You want to buy a $19,000 car. The company is offering a 5% 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 **loan amortization formula**:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount ($19,000 in this case).
- $ r $ is the monthly interest rate (annual rate divided by 12 months).
- $ n $ is the number of payments (36 months for a 3-year loan).

Given:
- $ P = 19,000 $
- Annual interest rate = 5%, so monthly interest rate $ r = \frac{5\%}{12} = 0.004167 $
- $ n = 36 $

Now let's calculate:

\[
M = \frac{19,000 \cdot 0.004167 \cdot (1 + 0.004167)^{36}}{(1 + 0.004167)^{36} - 1}
\]

Calculating step-by-step:

1. $ 1 + 0.004167 = 1.004167 $
2. $ (1.004167)^{36} = 1.1616 $
3. $ 0.004167 \cdot 1.1616 = 0.004842 $
4. $ (1.1616 - 1) = 0.1616 $
5. $ M = \frac{19,000 \cdot 0.004842}{0.1616} = \frac{91.998}{0.1616} \approx 569.38 $

So, your monthly payments will be **$569.38**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the total amount of interest paid over the loan term?
2. How would the monthly payments change if the interest rate were 4% instead of 5%?
3. What would happen to the monthly payments if the loan term were extended to 48 months?
4. How does the loan amortization process affect the total interest paid over time?
5. How is the loan balance calculated at any point during the loan term?

**Tip:** When comparing car loans, consider both the interest rate and the loan term, as longer terms reduce monthly payments but increase total interest paid.

Learn how to calculate the monthly payments for a $19,000 car loan with a 5% interest rate over 36 months. This problem explores key concepts like loan amortization and interest rate calculations, making it suitable for students in Grades 10-12.

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