To calculate mortgage amortization, take three numbers from your loan documents — the principal, the monthly interest rate, and the total number of monthly payments — run them through the standard payment formula to get your fixed monthly payment, then break each payment into interest and principal by multiplying the current balance by the monthly rate. That interest figure subtracted from the fixed payment is how much principal you actually paid off that month, and the new balance carries into the next month’s calculation. Repeat for every month of the loan and you have a full amortization schedule.
The Three Numbers You Need
Every amortization calculation runs on the same three inputs: the loan principal, the annual interest rate converted to a monthly figure, and the loan term expressed in months.
The principal is the total amount borrowed. It appears as “Loan Amount” on the first page of your Loan Estimate and on your monthly mortgage statement.1Consumer Financial Protection Bureau. Loan Estimate Explainer The annual interest rate is stated as a percentage on your promissory note; divide by 12 to get the monthly rate the formula actually uses. A 6% annual rate becomes 0.5% per month, or 0.005 as a decimal.
The term is usually quoted in years, but the math works in months. Multiply years by 12: a 30-year mortgage runs 360 payments, a 15-year runs 180. All three figures are fixed in the promissory note you sign at closing, which spells out the amount owed, the interest rate, payment dates, and repayment timeline.2Consumer Financial Protection Bureau. What Documents Should I Receive Before Closing on a Mortgage Loan If you’ve already closed, the same numbers are on your Closing Disclosure.
The Amortization Formula
The standard formula for a fixed monthly mortgage payment is:
M = P × [i(1 + i)^n] / [(1 + i)^n − 1]
- M is the fixed monthly payment for principal and interest only, not taxes or insurance.
- P is the loan principal.
- i is the monthly interest rate (annual rate ÷ 12).
- n is the total number of monthly payments.
The formula first computes (1 + i)^n, which is how a dollar of debt would grow over the full term at the monthly rate. That figure sits in both the top and bottom of the fraction. Multiplying it by the monthly rate in the numerator captures the interest cost; subtracting 1 in the denominator isolates the portion attributable to principal paydown. Multiplying the result by the loan amount gives a payment that zeroes out the balance on the final month.
Worked Example: $300,000 at 6% for 30 Years
Real numbers make the sequence concrete. Take a $300,000 loan at 6% annual interest with a 30-year term.
Convert the inputs first. Monthly rate: 0.06 ÷ 12 = 0.005. Total payments: 30 × 12 = 360.
Now calculate (1 + i)^n. That’s (1.005)^360, which comes out to roughly 6.0226. This exponent is the step that forces a calculator or spreadsheet; doing it by hand is impractical.
Build the numerator by multiplying the monthly rate by that result: 0.005 × 6.0226 = 0.030113.
Build the denominator by subtracting 1 from the same result: 6.0226 − 1 = 5.0226.
Divide the numerator by the denominator: 0.030113 ÷ 5.0226 = 0.005996.
Multiply by the principal: $300,000 × 0.005996 = $1,798.65. That’s your fixed monthly payment for principal and interest. Over 360 payments, the total comes to about $647,515, meaning roughly $347,515 goes to interest alone.
Splitting Each Payment Into Interest and Principal
The monthly payment stays the same, but the split between interest and principal changes every month. To find the interest portion, multiply the current outstanding balance by the monthly rate. For the first payment on the example loan: $300,000 × 0.005 = $1,500.00 in interest.
Subtract that from the total payment to get the principal portion: $1,798.65 − $1,500.00 = $298.65. That $298.65 is the only part of month one that actually reduces what you owe. The new balance becomes $300,000 − $298.65 = $299,701.35.
Month two recalculates interest on the lower balance: $299,701.35 × 0.005 = $1,498.51. Principal rises to $300.14. The shift is small at first but accelerates. By month 300, roughly two-thirds of each payment goes toward principal. Your servicer must show this breakdown on every periodic statement, with the interest and principal amounts itemized on the first page.3eCFR. 12 CFR 1026.41 – Periodic Statements for Residential Mortgage Loans
In the example loan, the first year’s 12 payments total $21,583.80, but only about $3,636 of that reduces principal. The rest is the cost of borrowing.
