Amortization Calculator

Reading the schedule

Take the worked example: a fictional $320,000 loan at 6.5% over 30 years. The engine returns a fixed payment of $2,022.62 a month. In year 1 the schedule records about $20,695 of interest against $3,577 of principal, leaving $316,423 owing at the end of the year. By year 30 the split has inverted — $833 of interest against $23,438 of principal. Across all 360 payments the loan pays $408,142 in interest on top of the $320,000 borrowed. Every payment, total and schedule row on this page is computed when the page is built by the same tested engine that powers the calculator above; the few derived figures — a month-one interest charge, a percentage share — are one step of arithmetic on those outputs, and the identities the prose asserts are re-checked while the page builds. The rates and amounts in the examples are illustrative inputs chosen for the arithmetic, not quotes.

What the engine computes, step by step

The form hands the loan amount, rate and term to one engine function, which validates them, runs the steps below in order, and returns a typed result — or an explicit, human-readable error if an input cannot be used. The interface only formats what comes back; it never does arithmetic of its own.

1. Validation. The loan amount must be positive, the rate cannot be negative, and the term must be a positive number of years within the engine's range. A rejected input stops the calculation before any arithmetic runs — for a loan amount of zero, the form shows "The loan amount must be greater than 0."
2. The fixed payment. The payment uses the standard amortized-loan (PMT) formula with monthly compounding, the convention behind US mortgages and most consumer loans: the annual rate ÷ 12 is the monthly rate, years × 12 is the number of payments (360 in Example A), and the result is the one fixed amount that retires the balance exactly at the last month — $2,022.62 here. At a 0% rate the principal is simply divided evenly across the term: Example A at 0% pays $888.89 a month and $0 of interest.
3. The month loop. Starting from the full loan, the engine charges one month's interest on the balance still outstanding — balance × (annual rate ÷ 12) — and the remainder of the fixed payment reduces the principal. The schedule is computed one month at a time so extra payments and payoff dates are exact.
4. The rows. After every twelfth payment the engine closes a row: the year number, the interest and principal paid in those twelve months, and the balance after the twelfth payment. A row also closes the moment the balance reaches zero.
5. The totals. Total interest is the sum of every monthly interest charge — $408,142 in Example A — and the total of payments is the loan amount plus that interest, $728,142. The engine also counts the payments it took to reach zero: 360 here, the full term, because no extra principal was added.

Month one and the crossover

In month one of Example A the balance is the whole $320,000, so interest is $320,000 × (6.5% ÷ 12) = $1,733.33, and only $289.28 of the $2,022.62 payment reaches principal: 85.7% of the first payment is interest. Month two charges interest on a balance that is smaller by exactly that first principal portion, so the interest charge is a little lower and a little more of the same fixed payment reaches principal. That small shift, repeated every month, is the whole mechanism — and the engine runs it one month at a time, which is why every row above is the sum of twelve such steps rather than an approximation.

The crossover is the point at which the principal portion of a payment exceeds the interest portion — the moment the interest charge falls below half the payment. The schedule above reports years, not months, so the event appears one level up: in Example A, year 20 is the first row whose Principal column ($12,257) exceeds its Interest column ($12,014), and the row before it — year 19 — still records more interest ($12,784) than principal ($11,488). The exact payment at which the flip happens is not on this screen; the companion guide works month by month on a fictional loan of its own and finds it there.

The slow start is visible in the cumulative figures. Through the first ten years of Example A the schedule records $193,998 of interest against $48,716 of principal, and at the end of year 15 — halfway through the term — the balance is still $232,189. The Balance column is the figure the Refinance Calculator's engine function takes as the amount to re-price; it is the remaining balance, not the original loan.

The first four columns are what the calculator renders for these inputs; the fifth is derived from them. The calculator lists all 30 rows.

What the term changes

The table below runs Example A's $320,000 at 6.5% through the six terms the form offers. A shorter term raises the fixed payment, which puts more of every payment into principal from month one, pulls the crossover forward and lowers the total interest.

Over 15 years the payment is $764.93 a month more than over 30, and total interest is $226,385 less. The engine compares; whether a higher payment for fewer years fits a household's budget is not a question the arithmetic answers.

