How We Calculate

Every number on this site comes from the formulas below. They run the same way on our server and in your browser, so a schedule you share by link shows exactly the figures you saw. Nothing is estimated from tables or rounded rules of thumb unless this page says so.

Last updated: November 6, 2026.

The monthly payment

All fixed-rate loans on the site use the standard amortization (annuity) formula:

M = P × (r(1+r)ⁿ) / ((1+r)ⁿ − 1)

  • M — the payment for each period (principal and interest only);
  • P — the amount borrowed;
  • r — the periodic interest rate: the annual rate divided by 12 for monthly payments, or by 52 for weekly ones;
  • n — the number of payments: years × 12, or the number of months or weeks you enter.

Example: $300,000 at 6.5% for 30 years. Here r = 0.065 / 12 and n = 360, so M = $1,896.20.

The amortization schedule

Each row of the schedule is one payment. Interest for the period is the remaining balance times r; the rest of the payment reduces the balance:

  1. interest = balance × r;
  2. principal = M − interest;
  3. new balance = balance − principal.

In the example above, the first payment carries $1,625.00 of interest ($300,000 × 0.065 / 12) and only $271.20 of principal. Yearly subtotal rows add up the twelve payments of each calendar year, starting from the start date you choose.

Rounding. We keep every intermediate value at full precision and round only what we display, to the cent. A lender rounds each payment to the cent and adjusts the final payment instead, so its last row can differ from ours by a few cents. Totals are unaffected beyond that.

Mortgage costs beyond principal and interest

On the mortgage calculator the loan amount is the home price minus the down payment. The other monthly costs are added on top of M:

  • Property tax, homeowners insurance and HOA dues — the annual amounts you enter, divided by 12, held constant for the whole term. In reality taxes and premiums usually rise over time, so treat later years as a floor.
  • PMI — the annual PMI rate you enter times the original loan amount, divided by 12. It applies only when the down payment is under 20% of the home price, and our schedule drops it in the month the scheduled balance falls to 80% of the original price — the point at which you can ask your servicer to cancel it. By law servicers must end it automatically at 78%, so if you never ask, it runs a little longer than shown (CFPB).

Example: a $375,000 home with 10% down at 6.5% for 30 years and PMI of 0.5% a year. Principal and interest are $2,133.23 a month, PMI adds $140.63, and the PMI ends after November 2033 (for a January 2026 start), costing $13,359.38 in total.

Extra payments and payoff

The payoff calculators first work out the payment your loan already requires from its balance, rate and remaining term. They then rerun the schedule with your extra monthly amount added to every payment, and apply a one-time lump sum before the first payment. Every extra dollar goes straight to principal. The time and interest saved are the differences between the two runs.

Example: adding $200 a month to the $300,000 loan above pays it off 6 years 11 months early and saves $103,448.79 in interest.

Auto loans

The amount financed is the vehicle price minus the down payment and the trade-in value, plus sales tax on the price. Some states tax only the price net of the trade-in; if yours does, enter the lower sales tax amount as a smaller rate.

Reverse mortgage (HECM)

The reverse mortgage calculator follows the FHA Home Equity Conversion Mortgage rules published by HUD:

  • the maximum claim amount is the lower of the home value and the FHA lending limit ($1,249,125 for 2026);
  • the principal limit is that amount times HUD's principal limit factor for the youngest borrower's age and the expected rate, interpolated between the published table values;
  • upfront mortgage insurance is 2% of the maximum claim amount; the origination fee is 2% of the first $200,000 and 1% above that, between $2,500 and $6,000;
  • in the first year you can draw up to 60% of the principal limit, or more when needed to pay off mandatory obligations such as an existing mortgage.

We update the lending limit and the factor table each year from HUD's mortgagee letters and never change them without a citation.

What the calculators do not model

  • adjustable rates: every rate is fixed for the whole term;
  • payment holidays, missed or late payments and late fees;
  • closing costs and points on the mortgage calculator, unless you add them to the loan amount yourself;
  • taxes on interest or any tax deduction;
  • your lender's specific day-count or rounding conventions, which can move individual rows by a few cents.

The results are estimates for planning. Your loan documents and your lender's figures are what you actually owe.

Editorial standards

  • Who writes it. The calculators and explanations are built and maintained by the Amortization-Calc.com team at ARSIDIAN LLC. Parts of the original site copy were written by the contributors listed on our About page.
  • Sources. We base rules on primary sources — HUD for reverse mortgages, the CFPB for consumer protections — and link to them where they apply.
  • Testing. The formulas are covered by automated tests, and payments are checked against an independent calculation, before any change goes live.
  • Independence. We do not sell loans or rank lenders. The site is free and supported by advertising, which never changes a result.

Corrections

If you find a number that looks wrong, write to us through the form on our About page with the inputs you used. We check every report against the formulas above and fix confirmed errors, noting the date of the change on this page.