What amortization actually means
"Amortization" just means paying off a debt gradually, through regular payments, over a set period of time. On a fixed-rate loan — a mortgage, an auto loan, most personal loans — the payment amount never changes, but what that payment buys changes every single month.
Every payment is split into two pieces: interest, which is the lender's charge for the money you still owe, and principal, which is the part that actually reduces your debt. Interest is calculated fresh each month on whatever balance is left — not on the original loan amount — so as the balance falls, the interest charge falls with it, and a bigger share of your fixed payment goes toward principal instead.
That's why the first few years of a 30-year mortgage can feel like you're barely making a dent: in month one of the $300,000 example below, over 85% of the payment is interest. By the final years of the loan, that flips almost completely the other way.
The formula, derived step by step
The monthly payment formula isn't arbitrary — it falls directly out of one requirement: after the last scheduled payment, the balance must be exactly zero. Here's the derivation.
Step 1 — define the variables.
Step 2 — write the balance after one payment. Each month, the balance first grows by one month's interest, then shrinks by the payment:
Step 3 — unroll the recurrence. Applying that same rule n times and simplifying the resulting geometric series gives the balance after n payments:
Step 4 — set the balance to zero and solve for M. A fully amortizing loan means Bₙ = 0 by definition, so:
Step 5 — the special case: r = 0. If the interest rate is zero, that formula divides by zero — (1 + r)ⁿ − 1 becomes 0. There's no interest to solve for, so the answer is simpler and doesn't need the formula at all:
Any calculator that skips this branch will crash or silently return the wrong number on a 0% promotional loan. This one checks for it explicitly.
A full worked example, with exact numbers
Take a $300,000 loan at 6.5% annual interest over 30 years (360 monthly payments), starting February 1, 2026 — the defaults already loaded into the calculator above.
Plugging into the formula:
The first payment, month by month:
| Item | Amount |
|---|---|
| Starting balance | $300,000.00 |
| Interest (balance × 0.00541667) | $1,625.00 |
| Principal (payment − interest) | $271.20 |
| Balance after payment 1 | $299,728.80 |
| Balance after payment 2 | $299,456.12 |
Over the full 30 years: total interest paid is $382,633.47, total paid (principal + interest) is $682,633.47, and the loan is paid off on January 1, 2056.
Enter these same numbers into the calculator above and every figure — the monthly payment, the first payment's interest/principal split, the totals — will match exactly, because it's the same formula and the same schedule logic running client-side.
Why extra payments help — and how much
Because interest is charged on the balance that's currently outstanding, any extra dollar of principal you pay today stops accruing interest for every remaining month of the loan. Pay $200 extra in month one of a 30-year loan and you're not just saving one month's interest on that $200 — you're saving 359 months of it.
On the $300,000 / 6.5% / 30-year example above, adding a flat $200 extra principal payment every month from the start:
Toggle "Add an extra monthly payment" in the calculator above and try your own number — even a small, consistent extra payment compounds more than most people expect, precisely because it acts earliest when the balance (and therefore the interest it generates) is largest.
Frequently asked questions
What is an amortization schedule?
An amortization schedule is a table that breaks every single payment on a loan into two parts — how much goes to interest and how much goes to paying down the principal — plus the remaining balance after that payment. It shows exactly where every dollar goes, payment by payment, from the first month to the day the loan is paid off.
How is my monthly payment calculated?
This calculator uses the standard fixed-rate amortization formula: M = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where P is the loan amount, r is the interest rate divided by 12 (the monthly rate), and n is the total number of monthly payments. See the full derivation above.
Why do my early payments go mostly toward interest?
Interest is charged on whatever balance is still outstanding, so in month one you're paying interest on the entire loan amount. As the balance shrinks with each payment, there's less balance left to charge interest on, so a growing share of each fixed payment goes toward principal instead.
What does the "extra payment" option actually do?
It adds a fixed amount to your principal every month on top of your required payment. Because interest is calculated on the remaining balance, a lower balance means less interest charged next month, which means more of next month's payment reduces principal too — the effect compounds.
Does a 0% interest loan need an amortization schedule?
Yes — the schedule is just simpler. With no interest, every payment is the same size and goes entirely to principal, so the payment is the loan amount divided by the number of payments. The standard formula can't be used directly here since it divides by zero when the rate is zero, so it has to be handled as its own case.
What's the difference between amortization and simple interest?
Simple interest charges a flat rate on the original principal for the life of the loan, so the interest amount is the same every period. Amortized loans charge interest only on the current outstanding balance, so the interest portion shrinks every month as the balance is paid down. Almost every consumer installment loan is amortized, not simple-interest.
Does the start date I choose change my payment amount?
No. The start date only changes the calendar dates shown next to each payment and the projected payoff date. It has no effect on the monthly payment amount, total interest, or total paid, all of which depend only on the loan amount, rate, and term.
Can I use this for a mortgage, auto loan, or personal loan?
Yes. The math is identical for any fixed-rate, fixed-term installment loan. For a mortgage specifically, this schedule covers principal and interest only — it doesn't include property tax, homeowners insurance, PMI, or HOA dues your servicer may bundle into the actual bill (often called PITI).
Why is my lender's payment a few cents different from this calculator?
Small differences usually come from rounding method or day-count conventions — some lenders round every monthly payment to the cent while others adjust only the final payment, and some use a 365/360 day-count that slightly changes the effective monthly rate. This calculator computes each month directly from the remaining balance and zeroes the schedule out exactly, which matches most lenders within a few cents.
What happens to my payment in the final month?
The final payment is adjusted so the remaining balance reaches exactly zero — if rounding across the schedule would otherwise leave a few cents owing or overpaid, that difference is absorbed in the last payment rather than carried forward.
Can I download the full schedule?
Yes — the "Download CSV" button exports every row (payment number, date, payment, principal, interest, and remaining balance) as a CSV file you can open in Excel, Google Sheets, or Numbers. There's also a print-friendly view if you'd rather keep a paper or PDF copy.
How much can extra payments actually save me?
It depends on how early in the loan you start and how large the extra payment is, because extra principal paid early avoids the most future interest. On a typical 30-year mortgage, an extra payment equal to roughly 10% of the required payment, made every month from day one, commonly cuts several years off the loan and saves tens of thousands of dollars in interest — enter your own numbers above to see your exact figures.
Is the rate I should enter the interest rate or the APR?
Enter your loan's stated interest rate (sometimes called the "note rate"), not the APR. The APR folds in lender fees and closing costs spread over the loan term, so it's higher than the interest rate and isn't the number used to calculate your actual monthly payment — the interest rate is.