Building the Full Schedule
An amortization schedule is a table that repeats the interest-and-principal split for every month of the loan. Set up columns for the month number, beginning balance, payment amount, interest paid, principal paid, and ending balance. The ending balance from one row becomes the beginning balance of the next.
The first three rows of the $300,000 example look like this:
- Month 1: beginning balance $300,000.00, interest $1,500.00, principal $298.65, ending balance $299,701.35.
- Month 2: beginning balance $299,701.35, interest $1,498.51, principal $300.14, ending balance $299,401.21.
- Month 3: beginning balance $299,401.21, interest $1,497.01, principal $301.64, ending balance $299,099.57.
Repeat for all 360 months. The final row’s ending balance should land at zero, or within a few cents due to rounding. If it doesn’t, a rounding error crept in somewhere, most likely in the exponent step.
Doing It in a Spreadsheet
Almost nobody builds an amortization schedule by hand. Excel, Google Sheets, and similar tools have a built-in PMT function that does the payment calculation in one cell. The syntax is PMT(rate, nper, pv), where “rate” is the monthly interest rate, “nper” is the total number of payments, and “pv” is the loan principal entered as a positive number. For the example loan, PMT(0.005, 360, 300000) returns −$1,798.65. The negative sign just means money leaving your account.
For the schedule itself, create a row for each month. In the interest column, multiply the current balance by the monthly rate. In the principal column, subtract the interest from the PMT result. Carry the reduced balance forward and drag the formulas down through month 360. The whole schedule builds in seconds, and changing the rate or principal in one cell recalculates everything.
What Extra Payments Do to the Math
The formula assumes you pay exactly the scheduled amount every month. Paying more collapses the schedule forward, because extra dollars go straight to principal. The recalculation is direct: after applying the regular payment’s principal portion, subtract the extra amount from the remaining balance, then use that lower balance as the starting point for next month’s interest calculation.
The savings compound quickly. On a $200,000 loan at 4% over 30 years, adding $100 per month to each payment can shorten the loan by more than four years and cut total interest by over $26,000. Doubling that extra amount to $200 per month can trim more than eight years off the term and save over $44,000 in interest. The earlier in the loan you start, the bigger the effect, because you’re reducing the balance that interest compounds on for the longest stretch of time.
Recasting After a Lump Sum
If you make a large lump-sum principal payment, you can ask your servicer to recast the loan. Recasting keeps your interest rate and original payoff date the same but recalculates the monthly payment based on the lower balance and the remaining term. You’re essentially re-running the formula with a smaller P and fewer months.
Most servicers require a minimum lump-sum payment, commonly $5,000 to $10,000, and charge an administrative fee between $150 and $500. The result is a lower required monthly payment for the rest of the loan. Recasting is different from refinancing: no credit check, no new appraisal, and no closing costs beyond the processing fee. Not every loan type is eligible, so check with your servicer before planning around it.
Adjustable-Rate Mortgages
Adjustable-rate mortgages follow the same formula during the initial fixed period. A 5/1 ARM holds its rate steady for the first 60 months, and the math works identically to a fixed-rate loan during that window. The complication arrives at each rate adjustment.
At every adjustment, the servicer recalculates the payment with three updated inputs: the current outstanding balance (not the original principal), the new rate, and the remaining number of months. If a 5/1 ARM started at $300,000 for 30 years and the rate adjusts after month 60, the new calculation uses whatever the balance is at that point, the adjusted rate, and 300 remaining months. Rate caps limit how far the rate can move at each adjustment and over the life of the loan.4Consumer Financial Protection Bureau. What Are Rate Caps With an Adjustable-Rate Mortgage (ARM), and How Do They Work Modeling best- and worst-case schedules means running the formula at the floor rate and the lifetime cap for every adjustment period.
When the Balance Grows Instead of Shrinking
Some loan structures allow a minimum payment lower than the monthly interest charge. When that happens, the unpaid interest is added to the principal, and the loan grows over time. This is negative amortization, and it means you end up paying interest on interest.5Consumer Financial Protection Bureau. What Is Negative Amortization
Negative amortization is rare in conventional fixed-rate loans but can appear in certain ARM products with a low introductory minimum payment. If your schedule shows the ending balance rising instead of falling in any month, the math is the same as normal amortization except the principal column shows a negative number and the ending balance is higher than the beginning balance. That’s a signal to look closely at your loan terms.