Every number on this site is generated from standard, publicly documented amortization mathematics — the same method mortgage servicers use to build an amortization schedule. This page documents the exact formulas, the assumptions we make, and the things we deliberately do not model, so you can check our results against your own loan statement or a spreadsheet.
The core amortization formula
A fully amortizing fixed-rate loan has a level payment calculated once, at origination:
M = P × r ÷ (1 − (1 + r)−n)
where:
- M = the scheduled monthly principal-and-interest payment
- P = the loan principal (or current balance, if you are modeling a loan already in progress)
- r = the periodic (monthly) interest rate
- n = the total number of scheduled monthly payments (loan term in years × 12)
This payment is the amount that brings the balance to exactly zero on payment number n, assuming every payment is made in full and on time and the rate never changes.
How we derive the monthly rate
For United States mortgages, the periodic rate is the nominal annual rate divided by 12:
r = annual rate ÷ 12
This is the convention used by essentially all U.S. fixed-rate first mortgages (conventional, FHA, VA and USDA). It matches the interest accrual shown on a standard U.S. mortgage statement, where interest for the period equals the outstanding principal balance multiplied by (annual rate ÷ 12).
The calculator also supports the United Kingdom and Australia (same annual-rate ÷ 12 convention) and Canada, where the federal Interest Act requires fixed-rate mortgage interest to be compounded semi-annually. For Canada we convert the semi-annual nominal rate to an equivalent monthly rate:
r = (1 + annual rate ÷ 2)1/6 − 1
The rest of this page describes the U.S. model, which is what the great majority of our visitors use.
Building the amortization schedule
We generate the schedule one month at a time. For each month:
- Interest for the month = current balance × r
- Scheduled principal = M − interest for the month
- Extra principal = any additional amount you have specified for that month (see below)
- New balance = current balance − scheduled principal − extra principal
When the remaining balance is smaller than the scheduled payment plus interest, the final payment is reduced to exactly retire the loan. The schedule ends the first month the balance reaches zero.
How each extra-payment type is applied
| Strategy | How we model it |
|---|---|
| Extra monthly amount | Added to principal every month, starting with month 1, for the life of the loan. |
| One-time lump sum | Added to principal once, in the specific month number you choose (month 1 = first payment). |
| Annual extra payment | Added to principal once every 12 months, in the calendar month you select. |
| Accelerated bi-weekly | Modeled as the mathematical equivalent of paying one extra full monthly payment per year (1/12 of M added to principal each month). This closely approximates a true 26-payments-per-year bi-weekly schedule; see the bi-weekly calculator for detail. |
All extra amounts are assumed to be applied directly to principal in the month they are made. In practice you may need to instruct your servicer to do this — see our guide on making sure an extra payment reduces principal.
What "interest saved" and "time saved" mean
We run the schedule twice: once with no extra payments (the baseline) and once with the extra payments you have entered. Then:
- Interest saved = total interest paid in the baseline schedule − total interest paid in the accelerated schedule.
- Time saved = number of months in the baseline schedule − number of months in the accelerated schedule, expressed in years and months.
- New payoff date = the loan start date (or today, if you do not enter one) plus the number of months in the accelerated schedule.
Assumptions and simplifications
These calculators are planning tools, not a substitute for your servicer's figures. Specifically, we assume:
- A fixed interest rate for the entire term. Adjustable-rate mortgages (ARMs) are not modeled after their initial fixed period.
- No prepayment penalty. Most U.S. fixed-rate mortgages originated after January 2014 cannot carry one under the Consumer Financial Protection Bureau's Ability-to-Repay / Qualified Mortgage rules, but older loans and some non-QM loans can. Check your note.
- Principal-and-interest only. We do not include property taxes, homeowners insurance, private mortgage insurance (PMI), or HOA dues. Those are real costs, but extra principal payments do not reduce them (though reaching 78–80% loan-to-value can end PMI).
- Payments are applied on schedule, with no late fees, missed payments, forbearance, or servicing transfers.
- No recasting. Extra payments shorten the term; they do not lower the scheduled payment. See recasting vs. extra payments.
- Results are rounded for display. Tiny differences versus your statement (a few dollars over the life of a loan) are normal and come from rounding and day-count conventions.
Sources and references
Our descriptions of U.S. mortgage rules draw on primary, government, and quasi-government sources, including:
- Consumer Financial Protection Bureau (consumerfinance.gov) — prepayment penalties, servicing rules, how payments are applied.
- Internal Revenue Service Publication 936, Home Mortgage Interest Deduction.
- Freddie Mac and Fannie Mae servicing guidelines — amortization and payment application standards.
- U.S. Department of Housing and Urban Development (HUD) — FHA loan servicing.
We review this page and the underlying calculator logic at least annually, and whenever a relevant federal rule changes. If you believe a result is wrong, please tell us on the contact page with the inputs you used — we investigate every report.