How Mortgage Payments Are Calculated
A fixed-rate mortgage amortizes over the loan term, meaning every monthly payment consists of both principal repayment and interest expense. The formula used across all major banks is:
M = P Γ [ r(1 + r)βΏ ] / [ (1 + r)βΏ β 1 ]
P = Loan AmountPurchase price minus down payment (e.g., $400,000 home β $80,000 = $320,000).
r = Monthly InterestAnnual interest rate divided by 12 months (e.g., 6.75% / 12 = 0.005625).
n = Number of MonthsLoan term in years Γ 12 months (e.g., 30 years Γ 12 = 360 payments).
Step-by-Step Mortgage Calculation Example
Suppose you purchase a $400,000 home with a 20% down payment ($80,000) at a 6.75% fixed interest rate on a 30-year term (360 months):
- Determine loan balance: $400,000 β $80,000 = $320,000 principal.
- Convert monthly rate: 6.75% Γ· 100 Γ· 12 =
0.005625. - Compute compound factor: (1 + 0.005625)Β³βΆβ° β
7.5255. - Calculate principal & interest: 320,000 Γ [0.005625 Γ 7.5255] / [7.5255 β 1] = $2,075.64 / month.
- Add escrow (taxes & insurance): $350/mo property tax + $116.67/mo homeowners insurance = $2,542.31 total monthly payment (PITI).
Frequently Asked Questions
Common questions and detailed answers regarding calculations and formulas.
The standard monthly mortgage principal and interest payment is calculated using the formula M = P [ r(1 + r)^n ] / [ (1 + r)^n β 1 ]. P is your total loan amount (home price minus down payment), r is the monthly interest rate (annual APR divided by 12), and n is total months (e.g. 360 months for a 30-year fixed loan).