You want to buy a $12,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be?

To find the monthly payment for the car loan, we use the formula for calculating the payment on a loan with interest:

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

Where:
- $M$ is the monthly payment
- $P$ is the principal amount (loan amount), in this case, $12,000
- $r$ is the monthly interest rate (annual interest rate divided by 12)
- $n$ is the total number of payments (loan term in months)

### Step 1: Convert the annual interest rate to a monthly interest rate
- Annual interest rate = 3%
- Monthly interest rate $r = \frac{3}{100 \times 12} = 0.0025$

### Step 2: Calculate the number of months
- Loan term = 3 years, so $n = 36$ months

### Step 3: Plug the values into the formula

\[
M = \frac{12,000 \times 0.0025 \times (1 + 0.0025)^{36}}{(1 + 0.0025)^{36} - 1}
\]

Let me calculate that for you.The monthly payment for the car will be approximately **$348.97** over 36 months.

Would you like further details on how this calculation works, or any specific questions answered?

Here are some related questions:
1. How does the interest rate affect the total amount paid over the loan period?
2. What happens if the loan term is extended to 48 months?
3. How would a down payment impact the monthly payments?
4. What is the total interest paid on this loan after 3 years?
5. How does the loan amortization schedule work?

**Tip**: Paying off a loan early can reduce the total interest paid, even if the monthly payment remains the same.

Discover how to calculate the monthly payments on a $12,000 car loan with a 3% interest rate over 36 months. This example covers algebraic concepts and the loan amortization formula, making it ideal for high school students or anyone learning how to manage finances.

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