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
Payments are calculated with standard mortgage formulas using full precision internally. Numbers are rounded only when shown on screen, not during the math steps. That keeps tiny rounding differences from stacking up across hundreds of payments.
The last payment is adjusted so the balance hits $0. Lenders may round interest or payments differently, so a statement can differ by a few cents from this schedule.
Amortization schedule
Every calculator on this site uses the same payment schedule logic. For each month it:
- Charges interest on the starting balance
- Applies the rest of the scheduled payment to principal
- Adds any extra principal you entered
- Updates the ending balance
- Adjusts the final payment to clear a leftover balance
Early payoff is treated as complete when the remaining balance falls to a negligible amount, so the schedule does not show 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. Lenders underwrite with credit, assets, and program rules this page does not model.
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. A simple break-even is calculated as cash closing costs ÷ monthly P&I savings (rounded up to whole months) only when costs are paid upfront and monthly savings are positive. When closing costs are financed into the new loan, that simple cash break-even is not shown because the costs increase the new loan balance and interest. When total interest increases despite a lower monthly payment, the calculator explicitly flags this condition.
Scenario Comparison
The scenario comparison tool runs the shared payment, PMI, and amortization engines independently for up to three input sets. Five- and ten-year remaining balance and principal paid come from the amortization schedule after 60 and 120 payments (or the final payment if the loan ends earlier). Estimated PMI until 80% LTV sums a constant monthly PMI amount while the beginning balance for each period stays above 80% of the original home value. Real PMI pricing and cancellation timing may differ by lender, loan terms, payment history, property value, and applicable mortgage-insurance rules — including that FHA mortgage insurance does not follow conventional PMI cancellation rules.
Recast, Lump Sum, and Refinance Strategies
The strategy comparison models four paths on one current mortgage:
- Do nothing — remaining schedule at the current rate and term.
- Lump-sum only — a one-time principal payment (capped at the balance) with the original scheduled payment unchanged.
- Lump-sum + recast — reduce principal, then recalculate P&I at the same rate and remaining term; an optional recast fee is included in upfront cash. Recast eligibility is not verified.
- Refinance — new loan at the entered rate and term; closing costs may be paid in cash or added to principal.
Five- and ten-year total cost figures add upfront cash to cumulative payments over those horizons. Summary text reports which strategy has the lowest payment or interest in the current results without recommending a choice. Refinance cash-cost break-even appears in the summary only when it is applicable; financed closing costs do not receive a simple upfront ÷ savings break-even claim.
Testing and updates
Calculation logic is checked against known reference examples for mortgage payment, amortization, PMI, affordability, refinance, and extra payment scenarios.
When mortgage rules or calculator behavior change, we update the relevant page and the last updated date shown on affected guides. Calculator pages are revised when methodology or assumptions change materially.
Report issues through the contact page. Verified calculation errors are fixed and covered by new or updated tests where appropriate.
Default values
Calculator default inputs (interest rate, term, PMI rate, DTI ratios) are starting points for exploration — not market quotes or lender recommendations. Defaults are chosen to produce reasonable example outputs. Always replace them with numbers from your Loan Estimate or lender.
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 where a refinance or strategy tool models them explicitly.
- Property tax and insurance estimates do not account for annual increases.
- PMI cancellation is not automatically modeled as a lender process; scenario totals use an LTV-threshold estimate only.
- Biweekly payment schedules are not modeled.
- Mortgage recast availability varies by servicer and loan type and is not checked by the site.