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The problem states:

- Christina bought a new car for $25,000.
- She made a 10% down payment and financed the remaining balance for 36 months with an APR (Annual Percentage Rate) of 3.5%.
- You are to determine the total interest Christina pays over the life of the loan, assuming she makes monthly payments.

### Step-by-step solution:

1. **Down payment**: 
   Christina makes a 10% down payment on the car's price:
   \[
   \text{Down payment} = 0.10 \times 25000 = 2500
   \]
   
2. **Amount financed**: 
   The amount Christina is financing is the car price minus the down payment:
   \[
   \text{Amount financed} = 25000 - 2500 = 22500
   \]

3. **Monthly interest rate**:
   The annual interest rate (APR) is 3.5%, so the monthly interest rate is:
   \[
   \text{Monthly interest rate} = \frac{3.5\%}{12} = \frac{0.035}{12} = 0.00291667
   \]

4. **Monthly payments**:
   The formula for the monthly payment on a loan is:
   \[
   M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
   \]
   where:
   - $M$ is the monthly payment,
   - $P$ is the principal (amount financed),
   - $r$ is the monthly interest rate,
   - $n$ is the total number of payments (36 months in this case).

   Substituting the values:
   \[
   M = 22500 \times \frac{0.00291667(1 + 0.00291667)^{36}}{(1 + 0.00291667)^{36} - 1}
   \]

Let me calculate the monthly payment and then find the total interest paid.It seems there was an issue calculating the monthly payment. I will guide you through the steps so you can calculate it manually or using a calculator.

### To calculate the monthly payment $ M $:
Substitute the values into the formula:
\[
M = 22500 \times \frac{0.00291667(1 + 0.00291667)^{36}}{(1 + 0.00291667)^{36} - 1}
\]

1. Compute $ 1 + 0.00291667 = 1.00291667 $.
2. Raise $ 1.00291667 $ to the power of 36.
3. Multiply this result by 0.00291667.
4. Divide the result by $ (1.00291667^{36} - 1) $.
5. Multiply this by 22500.

Once you have the monthly payment $ M $, you can calculate the **total interest** as follows:

### Total Interest
The total amount paid over the life of the loan is the monthly payment multiplied by the number of months:
\[
\text{Total payments} = M \times 36
\]
The total interest paid is:
\[
\text{Total interest} = \text{Total payments} - 22500
\]

Let me know if you'd like to continue or need further assistance!

---

Here are five related questions:
1. How does the down payment percentage affect the total interest paid?
2. What happens to the monthly payments if the loan term is increased from 36 months to 48 months?
3. How would an increase in the APR from 3.5% to 4.5% affect the monthly payments?
4. How do bi-weekly payments instead of monthly payments affect the total interest?
5. What is the relationship between principal amount and interest for larger loans?

**Tip:** When comparing loan options, always consider both the interest rate and the loan term, as both significantly affect the total cost.

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 total interest Christina pays over the life of the loan.

This problem involves determining the total interest paid on a $25,000 car loan with a 10% down payment and a 3.5% APR over 36 months. Learn how to calculate monthly payments and interest using key formulas like loan amortization.

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