You want to buy a house and will need to borrow $195,000. The interest rate on your loan is 5.17 percent compounded monthly and the loan is for 25 years. What are your monthly mortgage payments?

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

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal (amount borrowed)
- $ r $ = monthly interest rate
- $ n $ = total number of payments (months)

### Step 1: Identify the values
- $ P = 195,000 $
- Annual interest rate = 5.17% → Monthly interest rate $ r = \frac{5.17}{12 \times 100} = 0.0043083 $
- Loan term = 25 years → Total number of payments $ n = 25 \times 12 = 300 $

### Step 2: Plug in the values
\[
M = 195,000 \frac{0.0043083(1 + 0.0043083)^{300}}{(1 + 0.0043083)^{300} - 1}
\]

### Step 3: Calculate the monthly payment
\[
M = 195,000 \frac{0.0043083(1.0043083)^{300}}{(1.0043083)^{300} - 1}
\]

After calculating this step by step, the monthly mortgage payment is approximately:

\[
M \approx 1,165.04
\]

### Conclusion:
Your monthly mortgage payment will be approximately **$1,165.04**.

Would you like further details on the calculation or have any other questions?

Here are 5 related questions:
1. How much interest will you pay over the entire 25 years?
2. What is the total cost of the mortgage (loan + interest)?
3. How does the payment change if the interest rate drops to 4%?
4. How much would you save by reducing the loan term to 20 years?
5. What is the effect of making an additional payment each month?

**Tip:** A small reduction in interest rates or loan duration can lead to significant savings in total interest paid over the loan term.

Calculate monthly mortgage payments for a $195,000 loan at an interest rate of 5.17% compounded monthly over 25 years. Learn about loan amortization, the relevant formula, and step-by-step calculation. Suitable for Grades 11-12 and college-level financial math learners.

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