You want to buy a $35,000 car. You can make a 10% down payment, and will finance the balance with a 3% interest rate for 36 months (3 years). What will your monthly payments be?

To calculate the monthly payments for a car loan, we can use the **amortized loan payment formula**:

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

Where:
- $M$ is the monthly payment.
- $P$ is the loan principal (the amount you're financing after the down payment).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the number of payments (loan term in months).

### Step 1: Calculate the down payment and loan principal
- The car costs $35,000.
- Down payment is 10%, so:
  \[
  \text{Down payment} = 0.10 \times 35,000 = 3,500
  \]
- The loan principal $P$ is:
  \[
  P = 35,000 - 3,500 = 31,500
  \]

### Step 2: Determine the monthly interest rate and the number of payments
- The annual interest rate is 3%, so the monthly interest rate $r$ is:
  \[
  r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
  \]
- The loan term is 3 years, or $n = 36$ months.

### Step 3: Calculate the monthly payment $M$
Now we plug these values into the formula:
\[
M = \frac{31,500 \cdot 0.0025 \cdot (1 + 0.0025)^{36}}{(1 + 0.0025)^{36} - 1}
\]

Let me compute that.The monthly payment for the car loan will be approximately **$916.06**.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does increasing the loan term affect monthly payments?
2. What happens to the total interest paid if the interest rate rises to 5%?
3. How much total interest will be paid over the course of the loan?
4. What if the down payment were 20% instead of 10%—how would the payments change?
5. How does refinancing a car loan work?

**Tip:** When financing large purchases, making a larger down payment reduces the amount you finance, lowering your monthly payments and total interest paid.

Find out how to calculate the monthly payments for a $35,000 car loan with a 10% down payment and 3% interest rate over 36 months. This problem covers concepts in loan amortization, interest rates, and algebra. Ideal for advanced high school or college students.

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