How to Calculate a Mortgage Payment (PITI & Amortization)
A mortgage payment is usually quoted as **principal + interest (P&I)**. Lenders and listing sites often show P&I only, but your true housing cost adds **taxes, insurance, and sometimes HOA (PITI)**. This guide walks through the standard amortizing loan formula, what to add for a realistic monthly budget, and how to compare loan terms without spreadsheet errors.
Core formula
M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1] · P = principal, r = monthly rate, n = monthsStep by step
1. Gather loan inputs
You need loan amount (price minus down payment), annual interest rate, and term in years. Convert the annual rate to a monthly rate: r = APR ÷ 12 (as a decimal). Example: 6.5% APR → r = 0.065/12 ≈ 0.00542.
2. Apply the payment formula
For a fixed-rate amortizing loan, monthly P&I = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]. Use the same period for r and n (months). A calculator avoids rounding mistakes on (1+r)ⁿ.
3. Add PITI and stress test
Estimate monthly property tax (annual ÷ 12), homeowners insurance, and HOA. Add to P&I for PITI. Stress-test at **+1% rate** to see if the payment still fits your budget.
15-year vs 30-year mortgage (quick comparison)
Shorter terms raise the monthly payment but cut total interest. Always compare both payment and total cost for your expected hold period.
- 30-year fixed: Lower monthly P&I; more total interest if you keep the loan full term.
- 15-year fixed: Higher monthly P&I; less total interest; builds equity faster.
- ARM: Lower initial rate; payment can reset—model worst-case reset, not teaser rate only.
- Extra payments: Each extra dollar to principal reduces interest—amortization schedule shows impact.
Use our calculators
Common mistakes
- Using purchase price instead of loan amount (after down payment)
- Forgetting PMI when down payment is under 20%
- Comparing loans using payment only, not total interest over your horizon
FAQ
Does the formula include escrow?
No—escrow (tax/insurance) is added on top of P&I for a full housing budget.
Why doesn’t my bank match exactly?
Rounding, PMI, fees, and daily accrual vs monthly model can create small differences.