If you take out an auto loan of $11,250 at 6% interest for 36 months, what will your monthly payment be? Round your answer to the nearest cent.

To calculate the monthly payment for the auto loan, we can use the formula for the monthly payment of an amortized loan:

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

Where:
- $M$ = monthly payment
- $P$ = principal loan amount (in this case, \$11,250)
- $r$ = monthly interest rate (annual rate divided by 12)
- $n$ = total number of payments (loan term in months)

Given:
- $P = 11,250$
- Annual interest rate = 6% or 0.06, so the monthly interest rate $r = \frac{0.06}{12} = 0.005$
- Loan term $n = 36$ months

Now, we will calculate the monthly payment:

\[
M = \frac{11,250 \cdot 0.005 \cdot (1 + 0.005)^{36}}{(1 + 0.005)^{36} - 1}
\]

Let me calculate that for you.The monthly payment for the auto loan will be \$342.25.

Would you like further details or have any questions? Here are some related questions to explore:

1. How much will you pay in total over the 36 months?
2. How much of your payment goes toward interest versus the loan balance?
3. What would happen to your monthly payment if the interest rate were 5% instead of 6%?
4. What would your monthly payment be if the loan term were 48 months instead of 36 months?
5. How does the interest rate impact the total cost of the loan?

**Tip:** When calculating loan payments, always check whether the interest rate is annual or monthly to use the right figures in your formula.

Learn how to calculate the monthly payment for an auto loan of $11,250 at 6% annual interest over 36 months. This detailed solution covers financial mathematics, including the loan amortization formula, suitable for Grades 11-12.

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