Guides

Every calculator here runs on a small set of pure, typed functions — the engine — and the guides make the engine's definitions and conventions legible. Each guide takes one piece of the calculators' arithmetic, states the convention it rests on — the standard amortized-loan (PMT) formula with monthly compounding; interest at APR ÷ 12 in the debt engines; the methodology page's sentence "Affordability uses the 28/36 debt-to-income guidelines" — works it on a fictional loan or balance, and marks where the arithmetic stops. The guides quote no rate, price or market figure as a fact; every input is an illustrative number.

Every figure in the guides is computed when the site is built, by the engine itself; nothing is typed in by hand. The methodology page states the consequence: if the copy and the code ever disagreed, the site would fail to build rather than publish inconsistent numbers. This page is held to the same rule: the reference loan the methodology page names — a $200,000 loan at 6% over 30 years, an illustrative loan and not a quote — recomputes here to a payment of $1,199.10 and total interest of $231,676.

The seven guides below share one shape: what the engine computes; why, in terms of its conventions; where it stops — the calculators model fixed-rate, fully amortizing loans and, in the methodology page's words, "do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization"; how to read the output; and the common misreadings.

How the monthly payment formula works

The standard amortized-loan (PMT) formula with monthly compounding: the annual rate divided by twelve, the term in months, the payment factor, and the one fixed payment that retires the balance at the last month. A computed table shows what changes with term and rate; the engine's 0% convention — principal divided evenly across the term — is shown separately.

Reading an amortization schedule

What one year row of the engine's schedule records — the interest and principal paid across twelve payments and the balance left — and why the interest column starts large; the first-month split is the one single-month figure, derived as balance × rate ÷ 12. The year row in which principal overtakes interest is read from the schedule, not estimated, and a fixed extra payment is run to show its effect on the rows and the payoff month.

How affordability is estimated

The House Affordability Calculator in three steps: the two limits the debt-to-income guidelines place on a monthly housing budget, the payment factor that turns a budget into a loan amount, and the property-tax term — "solved with a closed-form rearrangement rather than an approximation," as the methodology page puts it. The guide also repeats what the number is not: "general lender guidelines, not an underwriting decision."

Refinance and break-even arithmetic

How the Refinance and Refinance Break-Even calculators price the current payment and the new one, take the monthly difference, divide the closing costs by it to find the break-even month, and compare lifetime interest on both paths — each the payment times its months, less the balance. The guide also runs the month-level variant, where the terms are entered in months and closing costs can be rolled into the new principal, and lists what the comparison does not include.

Fee-adjusted APR explained

Why the APR Calculator reports a rate different from the note rate, in this engine's arithmetic only: the payment is fixed at the note rate on the full loan, the amount received is the loan less the fees, and the engine searches for the rate that reconciles the two. A computed fee ladder shows what moves the gap.

Credit card payoff math

The credit engine's convention — interest at APR ÷ 12, one month at a time — applied to a single fictional card: how long a fixed payment takes to clear the balance, why a payment close to the first month's interest takes so long, the payment that clears the balance by a chosen month, and the balance-transfer arithmetic.

Snowball vs. avalanche as the engine runs them

How the Debt Payoff Calculator simulates both strategies on a fictional set of debts: a constant monthly budget of every minimum plus the extra, a fixed target order, and the rollover rule — when a debt is eliminated, its freed-up minimum rolls into the payment on the next target. The engine accepts up to 10 debts and reports plans longer than 1,200 months as out of range. No verdict is drawn.

The four original guides

Four earlier explainers predate the guides above and remain at their own addresses.

How Amortization Works — the introduction to the fixed-payment schedule: how each payment splits between interest and principal and how the balance falls across the term.
PMI, Explained — what the mortgage-insurance line in the Mortgage Calculator's purchase breakdown, and the loan-to-value flag in the Down Payment Calculator, refer to. The breakdown reports PMI as a monthly amount at the starting loan-to-value ratio and does not compute when it ends; this guide sets out the rules the engine leaves aside.
Fixed vs. Adjustable Rate — describes the loan structure this engine does not price; the calculators hold whatever rate you enter fixed for every month of the term.
Mortgage Discount Points and the Break-Even Math — the companion to the Mortgage Points Calculator: what a point is, and the break-even arithmetic between the upfront cost of points and the payment difference they produce.

Back to the calculators

The guides explain; the calculators compute on your own figures, entirely in your browser. The methodology page is the vetted statement of how the engine is built, tested and rounded, and of its limitations; every guide defers to it. The about page describes who publishes the site.

Not financial advice: the calculator models the arithmetic; it does not know your lender's terms. The figures in these guides are rounded views of full-precision values — your lender's figure may differ by a few cents depending on their rounding and day-count conventions, and the difference is presentational, not an error. For consequential financial decisions, verify results independently and consult a licensed mortgage professional. Values entered on any calculator are processed locally in your browser and never transmitted. See the methodology page.