To calculate the monthly mortgage payment, you can use the following formula:
\[ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \]
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 months)
- \( n \) is the total number of monthly payments (loan term in years multiplied by 12 months)
Here's a step-by-step guide to calculate the monthly mortgage payment:
1. Convert the annual interest rate to a monthly rate by dividing it by 12.
2. Determine the total number of monthly payments by multiplying the loan term in years by 12.
3. Use the formula above to calculate the monthly mortgage payment.
Let's use an example:
- Principal loan amount (P) = $250,000
- Annual interest rate = 4%
- Loan term = 30 years
1. Convert the annual interest rate to a monthly rate:
Monthly interest rate (r) = 4% / 12 = 0.04 / 12 = 0.00333333
2. Determine the total number of monthly payments:
Total number of payments (n) = 30 years * 12 months = 360
3. Calculate the monthly mortgage payment using the formula:
\[ M = 250,000 \times \frac{0.00333333(1+0.00333333)^{360}}{(1+0.00333333)^{360} - 1} \]
You can plug these values into the formula to find the monthly mortgage payment amount.