Calculator methodology

What this page is (and is not)

These are the formulas the site actually runs in your browser. They follow the standard fully amortizing fixed-rate payment equation used in most U.S. consumer calculators. They are not a substitute for a lender’s underwriting engine, a credit-based PMI quote, or a county tax bill.

We do not claim “bank-grade” or audited accuracy. If a lender’s worksheet disagrees, trust the lender — then compare assumptions (rate, tax basis, insurance, fees).

Amortization formula

For loan amount P, annual interest rate i (percent), and term in years y:

• Monthly rate r = i / 100 / 12
• Number of payments n = y × 12
• Monthly principal & interest: M = P × r(1+r)^n / ((1+r)^n − 1)
• If the rate is 0%, M = P / n

Each month, interest = remaining balance × r, and principal = M − interest. The schedule continues until the balance reaches zero. Extra-payment tools subtract the extra amount from principal after that split. The amortization chart on the main calculator and schedule page plots those same yearly principal and interest totals (SVG), not a separate model.

PMI model (illustrative)

Conventional private mortgage insurance is quoted by insurers from credit score, LTV, occupancy, and product. We do not have those quotes. When down payment is under 20% of home price, the conventional calculator applies a simplified annual rate to the loan amount, billed monthly:

Monthly PMI = loan × (annual rate / 100) / 12. The schedule stops adding PMI once the remaining balance reaches 78% of the original home price (a common automatic termination threshold on conventional loans). Real cancellation also depends on payment history, the original value vs. a new appraisal, and the loan contract.

FHA and VA tools use different insurance models (MIP and a funding fee). Those pages document their own assumptions. The affordability tool uses a single 0.90% PMI stand-in when down payment is under 20% — coarser than the LTV bands above.

Tax and insurance assumptions

• Property tax default is 1.2% of home price per year, divided by 12. That is a round placeholder, not your county millage. Assessed value often differs from purchase price.
• Calculators also offer a state tax preset dropdown. Those figures are illustrative statewide average effective rates, not your county bill, as of 2026— Tax Foundation Facts & Figures 2026, Table 33 (Census ACS calendar year 2024, owner-occupied housing). The U.S. mean in that table is 0.90%. County bills can be much higher or lower. The percent field stays editable after you pick a state.
• Homeowners insurance default is 0.30% of home price per year, divided by 12. Premiums vary widely by state, deductible, and coverage.
• HOA is whatever monthly amount you type; the default is $0.
• We do not add flood insurance, impound cushions, lender fees, or closing costs to the monthly PITI figure unless a specific tool says so.

Worked example

Inputs used on the main calculator defaults: $400,000 home, $40,000 down (10%), 6.5% interest, 30 years, tax 1.2%, insurance 0.3%, HOA $0. The 6.5% figure is an example rate, not a live weekly average.

1. Loan amount P = 400,000 − 40,000 = $360,000
2. r = 6.5 / 100 / 12 = 0.00541666… ; n = 360
3. Monthly P&I M ≈ $2,275.44
4. Monthly tax = 400,000 × 0.012 / 12 = $400.00
5. Monthly insurance = 400,000 × 0.003 / 12 = $100.00
6. LTV = 360,000 / 400,000 = 90%, which uses the 0.60% PMI band
7. Monthly PMI = 360,000 × 0.006 / 12 = $180.00
8. Estimated monthly total ≈ 2,275.44 + 400 + 100 + 180 = $2,955.44 (the UI rounds currency to whole dollars: $2,955)

Recalculate the same inputs on the mortgage calculator to confirm the implementation still matches this page.

Refinance comparison

Current P&I is computed from remaining balance, current rate, and remaining term (years + extra months) with the same formula as above. The new P&I uses the new rate, chosen term, and a balance that can include cash-out and rolled-in closing costs. Break-even months = closing costs ÷ monthly P&I savings. Remaining interest is summed from the amortization schedule, not a shortcut. Defaults (7.5% current / 6.25% new, $4,500 closing costs) are examples — not a weekly refinance average.

Rates we do not invent

We do not display a fabricated “average 30-year fixed this week,” and we do not invent a weekly national refinance average. For the official weekly survey, use Freddie Mac’s Primary Mortgage Market Survey, then enter that rate (or a lender quote) into the calculator. Defaults such as 6.5% (purchase tools) or 7.5% / 6.25% (refinance) are labeled examples.