To amortize a loan, calculate a fixed monthly payment with the formula M = P × [r(1 + r)^n] / [(1 + r)^n – 1], then break each payment into interest (the current balance times the monthly rate) and principal (whatever is left of the payment). Apply the principal to the balance, and repeat for every month of the term. That is the whole method for how to amortize a loan, and everything below is the mechanics of doing it accurately.
The Three Inputs You Need
Every amortization calculation runs on three numbers: the principal (P), the monthly interest rate (r), and the total number of monthly payments (n). Your loan estimate or closing disclosure lists the principal, annual rate, and term on the first page.
Convert before you calculate. Divide the annual interest rate by 12 for the monthly rate. Multiply the term in years by 12 for the number of payments. A 30-year loan at 6% annual interest gives you r = 0.005 and n = 360. Small conversion mistakes compound across hundreds of months, so this step matters.
The Amortization Formula
The fixed-payment formula has three moving parts inside it:
M = P × [r(1 + r)^n] / [(1 + r)^n – 1]
- M is the monthly payment
- P is the loan principal
- r is the monthly interest rate (annual rate ÷ 12)
- n is the total number of monthly payments (years × 12)
Work through a $250,000 loan at 6% for 30 years. The monthly rate is 0.005 and the payment count is 360. First compute (1 + 0.005)^360, which is roughly 6.0226. The numerator is 0.005 × 6.0226 = 0.030113. The denominator is 6.0226 – 1 = 5.0226. Divide to get about 0.005996, then multiply by the $250,000 principal. The monthly payment comes out to roughly $1,498.88, and it stays fixed for the life of the loan unless you refinance or modify the terms.
Federal disclosure rules require lenders to state the exact payment schedule, total of payments, and annual percentage rate before closing, so a standardized calculation is what lets you comparison-shop.1Consumer Financial Protection Bureau. Regulation Z 1026.18 – Content of Disclosures
One note on how the math scales. Payment moves in a straight line with principal: double the loan and the payment doubles. It does not move in a straight line with the interest rate. A jump from 5% to 7% raises the payment more than a jump from 3% to 5% on the same principal, which is why even a quarter-point rate change matters on a large loan.
Splitting Each Payment Between Interest and Principal
The fixed payment is only half the picture. To build the schedule, you have to split each month’s payment into its interest and principal components, and that split changes every month.
The procedure for any given month:
- Multiply the current outstanding balance by the monthly interest rate. That is the interest for the month.
- Subtract the interest from the fixed monthly payment. That is the principal for the month.
- Subtract the principal from the outstanding balance. That is next month’s starting balance.
On the $250,000 loan at 0.5% monthly, the first month’s interest is $250,000 × 0.005 = $1,250. Subtract that from the $1,498.88 payment and $248.88 goes to principal. The new balance is $249,751.12, and that number is what you multiply by 0.005 to start month two.
Because interest is charged on the outstanding balance, early payments are heavily weighted toward interest. In the first year of a 30-year mortgage, roughly two-thirds or more of each payment goes to interest, and principal moves slowly. As the balance falls, the interest charge falls with it, so a larger slice of the same fixed payment goes to principal each month. By the last years of the loan, almost the whole payment is principal. The last ten years retire far more debt than the first ten.
Building the Full Schedule
An amortization table is that month-by-month split laid out in rows. Each row has five columns: payment number, starting balance, interest, principal, and ending balance. The ending balance of one row becomes the starting balance of the next. In a spreadsheet you build row one manually and copy the formulas down through every remaining payment period.
The finished table tells you when you cross the halfway mark on principal, how much interest you will have paid by any given year, and how equity accumulates over time. It also lets you check your lender. If the servicer’s statement shows a different principal balance than your table predicts, that gap is worth investigating.
