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To solve this problem, let's analyze the provided details from the image and go through the calculations step-by-step.

### Given Data:
- **Loan Amount (Principal)**: $189,000
- **Interest Rate**: 5.1% per annum
- **Loan Term**: 10 years

### Part 1: Monthly Mortgage Payment Calculation

The formula for the monthly mortgage payment is:

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

where:
- $ M $ = monthly payment
- $ P $ = principal loan amount ($189,000)
- $ r $ = monthly interest rate (annual rate divided by 12)
- $ n $ = number of payments (loan term in years multiplied by 12)

1. **Calculate the monthly interest rate:**

\[ r = \frac{5.1\%}{12} = \frac{0.051}{12} = 0.00425 \]

2. **Calculate the number of payments:**

\[ n = 10 \times 12 = 120 \]

3. **Plug the values into the formula:**

\[ M = 189,000 \times \frac{0.00425(1 + 0.00425)^{120}}{(1 + 0.00425)^{120} - 1} \]

Let's calculate this step by step:

- Calculate $(1 + 0.00425)^{120}$:

\[ (1 + 0.00425)^{120} \approx 1.6768 \]

- Now calculate the numerator and the denominator:

\[ M = 189,000 \times \frac{0.00425 \times 1.6768}{1.6768 - 1} \]

\[ M = 189,000 \times \frac{0.0071254}{0.6768} \]

\[ M = 189,000 \times 0.0105285 \]

\[ M \approx 1,990.88 \]

So, the monthly mortgage payment is approximately **$1,990.88**.

### Summary of Results:

**Monthly Mortgage Payment:** \$1,990.88

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Do you want details or have any questions?

1. What is the formula for calculating monthly mortgage payments?
2. How do you convert an annual interest rate to a monthly interest rate?
3. What is the importance of the number of payments in the mortgage formula?
4. How can you calculate the total payment over the term of the loan?
5. How is the total interest paid over the life of the loan determined?
6. What assumptions are made in the standard mortgage payment formula?
7. How would an increase in the interest rate affect the monthly payment?
8. What are some methods to reduce the total interest paid over the term of the loan?

**Tip:** When dealing with mortgage calculations, it is helpful to use a financial calculator or spreadsheet software to ensure accuracy and efficiency, especially for complex computations involving exponentiation.

Learn how to calculate the monthly mortgage payment for a $189,000 loan at a 5.1% interest rate over 10 years. Step-by-step solution with detailed calculations using the monthly mortgage payment formula. Useful for understanding financial mathematics and loan repayment calculations.

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