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Let's break down the problem step by step:

- Christina buys a car for $25,000.
- She makes a 10% down payment.
- The remaining balance is financed for 36 months (3 years) at an APR (Annual Percentage Rate) of 3.5%.
- We need to find the total interest she pays over the life of the loan.

### Step 1: Calculate the down payment
Down payment = 10% of $25,000 = $ 0.10 \times 25,000 = 2,500 $.

### Step 2: Calculate the financed amount
Financed amount = Car price - Down payment = $ 25,000 - 2,500 = 22,500 $.

### Step 3: Use the formula for the monthly payment on a loan
The monthly payment for an amortized loan can be calculated using the formula:

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

Where:
- $ M $ = monthly payment
- $ P $ = principal amount (loan amount) = $22,500
- $ r $ = monthly interest rate = APR / 12 = 3.5% / 12 = 0.002917 (or 0.2917%)
- $ n $ = number of months = 36 months

### Step 4: Plug values into the formula to get the monthly payment

Now, I will calculate the monthly payment and total interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, I can walk you through how to calculate the monthly payment and total interest manually. Let me know if you'd like that, or if you have any questions about the process so far!

Here are some follow-up questions to think about:
1. How do you calculate monthly interest rates from APR?
2. How would the total interest change if the loan duration was longer?
3. What happens to the monthly payments if the interest rate increases?
4. Can you use this formula to calculate any loan payment?
5. How does a down payment affect the total amount financed?

**Tip:** When taking a loan, even a small change in the interest rate can have a significant effect on total payments, especially over long terms.

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%. Assuming she makes monthly payments, determine the total interest Christina pays over the life of the loan. Round your answer to the nearest cent, if necessary.

Learn how to determine the total interest Christina pays on her car loan with a 10% down payment, financed over 36 months at an APR of 3.5%. This problem involves loan financing, percentage calculations, and the use of the amortization formula. Suitable for students in Grades 10-12.

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