Now assume that the mortgage was 15 years, and the annual interest rate is 6.84%. Recalculate the montly payment for a 15 year loan. Show formula and numbers in the calculation

To calculate the monthly payment for a mortgage, we use the formula for the monthly payment \( M \) of a fixed-rate mortgage:

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

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

### Given:
- The loan term is 15 years, so \( n = 15 \times 12 = 180 \) months.
- The annual interest rate is 6.84%, so the monthly interest rate \( r = \frac{6.84\%}{12} = 0.0057 \) (or \( 0.0684 / 12 \)).
- We do not know the loan principal \( P \), so we will leave it as a variable for now.

### Formula Substitution:

\[
M = P \times \frac{0.0057(1 + 0.0057)^{180}}{(1 + 0.0057)^{180} - 1}
\]

Now, I'll calculate the expression to simplify the result.The simplified factor for the monthly mortgage payment formula is approximately \( 0.008899 \). Therefore, the monthly payment \( M \) can be calculated using the following formula:

\[
M = P \times 0.008899
\]

Where \( P \) is the principal loan amount.

If you know the loan principal, you can now multiply it by this factor to find the monthly payment.

Would you like to proceed with a specific loan amount?

Here are 5 questions to deepen your understanding:
1. How does changing the loan term (years) affect the monthly payment?
2. How would a lower interest rate impact this calculation?
3. What happens to the monthly payment if the loan principal increases?
4. Can you derive the monthly payment for an interest-only mortgage?
5. How does an amortization schedule break down these monthly payments?

**Tip:** Understanding the relationship between loan duration and interest rates helps you make more informed financial decisions when taking out a loan.

Now assume that the mortgage was 15 years, and the annual interest rate is 6.84%. Recalculate the monthly payment for a 15-year loan. Show formula and numbers in the calculation.

Learn how to calculate the monthly payment for a 15-year mortgage with an annual interest rate of 6.84%. This guide explains the step-by-step process, using the compound interest formula, suitable for students in Grades 10-12.

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