Methodology
Every formula these calculators use, and every rate, fee and threshold they apply — each with the body that publishes it and the year it takes effect. Nothing here is a magic number, and anything that changes annually says so.
The formulas
Standard, and stated so you can check our arithmetic against your own.
Monthly principal and interest
M = P · [ r(1+r)ⁿ ] / [ (1+r)ⁿ − 1 ]
P is the loan amount, r the monthly rate (annual ÷ 12), n the number of payments (years × 12).
Degenerates to P ÷ n when the rate is zero, because the general form divides by zero there.
Amortization split, month by month
interest = balance · r principal = M − interest
The balance falls by the principal portion each month, so the split shifts over time.
Extra principal reduces the balance directly, which lowers every subsequent interest charge — this is why paying extra early is worth more than paying extra late.
Loan-to-value
LTV = balance ÷ original value
Original value is the lesser of purchase price and original appraised value, not today's market value.
PMI cancellation thresholds are measured against original value by statute, which is why an appreciating market does not automatically end PMI.
Debt-to-income
front-end = housing ÷ income back-end = (housing + debts) ÷ income
Income is gross monthly, before tax. Housing is the full PITI plus HOA.
The back-end ratio is the one that usually binds, which is why paying down a car loan raises your budget more than it seems it should.
Annual percentage rate
solve for i: Σ M / (1+i)ᵗ = loan − finance charges
The rate at which the payment stream discounts back to what you actually received.
No closed form exists. Solved numerically by bisection, which converges without a derivative and cannot diverge on a zero rate or a one-month term.
Published assumptions
12 values, rendered from the engine's own manifest rather than typed onto this page — so this table cannot claim an assumption the calculators do not use. The same list is available as JSON at /api/v1/assumptions.
| Assumption | Value | As of | Source |
|---|---|---|---|
| fha.upfrontMipPercent | 1.75% | 2025 | U.S. Department of Housing and Urban Development |
| fha.annualMipPercent | 0.55% | 2025 | U.S. Department of Housing and Urban Development |
| va.fundingFee.firstUse.zeroDown | 2.15% | 2025 | U.S. Department of Veterans Affairs |
| va.fundingFee.subsequentUse.zeroDown | 3.3% | 2025 | U.S. Department of Veterans Affairs |
| usda.upfrontGuaranteeFeePercent | 1% | 2025 | U.S. Department of Agriculture Rural Development |
| usda.annualFeePercent | 0.35% | 2025 | U.S. Department of Agriculture Rural Development |
| conventional.pmiAnnualPercent | 0.6% | 2025 | Consumer Financial Protection Bureau |
| loanLimits.baselineConforming | 806,500 | 2025 | Federal Housing Finance Agency |
| loanLimits.fhaFloor | 524,225 | 2025 | U.S. Department of Housing and Urban Development |
| loanLimits.fhaCeiling | 1,209,750 | 2025 | U.S. Department of Housing and Urban Development |
| dti.frontEndPercent | 28% | 2025 | Consumer Financial Protection Bureau |
| dti.backEndPercent | 36% | 2025 | Consumer Financial Protection Bureau |
The property tax data
Average effective rates for all 50 states, compiled from U.S. Census Bureau, American Community Survey 5-year estimates. Data: ACS 2019-2023 5-year estimates, last reviewed September 2026. 5-year estimates pool 2019-2023 and are not a single-year reading. Use the 1-year historical series for year-on-year comparison.
An effective rate here is the state's median real estate taxes paid (ACS table B25103) divided by its median home value for owner-occupied units (B25077) — not a statutory millage rate, which is applied to an assessed value that is often a fraction of market value and is therefore not comparable across states. Both figures come from the same release, so the rate and the annual bill quoted on this site describe the same households over the same period rather than being combined across different years. Every figure is a statewide median: counties within a state routinely differ by a factor of two or more, so a specific parcel should always be confirmed with its county assessor.
What we do not model
Stating the limits is part of publishing the method.
- County and municipal variation. State averages only. Local levies, school districts and special assessments are not applied.
- Homestead and other exemptions. Described per state in the data, but not deducted from the estimate — eligibility depends on facts we do not ask for.
- Adjustable rates. The calculators assume a fixed rate for the full term. An ARM's payment after the introductory period depends on an index nobody can forecast.
- Your actual pricing. Rates and mortgage insurance premiums are quoted to you based on credit score, loan-to-value, occupancy and the lender's own margins. We apply published averages.
Citing this data
Both datasets are deposited on Zenodo under a concept DOI, which always resolves to the newest version — cite the DOI rather than this page when a persistent identifier is required.
- US State Property Tax Rates and Median Home Values. https://doi.org/10.5281/zenodo.22674085
- US Mortgage Financing Constants: Loan Limits, Insurance Premiums and Underwriting Assumptions. https://doi.org/10.5281/zenodo.22676274
Ready-made APA, MLA, Chicago, BibTeX and RIS citations are on the datasets page.
Corrections and reuse
If a figure here is out of date or wrong, please tell us — the source is published precisely so it can be checked. The assumptions, the state dataset and every calculator are available free over the REST API for research and teaching, with no key and no rate limit. Engine version 0.1.0.