Supported model
Formula version 1.0 models level-payment, fully amortizing, fixed-note-rate loans with one payment each month. It supports a principal from $0.01 through $100,000,000, a nominal annual note rate from 0% through 25%, and an integer term from 1 through 600 months.
Optional non-negative estimates can be included for property tax, homeowners insurance, mortgage insurance, HOA dues, and recurring extra principal. These amounts remain user assumptions; the calculator does not retrieve a personalized lender quote, tax assessment, insurance premium, or mortgage-insurance eligibility decision.
Fixed-rate principal and interest
For principal P, monthly note rate r, and term in months n:
payment = P × r ÷ (1 − (1 + r)−n)
The engine converts the annual note-rate percentage to a monthly decimal rate by dividing by 100 and then by 12. At a zero rate, payment is P ÷ n. The implementation uses numerically stable functions near zero and rejects non-finite results rather than displaying infinity or an undefined value.
Estimated payment and housing cost
estimated mortgage payment = principal and interest + annual property tax ÷ 12 + annual homeowners insurance ÷ 12 + monthly mortgage insurance
estimated total housing cost = estimated mortgage payment + monthly HOA dues
HOA dues are shown separately because they are commonly paid outside the lender’s mortgage payment. Neither result is an escrow analysis, lender quote, Closing Disclosure, approval, or commitment to lend.
Rate impact
The rate-impact tool calculates two otherwise identical fixed-rate principal-and-interest payments. Monthly difference equals comparison payment minus starting payment; annual difference equals that monthly difference multiplied by 12. It does not model points, closing costs, qualification, APR, or an available refinance offer.
Extra principal
Each schedule row calculates interest from the starting balance, applies the scheduled payment remainder to principal, then applies requested extra principal without exceeding the remaining balance. The tool compares payoff month, modeled total interest, and row-by-row balances with and without the recurring extra amount.
Rounding contract
- The engine retains floating-point precision for payments, interest, principal, balances, and totals.
- Displayed currency formatting does not feed rounded values back into the schedule.
- The final row pays the remaining modeled balance rather than leaving a small floating-point remainder.
- Total modeled interest is the sum of row interest, not the displayed rounded payment multiplied by the term.
Lenders and servicers can use documented intermediate-rounding conventions that differ from this full-precision estimate. A difference of cents in a row can accumulate over a long term, so the public schedule is not represented as a payoff statement or servicing ledger.
Engineering validation
Engineering validation was completed on August 2, 2026. That statement is limited to software and formula checks; it is not a professional mortgage review.
- Invalid, non-finite, negative, fractional-term, and out-of-range values fail explicitly.
- Property sweeps check payment linearity in principal, monotonic rate and term behavior, exact modeled payoff, and finite totals across supported ranges.
- Schedule tests check principal conservation, payment composition, final balance zero, and agreement between row totals and summary totals.
- Published examples from CFPB, Regulation Z, and Fannie Mae are maintained as independent validation vectors.
| Source example | Engine acceptance check |
|---|---|
| CFPB: $100,000, 30 years, 4% | Rounds to about $477 monthly P&I and about $90,448 balance after five years; modeled balance reaches zero in month 360. |
| CFPB: $200,000, 30 years, 4% and 5% | Rounds to the published payments of about $955 and $1,074. |
| CFPB Loan Estimate: $162,000, 30 years, 3.875% | Formats to $761.78 P&I and rounds five-year principal reduction to about $15,773. |
| Regulation Z: $200,000, 30 years, 7% | Rounds to the published payment of about $1,331. |
| Fannie Mae: $70,000, 30 years, 15.5% | Full-precision payment formats to $913.16; servicing-row rounding remains deliberately distinct. |
Limitations and excluded cases
The engine does not model adjustable rates, balloon payments, interest-only periods, negative amortization, odd first periods, daily-interest servicing, recasts, prepayment penalties, late or skipped payments, biweekly schedules, changing taxes or premiums, tax deductibility, investment returns, or lender underwriting.
Unless a user explicitly enters an amount, results also exclude closing costs, utilities, maintenance, special assessments, flood insurance, and mortgage-insurance rules. The note rate is not APR. APR can include certain costs and requires a separate Regulation Z computation that this tool does not perform.
Primary source register
These sources support the formulas, disclosures, and independent examples above. An external source does not endorse this project.
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How do mortgage lenders calculate monthly payments? — Consumer Financial Protection Bureau
Fixed-rate payment explanation and the published $100,000 validation example.
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Your mortgage calculator may be setting you up for a surprise — Consumer Financial Protection Bureau
Published payment comparisons and the distinction between principal and interest and fuller ownership costs.
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Fixed-rate Loan Estimate sample — Consumer Financial Protection Bureau
Independent payment and five-year principal-reduction validation values.
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Regulation Z § 1026.43: Minimum standards for transactions secured by a dwelling — Consumer Financial Protection Bureau
A published fixed-rate mortgage example used as an additional whole-dollar payment vector.
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Fixed-installment calculation and amortization exhibits — Fannie Mae
Comparison with a documented servicing-rounding convention and its fixed-installment example.
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Homebuyer frequently asked questions — Fannie Mae
Explanation of the monthly interest and principal-allocation sequence used to check each schedule row.
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Principal and interest payment versus total monthly payment — Consumer Financial Protection Bureau
Disclosure language for taxes, insurance, escrow, and the difference between loan payment and broader housing cost.
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Mortgage interest rate versus APR — Consumer Financial Protection Bureau
The boundary between the user-entered note rate and a broader annual percentage rate.
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Regulation Z Appendix J: Annual Percentage Rate Computations — Consumer Financial Protection Bureau
Primary regulatory reference explaining why this fixed-rate payment engine does not calculate or label its note rate as APR.
Change and review control
A material change to supported ranges, formula behavior, rounding, payment components, or terminology requires updated validation vectors and a new review record. Before public financial-guidance claims, the release record must identify a qualified mortgage reviewer, relevant qualifications, review date, formula version, supported scope, rounding disclosure, and correction channel.