Extra principal: what this schedule leaves out

The form on this page runs the schedule with no extra principal, so every row assumes exactly the fixed payment. The same engine function accepts a fixed extra amount each month, and the Mortgage Payoff Calculator runs it twice — once without the extra and once with it — and reports the difference. Computed here on Example A with a fictional extra of $150 a month: the amount paid each month becomes $2,172.62, the loan reaches zero after 296 payments instead of 360 — 5 yr 4 mo sooner — and total interest falls from $408,142 to $322,908. The required payment itself does not fall; the loan simply runs out of balance before it runs out of term, so the shortened schedule has 25 rows instead of 30 and its last row — year 25 — covers 8 payments rather than twelve, with a final payment of only whatever balance remains. This is arithmetic, not a recommendation: whether prepaying makes sense depends on facts outside the formula.

The reference figure, recomputed

The methodology page names the figure the engine is validated against: a $200,000 loan at 6% over 30 years. Recomputed here when the page is built, the same schedule function returns a payment of $1,199.10, total interest of $231,676, payoff after 360 payments and a schedule of 30 rows — the figures the methodology page and the automated tests expect. If the copy and the code ever disagreed, the site would fail to build.

How to read the result

• The large "/ month" figure is the fixed principal-and-interest payment, shown to the cent — $2,022.62 in Example A.
• Total interest is the sum of every monthly interest charge over the whole schedule, in whole dollars; Total of payments is the loan amount plus that interest — $728,142 in Example A.
• Year counts blocks of twelve payments from the first payment; row 1 is payments 1 to 12. The engine has no calendar, so matching a row to a calendar year or to a statement is the reader's step, not the engine's.
• Principal and Interest are the twelve-month sums for that row, each rounded independently to whole dollars.
• Balance is the amount still owed after the row's last payment, not an average for the year. The final row's balance is $0.
• Copy summary places the monthly payment and the total interest on your clipboard as one line; Reset clears the fields and the schedule.

The fields accept money and rates the way people type them: the form strips a dollar sign, grouping commas and a percent sign before handing the text to the shared parser, which itself accepts only plain digits, an optional minus sign and a decimal point. Internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic, and nothing is rounded between steps. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.

Common misreadings

• "The interest is front-loaded." No step in the engine weights the early months. Interest is the balance times the monthly rate in every month, and the balance is simply larger early on; the 85.7% interest share in month one of Example A is $320,000 × (6.5% ÷ 12), nothing else.
• "Total interest is the rate times the loan times the years." That simple-interest arithmetic would give $624,000 for Example A. The engine's total is $408,142, because each month's charge is on a balance that falls.
• "Halfway through the term, half the loan is paid." At the end of year 15 of Example A the balance is $232,189 — 72.6% of the loan still owed — because the early rows are mostly interest.
• "The rate is monthly" or "the rate compounds daily." This engine's convention is monthly compounding of an annual rate: the rate you enter is annual, each month charges one-twelfth of it on the balance, and nothing compounds within the month.

Where the calculator stops

The limits are the engine's, and the methodology page states them. The calculators model fixed-rate, fully amortizing loans. They do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization: whatever rate you enter is held fixed for every month of the term, and the Fixed vs. Adjustable Rate guide describes the structure this engine does not price. The schedule is principal and interest only — property tax, insurance, PMI, and HOA are estimates from the rates and amounts you enter on the Mortgage Calculator, and none of them appears in these rows. There is no extra-payment, fee or points input here, and no calendar: the engine does not know your payment dates or your lender's day-count or rounding conventions. A rejected input returns the engine's message instead of a number — a negative rate "The interest rate cannot be negative.", a term beyond the engine's range "Terms are limited to 60 years." The last limit is not the engine's but the methodology page's: a correct calculation can still be the wrong calculation for your situation — choosing the right loan for a real-world decision is judgment we cannot automate.

Frequently asked questions

Not financial advice: a general educational estimate. Your actual schedule depends on the exact rate, payment timing, and any fees. Values are processed locally in your browser and never transmitted. See the methodology page.