Amortization Calculator

What is loan amortization?

Amortization is the process of repaying a loan in instalments that cover both the interest accrued since the last payment and part of the principal. Because the payment is fixed and the balance falls, the split between those two parts moves across the loan: the same instalment buys less interest and more principal every period until the balance reaches zero.

That is the whole mechanism. Nothing about it is specific to a mortgage, a car loan or a business note — the arithmetic is identical, which is why this calculator is generic and the presets only change the labels around it.

How an amortization schedule works

A schedule is the loan written out payment by payment. For each period it charges interest on the balance carried into that period, applies the rest of the instalment to principal, and carries the reduced balance forward. Repeat until the balance is gone.

1. Interest for the period = balance × periodic rate.
2. Principal for the period = scheduled payment − interest (plus any extra payment, which goes entirely to principal).
3. New balance = old balance − principal.
4. The final instalment is adjusted so the balance closes at exactly zero.

Because step 1 always uses the balance before the payment, money paid earlier removes far more future interest than the same money paid later.

How to read the schedule

Payment #

The instalment number, 1 to the last. With a first payment date entered, the date column names the day each one falls due.

Scheduled payment

The contractual instalment. It is the same every period except the last.

Extra payment

Anything paid on top in that period. It goes entirely to principal.

Interest and Principal

How that instalment split. Interest is charged first; principal is what is left.

Cumulative principal and Cumulative interest

Running totals. The point where the cumulative principal line overtakes the cumulative interest line is the loan turning in your favour.

Ending balance

What is still owed after that payment. The last row is zero on a fully amortizing loan, and the balloon balance on a balloon note.

The amortization formula

The level payment on a fully amortizing fixed-rate loan is the standard annuity formula:

M = P × [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ − 1 ]

• M — the payment per period.
• P — the principal financed (the amount borrowed, plus any fee you chose to finance).
• i — the periodic interest rate: the nominal annual rate converted to one payment period.
• n — the number of payments over the term.

The zero-rate branch. At i = 0 that expression divides by zero, so it is not used. An interest-free loan repays M = P / n exactly, and this calculator returns exactly that: total interest of precisely zero, not a rounding artefact.

Worked example. $250,000 at 6.5% over 30 years: i = 6.5% ÷ 12 = 0.5417% a month and n = 360, so M = $1,580.17 and the loan charges $318,861.22 of interest in total.

A worked schedule, computed by this page

Six points from the $250,000 at 6.5% over 30 years example. Every figure is produced by the engine that runs the calculator above and is pinned by an automated test, so prose and arithmetic cannot drift apart.

Why early payments contain more interest

Interest is charged on what is still owed, and at the start almost nothing has been repaid. On the worked example, 86% of the very first instalment is interest and only $226.00 reduces the balance. Twelve payments in, $16,167.73 of interest has been charged against $2,794.31 of principal.

The balance falls slowly at first, so the interest charge falls slowly too — and since the instalment is fixed, the principal share can only rise slowly. Principal does not overtake interest until payment 233 of 360. This is arithmetic, not a lender practice: no interest is charged in advance and nothing is front-loaded by design.

Extra payments and early payoff

An extra payment reduces the balance that accrues interest for every remaining period, so the saving compounds rather than being the extra amount times the rate. This calculator models four shapes together — an extra on every instalment, an annual lump sum, a one-time payment, and a list of dated payments — and reconciles the result against the same loan without them: original and new payoff dates, payments eliminated, interest before and after, and the net saving.

The convention used here, which is the standard principal-curtailment treatment: the period's interest is charged first, then the scheduled principal is credited, then the extra goes entirely to principal. The reduced balance is what accrues the next period's interest — never the current one. An extra larger than the balance is cut to exactly the balance, so no payment can drive the loan below zero.

Some agreements charge a prepayment penalty. Where one applies, the page shows the gross interest saved, the penalty and the net saving separately, and says plainly when the penalty is the larger of the two.

Monthly vs biweekly payments

A biweekly schedule is 26 payments a year, not 24. Paying half the monthly instalment every two weeks therefore contributes the equivalent of thirteen monthly payments a year rather than twelve, and the extra one is what shortens the loan — the fortnightly cadence itself is a minor effect.

This calculator models biweekly, semi-monthly (24 a year, which is genuinely twice a month and not the same thing), weekly, quarterly and annual schedules on their own cadence rather than approximating them from a monthly figure. To compare the two honestly, set the frequency and read the payoff date, not just the instalment.

Mortgage amortization

A mortgage amortizes exactly like any other fixed-rate loan; what is different is everything around it. Property taxes, homeowners insurance, HOA dues and mortgage insurance are costs of owning the property, not of borrowing the money, so the mortgage preset shows them as separate housing costs and keeps them out of the schedule. Mixing escrow into an amortization table would overstate both the principal repaid and the payoff speed.

The figures to read together are principal and interest (which is what the schedule amortizes), other housing costs, and the estimated total monthly housing cost.

Car loan amortization

An auto loan is a short, fully amortizing note, usually 36 to 84 months. Because the term is short, principal overtakes interest early — often within the first year — and the total interest is a much smaller multiple of the principal than on a mortgage of the same rate.

Enter the amount actually financed: the price after any down payment, trade-in and rebate. A dealer-arranged rate quoted as APR already includes some fees, so entering it as the interest rate will slightly overstate the interest charged; where you know the fees, put them under Advanced options instead.

