The Math & Methodology

Principles

Show the working. Every calculator prints the arithmetic that produced its answer, not just the answer.
Simulate rather than approximate. Where a closed-form shortcut would be inexact — extra payments, debt payoff ordering — we run a real month-by-month loop.
State the omissions. Reality Check boxes exist because the number a calculator gives you is usually less dangerous than the costs it silently excludes.
Cite primary sources. Rates from Freddie Mac, APRs from the Federal Reserve, scoring weights from myFICO, rules from the CFPB and statute. Never a secondary blog.
Refuse false precision. Where the underlying model is not public — credit scoring — we report a range and say so.

Core formulas

Monthly payment on an amortizing loan

M = P · [ i(1+i)ⁿ / ((1+i)ⁿ − 1) ]

Where P is principal, i is the periodic (monthly) interest rate, and n is the number of payments. When i = 0 the formula is undefined, and we fall back to P / n. Used by the mortgage payment, amortization and refinance calculators.

Principal from a payment (solving in reverse)

P = M · [ ((1+i)ⁿ − 1) / (i(1+i)ⁿ) ]

The same relationship rearranged. Used by the affordability calculator, which starts from the largest payment your income supports and works back to a price. We verify this numerically: feeding the output of one formula into the other returns the original figure to the cent.

Amortization loop

for each month:
  interest = balance × i
  principal = min(payment + extra − interest, balance)
  balance   = balance − principal

Run until the balance reaches zero, with a hard cap to prevent infinite loops when payments cannot cover accruing interest. Biweekly payments are modeled as their exact monthly equivalent: one extra monthly payment per year, i.e. an added 1/12th each month.

28/36 affordability test

front-end = 0.28 × gross monthly income
back-end = 0.36 × gross monthly income − other monthly debt
allowed housing payment = min(front-end, back-end)

Property tax and insurance are then subtracted before solving for principal. Because property tax is a function of the home price we are solving for, the calculation is circular; we resolve it by iterating until the price converges.

PMI and its termination points

monthly PMI = loan amount × annual PMI rate ÷ 12

We report two dates from the amortization schedule: the month the balance is scheduled to reach 80% of original value (the point at which you may request cancellation) and 78% (the point at which the servicer must terminate automatically, if you are current). Both are measured against original value per the Homeowners Protection Act, so appreciation is not modeled.

Refinance break-even

break-even months = closing costs ÷ monthly payment savings

We also compute total lifetime interest on both paths, because a lower payment on a restarted term frequently increases total cost. Both numbers are shown; neither is hidden.

Debt payoff simulation

Month by month: accrue interest on each balance at APR/12, pay each minimum, then apply all remaining funds to a single target debt — smallest balance for snowball, highest APR for avalanche. When a debt clears, its minimum rolls into the following month's available funds. Both strategies run against the same inputs, and we report the difference.

Credit score factor model

estimated score = 300 + 550 × Σ (factor score × published weight)

This is the one model on the site that is our own estimate, and we want to be explicit about that. The category weights (35/30/15/10/10) are published by FICO. The shape of the curve within each category is not published — FICO's algorithm is proprietary. We constructed those curves from FICO's and the CFPB's qualitative guidance.

Consequently the tool reports a range rather than a point, widens that range for thin files, and is framed as a factor estimator rather than a score predictor. Treat the ranking of your factors as meaningful and the number as indicative only.

Where our default numbers come from

Mortgage rates (6.65% / 5.95%) — Freddie Mac Primary Mortgage Market Survey, week ending 2026-08-20.
Credit card APR (22.15%) — Federal Reserve G.19, 2026 Q2, accounts assessed interest.
Average FICO Score (714) — FICO Score Credit Insights, Fall 2026.
Scoring weights — myFICO, "What's in my FICO Scores?".
PMI, DTI and inquiry rules — Consumer Financial Protection Bureau.

Defaults are illustrative starting points. Replace them with the figures you have actually been quoted — a calculator run on someone else's rate tells you nothing about your loan.

What we deliberately do not model

Taxes. Mortgage interest deductibility depends on itemization, filing status and SALT limits. We do not guess.
Home appreciation. Unknowable, and modeling it makes buying look better than it is by an arbitrary amount.
Rate forecasts. Nobody can do this reliably, ourselves included.
Adjustable-rate schedules. Caps and index behavior vary too much per contract for a generic tool to be honest about.
Declining card minimums. Real minimums shrink with the balance, lengthening payoff. Holding them fixed makes our debt figures the optimistic case, and we say so on the page.

Verification

The shared math library is tested against known values before release: a $300,000 loan at 6.5% over 360 months returns $1,896.20/month; the inverse formula returns $300,000 from that payment; a 0% loan divides evenly; and the debt simulator is checked against a hand-computed case where snowball and avalanche diverge. Errors are corrections, not opinions — if you find one, tell us and we will fix it and note the change.

The math & methodology