Calculation Methodology
Mortgage Payment Formula
The monthly principal and interest payment uses the standard amortizing mortgage formula:
Where:
- P = Principal (loan amount)
- r = Monthly interest rate = Annual rate ÷ 12 ÷ 100
- n = Total monthly payments (years × 12 + months)
- M = Monthly P&I payment
For a 0% interest rate, the formula simplifies to M = P / n (equal principal payments with no interest).
Rounding Methodology
All intermediate calculations use full IEEE 754 double-precision floating-point arithmetic. Values are rounded only when displayed to the user — never during intermediate calculation steps. This prevents compounding rounding errors.
The final amortization payment is adjusted to bring the remaining balance to exactly $0. This means the last payment may differ slightly from the standard scheduled payment due to rounding across the full loan term.
Amortization Engine
All calculators on this site share a single amortization engine. For each payment period, the engine calculates:
- Interest accrued = Beginning balance × monthly rate
- Scheduled principal = Scheduled payment − Interest
- Extra principal applied (if entered)
- Ending balance = Beginning balance − Total principal paid
- Final payment adjusted to eliminate any residual balance
Early payoff is detected when the balance falls to or below a small epsilon (0.005) to handle floating-point edge cases without creating a meaningless negative balance.
Property Taxes and Insurance
Annual property tax and homeowners insurance amounts are divided by 12 to produce monthly estimates. These values are based entirely on user input — we do not estimate them independently by location. Actual costs vary significantly by state, county, municipality, and property.
PMI Calculation
PMI is estimated as an annual percentage of the loan amount, divided by 12. The LTV threshold for PMI applicability is 80% (loan balance ÷ home price). PMI is applied to the original loan amount in this calculator, not the declining balance, unless the lender uses a different structure.
Actual PMI rates depend on credit score, loan type, lender, and other factors. Our calculator uses the rate you enter and discloses that actual rates vary.
Affordability Estimation
The affordability calculator uses editable front-end and back-end DTI ratios (defaulting to 28% housing and 36% total debt as planning assumptions) to determine the maximum monthly housing payment, then inverts the mortgage formula to derive the maximum loan amount. Estimated housing costs may include principal and interest, property taxes, homeowners insurance, applicable estimated PMI when LTV exceeds 80%, and HOA fees.
The result is an educational estimate. Actual lender qualification uses comprehensive underwriting.
Refinance Calculations
The refinance calculator computes the remaining balance on the current loan and applies the mortgage formula to both the current and new loan scenarios. Break-even is calculated as: Closing Costs ÷ Monthly Savings (rounded up to whole months). When total interest increases despite a lower monthly payment, the calculator explicitly flags this condition.
Known Limitations
- Calculations assume fixed-rate, standard amortizing loans. Adjustable-rate mortgages are not modeled.
- FHA mortgage insurance premiums (MIP), VA funding fees, and USDA guarantee fees are not calculated separately.
- Closing costs are not included in P&I calculations (except in the refinance calculator's break-even analysis).
- Property tax and insurance estimates do not account for annual increases.
- PMI cancellation is not automatically modeled in the amortization schedule.
- Biweekly payment schedules are not modeled.