You want to buy a $29,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be?

To find your monthly car payment, we can use the formula for calculating the monthly payment on an auto loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (in this case, $29,000).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the number of payments (36 months in this case).

First, let's break this down:

- The annual interest rate is 3%, so the monthly interest rate is:

\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

- The number of months for the loan is 36.

Now, we can substitute these values into the formula and calculate the monthly payment.

\[
M = \frac{29,000 \cdot 0.0025 \cdot (1 + 0.0025)^{36}}{(1 + 0.0025)^{36} - 1}
\]

Let me calculate that.The monthly payment for a $29,000 car loan at a 3% interest rate over 36 months would be approximately **$843.36**.

Would you like more details on the calculation, or do you have any questions?

Here are 5 related questions you might find helpful:
1. What if the interest rate was 4% instead of 3%?
2. How much total interest will you pay over the loan period?
3. What would the monthly payment be for a 48-month loan term?
4. How would a larger down payment affect the monthly payment?
5. How can early repayment impact the total interest paid?

**Tip:** Even a small change in the interest rate or loan duration can significantly affect your monthly payment and the total interest paid over time.

Learn how to calculate the monthly car payments for a $29,000 loan with a 3% interest rate over 36 months. This example covers key concepts such as loan amortization, interest rate calculations, and the use of the loan payment formula. Suitable for students in Grades 10-12.

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