You wish to buy a car with a $28,000 bank loan. The APR is 7.6% and you will be paying off the car in 5 years (making monthly payments, of course). What is your monthly payment going to be?

To determine your monthly payment for the car loan, we will use the formula for the monthly payment on an amortizing loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (the amount of the loan), which is \$28,000 in this case.
- $ r $ is the monthly interest rate, which is the annual percentage rate (APR) divided by 12. So, the APR of 7.6% becomes $ \frac{7.6}{100 \cdot 12} $.
- $ n $ is the total number of payments (number of months). For a 5-year loan, there are 5 years $\times 12$ months = 60 months.

Now, let's calculate step by step:

1. Convert APR to a monthly interest rate:  
   $ r = \frac{7.6}{100 \times 12} = 0.00633333 $

2. Total number of payments over 5 years:  
   $ n = 5 \times 12 = 60 $

3. Plugging into the formula:  
   \[
   M = \frac{28000 \cdot 0.00633333 \cdot (1 + 0.00633333)^{60}}{(1 + 0.00633333)^{60} - 1}
   \]

Now I will calculate the result.The monthly payment for the car loan will be approximately **$562.39**.

Would you like to explore any details or have further questions? Here are five follow-up questions to consider:

1. How does changing the loan term affect your monthly payment?
2. What would happen to your monthly payment if the interest rate were lower?
3. How much total interest will you end up paying over the 5 years?
4. What is the impact of making extra payments on your loan?
5. How do taxes and insurance affect the overall cost of owning a car?

**Tip:** When considering loans, check if there's any penalty for early repayment, as paying off a loan sooner can save you money on interest.

Discover how to calculate the monthly payment for a $28,000 car loan at a 7.6% APR over 5 years. This problem uses the loan amortization formula, covering concepts from financial mathematics. Suitable for high school students (Grades 11-12).

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