Why the Final Payment Is Slightly Off
The last payment almost never matches the standard monthly amount. The reason is rounding. Your calculated payment gets rounded to the nearest cent, and the fractional over- or underpayment accumulates across hundreds of months. If the payment was rounded up, you overpay slightly each month and the final payment shrinks to compensate. If it was rounded down, the final payment is slightly larger. The difference is usually pennies to a few dollars.
The Spreadsheet Shortcut
You do not have to type the full formula. Excel and Google Sheets both have a PMT function that returns the fixed monthly payment in one step.2Microsoft. PMT Function
=PMT(rate, nper, pv)
- rate is the monthly interest rate (annual rate divided by 12)
- nper is the total number of payments (years × 12)
- pv is the loan principal
For the running example, =PMT(0.06/12, 360, 250000) returns approximately –$1,498.88, matching the manual calculation. The result is negative because it represents cash flowing out. To build the full table from there, create three formulas in your first row: interest = balance × monthly rate, principal = payment – interest, and new balance = old balance – principal. Drag the row down for the remaining periods.
Two related functions check a single month without building the whole schedule. IPMT returns the interest portion of a specific payment, and PPMT returns the principal portion. Both use the same arguments as PMT plus a period number.
How Extra Payments Change the Schedule
Because interest is calculated on the outstanding balance each month, every extra dollar toward principal shrinks the base that interest is charged on for every future month. Modest additional payments early in a 30-year loan can cut years off the term and save substantial interest over the life of the debt.
Extra payments can affect the schedule two ways. The default at most servicers is to keep the monthly payment the same and shorten the term. You finish faster and save the most interest. The alternative is recasting, where the lender recalculates a lower monthly payment based on the reduced principal while keeping the original term and rate. Recasting costs less than refinancing and does not require a credit check, but not every loan or servicer offers it.
Federal law largely prohibits prepayment penalties on residential mortgages originated after January 2014. Where a penalty is permitted at all, the loan must carry a fixed rate, be a qualified mortgage, and not be a higher-priced loan. The caps are strict: no more than 2% of the prepaid balance during the first two years, no more than 1% during the third year, and no penalty after three years.3eCFR. 12 CFR 1026.43 – Minimum Standards for Transactions A lender offering a loan with a prepayment penalty was also required to offer an alternative without one.
When the Standard Method Doesn’t Apply
A few loan structures break the assumption that the schedule you calculate today will hold for the full term.
Balloon Loans
A balloon loan uses monthly payments calculated on a longer amortization (often 30 years) but requires the remaining balance in one lump sum after a shorter period, commonly five or seven years. The month-to-month math works exactly the same way. The schedule just stops with a large balance still owed rather than tapering to zero. On an $800,000 loan at 8% with a three-year balloon, the monthly payment might be around $5,929 with roughly $786,000 still due at the end.
Adjustable-Rate Mortgages
An ARM starts fixed for an introductory period, then resets based on a market index. At each reset, the lender rebuilds the schedule from three inputs: the current balance, the new interest rate, and the months remaining on the original term. The formula is identical. It just restarts with new numbers, and the payment can move meaningfully if the rate has changed.
Negative Amortization
Negative amortization occurs when a monthly payment does not cover the interest due and the unpaid interest is added to principal, so the balance grows instead of shrinks. Federal law prohibits negative amortization in qualified mortgages: the scheduled payments must not increase the principal balance.4Office of the Law Revision Counsel. 15 USC 1639c – Minimum Standards for Residential Mortgage Loans A loan that allows the balance to rise falls outside that category.
Escrow Isn’t in the Formula
The amortization formula produces only the principal-and-interest portion of a mortgage payment. Most lenders also collect monthly amounts for property taxes, homeowners insurance, and, where applicable, private mortgage insurance, holding them in escrow. Your total obligation (PITI) is higher than the formula output, and it can change annually as tax and insurance costs move, even on a fixed-rate loan. If your payment changes and the loan is fixed-rate, the principal-and-interest portion is unchanged; the escrow line is where to look.