Fritz Benjamin buys a car costing $24,400. He agrees to make payments at the end of each monthly period for 4 years. He pays 9.6% interest, compounded monthly.
What is the amount of each payment?

This problem involves calculating the monthly payment on a car loan, which can be solved using the formula for the **present value of an annuity**. The formula to calculate the monthly payment $ P $ is:

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

Where:
- $ A $ is the principal loan amount (in this case, $24,400),
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the total number of payments (months),
- $ P $ is the monthly payment.

### Step 1: Identify the given values
- **Principal** $ A = 24,400 $
- **Annual interest rate** $ 9.6\% $ or $ 0.096 $ in decimal form
- **Loan term** is 4 years, which is $ 4 \times 12 = 48 $ months
- **Monthly interest rate** $ r = \frac{0.096}{12} = 0.008 $

### Step 2: Substitute values into the formula
\[
P = \frac{24,400 \times 0.008 \times (1 + 0.008)^{48}}{(1 + 0.008)^{48} - 1}
\]

Let me calculate this for you.The amount of each monthly payment is approximately **$614.17**.

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the monthly payment change if the interest rate were lower?
2. What would the monthly payment be if the loan term was only 3 years instead of 4?
3. How much total interest will Fritz Benjamin pay over the 4 years?
4. How does compound interest differ from simple interest in this type of loan?
5. How would a larger down payment affect the monthly payments?

**Tip:** Always check the total interest paid over the term of a loan—it can be a significant amount, especially with long terms or high interest rates.

Fritz Benjamin buys a car costing $24,400. He agrees to make payments at the end of each monthly period for 4 years. He pays 9.6% interest, compounded monthly. What is the amount of each payment?

Learn how to calculate monthly car payments for a $24,400 loan over 4 years with a 9.6% interest rate compounded monthly. This problem covers the present value of an annuity formula and is suitable for students in Grades 11-12.

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