Christina bought a new car for $25,000.  She paid a 10% down payment and financed the remaining balance for 36 months with an APR of 3.5%.  Determine the monthly payment that Christina pays.  Round your answer to the nearest cent, if necessary.

To calculate Christina's monthly payment, let's follow these steps:

### Step 1: Calculate the Down Payment
The car costs $25,000, and Christina makes a 10% down payment.

\[
\text{Down Payment} = 25,000 \times 0.10 = 2,500
\]

### Step 2: Determine the Amount Financed
Subtract the down payment from the total cost to find the amount financed.

\[
\text{Amount Financed} = 25,000 - 2,500 = 22,500
\]

### Step 3: Use the Loan Payment Formula
The formula for the monthly payment $ M $ on a loan with monthly compounding interest is:

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

where:
- $ P = 22,500 $ (the loan principal),
- $ r = \frac{3.5\%}{12 \times 100} = \frac{0.035}{12} \approx 0.0029167 $ (monthly interest rate),
- $ n = 36 $ (loan term in months).

Substitute these values into the formula:

\[
M = 22,500 \cdot \frac{0.0029167 \times (1 + 0.0029167)^{36}}{(1 + 0.0029167)^{36} - 1}
\]

Let’s calculate that:

1. Compute $ (1 + 0.0029167)^{36} $,
2. Multiply by $ r = 0.0029167 $,
3. Then divide by $ (1 + 0.0029167)^{36} - 1 $.

#### Calculating:
Upon solving, we get:

\[
M \approx 661.35
\]

### Final Answer
Christina's monthly payment is approximately **$661.35**.

Would you like more details or have any questions?

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### Related Questions
1. What would her monthly payment be if the loan term were 48 months?
2. How much total interest does Christina pay over the 36 months?
3. What would the monthly payment be with a down payment of 20% instead?
4. How does a higher APR affect the monthly payment?
5. If the APR were reduced to 2.5%, what would her new monthly payment be?

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**Tip:** To lower monthly payments, consider extending the loan term—but keep in mind this increases total interest paid.

Christina bought a new car for $25,000. She paid a 10% down payment and financed the remaining balance for 36 months with an APR of 3.5%. Determine the monthly payment that Christina pays. Round your answer to the nearest cent, if necessary.

Find out how to calculate the monthly car loan payment for a $25,000 vehicle with a 10% down payment, financed over 36 months at a 3.5% APR. This solution breaks down key finance concepts, including loan amortization and interest calculation. Suitable for high school students in Grades 10-12.

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