Seller financing and balloon payments

Seller-financed notes typically amortize on a long schedule — 20 or 30 years — but mature far sooner, leaving a balance due in full at maturity. Set the repayment type to Balloon, enter the amortization term, and enter the balance that falls due; the page then reports the regular payment, the balloon balance at maturity, the interest charged before it and the final payment date.

An interest-only note is the limiting case: every instalment is exactly the interest, the balance never falls, and the whole principal is the balloon. A single payment at maturity goes further still — nothing is paid until the end and the interest capitalises into the balance.

Interest-only and negative amortization

Interest-only means the instalment covers the interest and nothing more, so the balance is the same at the end of the period as at the start. It is modelled here as its own repayment type.

Negative amortization is what happens when the payment does not even cover the interest: the shortfall is added to the balance and the debt grows. This calculator refuses that case rather than drawing it — if you ask it to solve a term from a payment below one period's interest, it says the balance would never fall instead of returning a number. That is deliberate: a schedule that quietly grows is the one place an amortization table can mislead badly.

Amortization vs depreciation

Three different things share the word. Loan amortization is the repayment schedule above. Straight-line amortization writes the cost of an intangible asset off evenly over its useful life. Depreciation does the same job for a tangible asset — a vehicle, a machine, a building.

Amortization and depreciation are the same arithmetic applied to different classes of asset; neither has anything to do with a loan balance, an interest rate or a payment. The mini-tool further down handles the straight-line case and is deliberately kept apart from the loan calculator so the two are never confused.

Interest rate vs APR

They are not synonyms, and this page never treats them as one.

The interest rate is the contractual rate on the note. It is what accrues on the balance, what every row of the schedule is built from, and it is the number this calculator asks you for.

The estimated APR is worked backwards out of the cash actually exchanged: the money that reaches you at closing against every instalment you pay. Because fees change that cash without changing the note rate, any fee pushes the APR above the rate — and the timing of the payments affects it too. With no fees at all, the two coincide.

It is an estimate from your figures, not a lender's disclosure. A legally disclosed APR follows its own rules about which charges count as finance charges and how odd days and rounding are handled, and those rules differ by product and by country. Use the figure here to compare offers you have entered on the same basis.

Amortization calculator methodology

Formula

M = P × [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ − 1 ], with the exact branch M = P / n at a zero rate.

Periodic rate

i is the nominal annual rate converted to one payment period. When the payment and compounding frequencies match, i is simply the annual rate divided by the number of payments a year.

Compounding convention

The rate entered is a nominal annual rate compounded at the compounding frequency. Where the two frequencies differ they are reconciled through the effective annual rate: i = (1 + j/m)^m/p − 1, with j the nominal annual rate, m compounds per year and p payments per year.

Payment frequency

Monthly, semi-monthly (24 a year), biweekly (26 a year), weekly, quarterly and annual are each modelled on their own cadence. Semi-monthly and biweekly have no compounding counterpart and default to a monthly compounding basis.

Fees

An origination percentage, a fixed fee and other fees can each be deducted from the advance, added to the financed balance or paid separately at closing. Contractual principal, financed balance, cash proceeds and upfront cash cost are kept separate throughout.

Extra payments

Period interest first, then scheduled principal, then the extra straight to principal. The reduced balance accrues the next period’s interest. An extra larger than the balance is cut to exactly the balance, and no period can end below zero.

Rounding

Full floating-point precision throughout; rounding to cents happens only at the display, copy and export boundary. A rounded row is never fed back in as the next row’s input.

Dates

Dates appear only when you supply a first payment date. Instalments advance by whole periods, with the day clamped to the length of the target month, so 31 January plus one month is 28 or 29 February. Leap years are handled by the calendar, not approximated. No adjustment is made for weekends, holidays or day-count conventions, and interest accrues per period rather than per day.

Final payment

The final instalment is adjusted to bring the balance to exactly $0.00, absorbing the residue level-payment arithmetic leaves behind.

APR

The estimated APR is the internal rate of return of your own cash flows — net cash at closing against every instalment, extra payment and penalty — annualised nominally, the Regulation Z convention. The effective (compounded) annualisation is available alongside it.

Assumptions

Fixed rate for the whole term; a constant payment frequency; the first instalment one period after drawdown unless you say otherwise; extra payments made with the instalment of their period.

Limitations

Variable and adjustable-rate loans, rate resets, payment holidays, capitalised arrears, escrow analysis, daily-accrual conventions and lender-specific rounding are not modelled. Nothing here is a lender quotation, an eligibility test, a tax position or financial advice.

Model version

general-loan-engine-1.0.0

Last reviewed

August 16, 2026

Where a specialist calculator fits better

This page is the general amortization tool. Where a loan type has rules, fees or repayment programmes of its own, a dedicated calculator models them properly:

• Loan Calculator — the same engine with affordability, offer comparison and refinance break-even.
• Mortgage Calculator — property loans with taxes, insurance and mortgage insurance modelled in full.
• Auto Loan Calculator — dealer worksheets, trade-ins, rebates and promotional APR.
• Personal Loan Calculator — unsecured lending with origination fees and estimated APR.
• Student Loan Calculator — federal repayment plans and forgiveness paths.
• Debt-to-Income Ratio Calculator — where a new payment leaves your ratio.