The average amount taken out for a mortgage in South Carolina is $165,649. Find the monthly payment if your interest rate is 7.087%, compounded monthly for 30 years.

To find the monthly payment for a mortgage, we can use the formula for the **monthly mortgage payment**:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the principal amount (the loan amount, $165,649 in this case).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (number of months over the loan period).

### Given:
- Principal $ P = 165,649 $
- Annual interest rate = 7.087%, so monthly interest rate $ r = \frac{7.087\%}{12} = \frac{0.07087}{12} = 0.005906 $
- The loan is for 30 years, so $ n = 30 \times 12 = 360 $ months.

Now, let's plug these values into the formula and calculate $ M $.The monthly mortgage payment would be approximately **$1,111.76**.

Would you like any more details or clarifications on this? Here are 5 related questions:

1. How do changes in the interest rate affect monthly mortgage payments?
2. How does the length of the loan impact the total interest paid over time?
3. What happens if you make extra payments on your mortgage?
4. How is the total cost of the mortgage calculated, including interest?
5. What other types of compounding interest calculations are commonly used in loans?

**Tip:** If you're looking to save on interest, consider making extra payments or refinancing to a lower interest rate!

Learn how to calculate the monthly mortgage payment for a loan of $165,649 with a 7.087% interest rate, compounded monthly over 30 years. This problem covers key mathematical concepts such as compound interest, amortization, and the loan payment formula. Suitable for high school and college students.

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