Calculation methodology

By Knobugsoft Engineering · Knobugsoft LLC · Last reviewed August 14, 2026 · Methodology

Every number on this site comes from a documented formula, not an approximation. This page states exactly what each calculator computes, which assumptions it makes, how it rounds, and where its default data comes from — so you can reproduce any result yourself in a spreadsheet.

Monthly payment and amortisation

Principal and interest use the standard fixed-rate annuity payment, with the nominal annual rate divided by twelve to get the periodic rate and the term expressed in months.

i = annual_rate / 12
n = years × 12
payment = P × i / (1 − (1 + i)^−n)

The schedule is then built period by period: interest for the month is the opening balance multiplied by i, principal is the payment less that interest, and the closing balance is the opening balance less principal. The final period is trued up so the balance closes at exactly zero rather than a fraction of a cent. Interest is not compounded intra-month, and payments are treated as made at the end of each period (an ordinary annuity), which matches how US fixed-rate mortgages are serviced.

Escrow: property tax, insurance and HOA

Property tax is an effective annual rate applied to the home value and divided by twelve. Homeowners insurance and HOA dues are entered as annual or monthly amounts and added to the payment without interest, because escrowed items are pass-through costs, not financed principal. Where you enable growth rates, tax and insurance are escalated annually and re-applied from the following January, which is why the total payment in year ten is higher than the payment in year one even on a fixed-rate loan.

Maintenance and closing costs, where a tool includes them, are treated as cash outflows in the investment analysis but are never added to the loan balance unless you explicitly finance them.

PMI and cancellation thresholds

Private mortgage insurance is charged when the loan-to-value ratio at closing exceeds 80%. The monthly premium is the annual PMI rate multiplied by the loan amount and divided by twelve.

monthly_pmi = loan × pmi_rate / 12
request cancellation when scheduled balance ≤ 80% of original value
automatic termination when scheduled balance ≤ 78% of original value

Both thresholds are measured against the original property value, following the Homeowners Protection Act, not the current market value. That is deliberate: appreciation-based removal generally requires a new appraisal and a written request, so treating it as automatic would understate the true cost. Our schedules stop charging PMI in the month the 78% test is met, and extra principal payments therefore pull the cancellation date forward.

Overpayments, bi-weekly payments and recasting

Extra principal is applied after the scheduled interest and principal split for that month, so it reduces the balance the next month's interest is computed on. Recurring monthly extras, one-off lump sums and annual extras are supported and combine additively.

A bi-weekly schedule pays half the monthly payment every fourteen days, producing 26 half-payments — 13 monthly equivalents — per year. We model the accelerated payoff on that 26-period basis rather than the common shortcut of adding one extra payment in December, because the timing of the extra principal materially changes the interest saved.

A recast keeps the original interest rate and maturity date but re-amortises the reduced balance over the remaining term, lowering the payment. That is the opposite trade-off from an overpayment, which keeps the payment and shortens the term — the recast calculator shows both side by side.

NPV, IRR and future value

The investment analysis treats the transaction as a cash-flow series: the down payment and closing costs are outflows at time zero, monthly carrying costs are outflows in each period, and net sale proceeds (sale price less selling costs and remaining balance) are an inflow in the final period.

NPV = Σ CFt / (1 + r)^t
IRR = r such that NPV(r) = 0
FV  = PV × (1 + r)^n + PMT × ((1 + r)^n − 1) / r

IRR is solved numerically; where a cash-flow series has no sign change or multiple sign changes, the tool reports that IRR is undefined rather than returning a misleading root. The default discount rate is the current 10-year US Treasury yield, used as a risk-free benchmark — if a purchase cannot clear that hurdle, the analysis says so. You can override the discount rate with your own cost of capital at any time.

Rent versus buy

A fair comparison requires the renter to invest the money the buyer spent. Each year we track four series: home value grown at your appreciation rate, the loan balance from the amortisation schedule, owner equity as value less balance less selling costs, and the renter's portfolio, seeded with the down payment and closing costs and contributed to monthly with any positive difference between owning costs and rent, compounding at your investment return. Rent is grown annually at the rate you set. The break-even year is the first year in which owner net worth exceeds renter net worth and stays above it.

Refinance break-even

Break-even is not simply closing costs divided by payment savings. We compare the remaining schedule of the existing loan against a new loan for the same balance at the new rate and term, including financed closing costs, and find the month at which cumulative total cost — payments plus costs — of the new loan first falls below the old. Where the new term is longer than the remaining term, we also report lifetime interest, because a lower payment often means more total interest.

Precision, rounding and rate conventions

• Calculations run in exact decimal arithmetic on the server, not in binary floating point in your browser, so cents do not drift across 360 periods.
• Displayed currency is rounded to the nearest cent for line items and to the nearest whole unit for headline figures; totals are summed from unrounded values, so a column may differ by a cent from the sum of its displayed rows.
• Rates are entered as nominal annual percentages compounded monthly (APR-style presentation, monthly compounding), the standard US convention. We do not convert to an effective annual rate unless a tool says so explicitly.
• Percentages of home value (tax, PMI, appreciation) are applied to the value in force at that point in the schedule, not the original value, except PMI thresholds as described above.

Data sources

• Discount rate default — the current 10-year US Treasury constant maturity yield, published by the US Department of the Treasury.
• State cost defaults — median home prices, effective property tax rates and typical homeowners insurance premiums used in the state guides are representative published averages, refreshed periodically and labelled as illustrative. They are starting points for your own inputs, not quotes or appraisals.
• PMI and cancellation rules — the Homeowners Protection Act of 1998 and standard lender servicing practice.
• Everything else — supplied by you. We do not pull your credit, price your loan, or infer a rate you did not enter.

Editorial and advertising standards

• Content is written and reviewed in-house by Knobugsoft LLC. We do not publish syndicated, spun or auto-generated filler articles.
• Calculation changes ship with regression tests. If a result is wrong, we treat it as a defect and correct it; material corrections are noted on the affected page.
• Advertising and sponsored placements are labelled. They never influence a calculation, the ordering logic of a comparison, or the wording of editorial content.
• We publish no testimonials, ratings, guarantees or performance claims that we cannot substantiate, and no page here constitutes financial, tax, legal or mortgage advice.

Spotted an error or disagree with an assumption? Tell us on the contact page — include your inputs and expected result and we will reproduce it.