Methodology

The amortisation formula

Every payment figure on the site comes from the standard level-payment formula:

A = P × i × (1 + i)^n ÷ ((1 + i)^n − 1)

At exactly 0% the formula is indeterminate, so we use its limit, A = P ÷ n. Zero or negative inputs return zero rather than a meaningless number.

The interest rate convention we use

We divide the nominal annual rate by the number of payment periods in a year. A 6.5% annual rate with monthly payments becomes 6.5% ÷ 12, not the twelfth root of 1.065 minus one. This is the convention US lenders use to quote and calculate mortgage, auto and consumer credit payments, so our instalment agrees with the lender's own statement to the cent. Agreeing with the statement matters more than theoretical purity: a calculator that disagrees by a few cents is one nobody trusts.

Periods per year are monthly 12, biweekly 26, weekly 52, quarterly 4, semiannual 2 and annual 1. UK lenders often accrue interest daily on the outstanding balance, which can shift the final payment and the effect of mid-month overpayments; our models accrue interest once per payment period.

Remaining balance in closed form

The balance after k payments is solved directly rather than by looping through the schedule:

B(k) = P × (1 + i)^k − A × ((1 + i)^k − 1) ÷ i

Payment 340 of a 40-year loan is therefore as exact as payment one, with no accumulated floating-point drift. The unit tests check this formula against a period-by-period simulation and require agreement to within one cent across 120 periods.

How extra payments are applied

Extra payments are applied to principal after the scheduled interest for the period is covered, which is the standard lender default. The schedule stops when the balance reaches zero, so the reported term is the real payoff date rather than the contractual one, and the saving is measured against the same loan with no extra payments. A one-time lump sum can be applied in a period you choose. If an extra payment would exceed the remaining balance it is reduced, so principal is never overpaid and the final scheduled payment shrinks accordingly.

Affordability and the 28/36 guideline

The affordability calculator uses the two ratios that dominate conventional underwriting. The front-end ratio is total monthly housing cost divided by gross monthly income. The back-end ratio, or debt-to-income ratio, is all monthly debt payments including housing divided by gross monthly income. The conventional guideline is 28% front-end and 36% back-end; FHA loans and some programmes allow more.

We take the lower of the two limits, income × 28% and income × 36% minus your existing debts, and solve in one step for the property price whose total monthly cost, principal and interest plus property tax, insurance, HOA fee and mortgage insurance, equals that budget. Defaults are 1.2% a year for property tax and 0.5% for mortgage insurance, both editable. Real underwriting also weighs credit score, reserves and automated underwriting findings, so treat the result as a starting point.

Rounding policy

Calculations run at full double precision; only the display is rounded, to the cent, with halves rounded away from zero. Totals are computed from unrounded values and then rounded once, so the rows printed in a table may add up to a figure a cent away from the printed total. That matches how a servicer rounds the payment rather than the underlying balance.

How we test

Every formula lives in one calculation module and is covered by an automated test suite that runs with a single command, using the runtime's built-in test runner. The suite checks identities rather than snapshots: interest plus principal must equal the payment in every period, principal repaid must equal the amount borrowed, a zero rate must produce zero interest, extra payments must shorten the term, and a payment that cannot cover interest must be flagged, not silently scheduled. Reference cases are checked against published figures: $300,000 at 6.5% over 30 years must return $1,896.20 a month and about $382,633 of total interest, and the same loan with $200 a month extra must clear in 277 payments instead of 360 and save roughly $103,400.

What the models do not include

• daily interest accrual and intra-period balance changes;
• servicer-specific rounding rules;
• escrow and impound projections, and tax or insurance reassessment;
• variable and tracker rate resets, caps and collars;
• discounted or stepped rates, buydowns and introductory periods;
• prepayment penalties, early repayment charges and exit fees;
• mortgage insurance removal thresholds and lender-specific insurance rules;
• tax deductibility, state and local taxes, stamp duty and registration charges;
• credit score effects, lender fees and individual underwriting decisions;
• negative amortisation, which is reported as a warning rather than modelled;
• balloon payments and interest-only periods.

Report a discrepancy

If a figure here disagrees with your lender, your statement or another reputable calculator, tell us at hello@amortgrid.com. Include the calculator you used, every input, the result you saw and the result you expected. We treat a disagreement as a bug until it is proved otherwise, and corrections take priority over new features.

Last reviewed 2026-09-27.