with an APR (Annual Percentage Rate) of 4.5%. We need to determine the monthly payment she will make.

### Step 1: Calculate the Loan Amount
Since Christina pays a 20% down payment, the loan amount is the remaining 80% of the car's price.

\[
\text{Loan Amount} = 26000 \times (1 - 0.20) = 26000 \times 0.80 = 20800
\]

### Step 2: Monthly Interest Rate
The APR is 4.5%, which is the annual interest rate. To get the monthly interest rate, divide by 12:

\[
\text{Monthly Interest Rate} = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

### Step 3: Apply the Loan Payment Formula
The formula for the monthly payment on an amortized loan is:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount = $20,800
- $ r $ = monthly interest rate = 0.00375
- $ n $ = total number of months = 48

Now, substitute the values:

\[
M = \frac{20800 \cdot 0.00375 \cdot (1 + 0.00375)^{48}}{(1 + 0.00375)^{48} - 1}
\]

### Step 4: Solve for Monthly Payment
I'll calculate this for you.The monthly payment that Christina will need to make is approximately **$474.31**.

Would you like more details or have any questions?

Here are five related questions to expand on this:
1. How would the payment change if the APR were higher or lower?
2. What is the total amount Christina will pay over the 48 months?
3. How much interest will Christina pay over the life of the loan?
4. What happens if Christina decides to pay off the loan early?
5. How would the down payment affect the monthly payments if it were increased or decreased?

**Tip:** Increasing your down payment can significantly reduce the amount of interest paid over the life of a loan.

Christina bought a new car for $26,000. She paid a 20% down payment and financed the remaining balance for 48 months with an APR of 4.5%. Determine the monthly payment Christina pays. Round your answer to the nearest cent, if necessary.

Determine the monthly car loan payment for a $26,000 purchase with a 20% down payment and a 4.5% APR over 48 months. Step-by-step solution includes loan amount, monthly interest rate, and amortization formula.

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