You want to buy a house and will need to borrow $200,000. The interest rate on your loan is 5.23 percent compounded monthly and the loan is for 30 years. What are your monthly mortgage payments?

To calculate your monthly mortgage payments, we'll use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$200,000),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the number of total payments (loan term in years multiplied by 12).

### Given dataTo calculate your monthly mortgage payments, we'll use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$200,000),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the number of total payments (loan term in years multiplied by 12).

### Given 
- Loan amount ($P$) = \$200,000
- Annual interest rate = 5.23% = 0.0523
- Monthly interest rate ($r$) = $\frac{0.0523}{12} = 0.00435833$
- Loan term = 30 years, so $n = 30 \times 12 = 360$ months

Let's calculate the monthly payment (M).Your monthly mortgage payment would be approximately \$1,101.93.

Do you need further details or have any other questions?

Here are some related questions for further exploration:
1. How much total interest will you pay over the life of the loan?
2. How would the monthly payment change if the interest rate was 4.5% instead?
3. What if the loan term was reduced to 15 years? How would that affect the payments?
4. What is the effect of making extra monthly payments toward the principal?
5. How does the loan balance decrease over time (amortization schedule)?

**Tip:** Even small extra payments towards the principal can significantly reduce the total interest you pay over the life of a loan.

Learn how to calculate monthly mortgage payments for a $200,000 home loan at an interest rate of 5.23% compounded monthly over 30 years. Using the mortgage payment formula, this guide provides a step-by-step solution suitable for high school students in Grades 10-12.

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