To calculate the monthly payments on a mortgage, we can use the formula for a fixed-rate mortgage, which is:
M = P[r(1 + r)^n] / [(1 + r)^n – 1]
Where:
- M = total monthly mortgage payment
- P = the principal loan amount (in this case, $150,000)
- r = monthly interest rate (annual rate divided by 12 months)
- n = number of payments (loan term in months)
For this mortgage:
- The principal amount (P) is $150,000.
- The annual interest rate is 6%, so the monthly interest rate (r) is 0.06 / 12 = 0.005.
- The number of payments (n) for a 30-year mortgage is 30 x 12 = 360 months.
Now substituting these values into the formula:
M = 150000[0.005(1 + 0.005)^{360}] / [(1 + 0.005)^{360} – 1]
Calculating the above expression, we find:
M ≈ 899.33
Therefore, the monthly payment on a 30-year mortgage of $150,000 at a 6% interest rate is approximately $899.33. This payment covers both principal and interest, and over the life of the loan, you’ll pay a significant amount in interest in addition to the original loan amount.