Finance
Amortization
How a fixed loan payment splits between interest and principal each period — and why the same payment pays down more principal, and less interest, over time.
Definition
Amortization, in the loan sense, is the process of paying off a loan through a series of regular, fixed payments, where each payment covers the interest owed for that period plus a portion of the original amount borrowed (the principal). Over the life of the loan, the split between interest and principal within each payment shifts — early payments are mostly interest, later payments are mostly principal — even though the total payment amount stays the same. The same math applies whether the loan is a mortgage on a house, an auto loan, a personal loan, or a business term loan — any loan repaid through fixed periodic payments works this way.
Why this exists
A loan like a mortgage, a car loan, a personal loan, or a business term loan is really just interest applied to whatever principal is still outstanding, recalculated every period. If a borrower only ever paid the interest due each period and never touched the principal, they'd owe just as much at the end as at the start — interest with no repayment. A fixed loan payment has to do two things at once: cover the interest that's accrued since the last payment, and chip away at the amount still owed, so the balance eventually reaches zero.
Amortization is the schedule that makes this work with a constant payment amount every period, despite the interest portion of that payment shrinking over time. Early on, the loan balance is largest, so the interest owed each period is largest too — meaning most of an early payment goes toward interest, and only a small slice actually reduces the principal. As the balance shrinks, the interest owed each period shrinks with it, so a growing share of each identical payment goes toward principal instead. The payment amount never changes, but what it accomplishes shifts dramatically over the life of the loan.
This is why paying even a little extra toward principal early in a loan can save a disproportionate amount of interest over the life of the loan: reducing the principal sooner means every future period's interest is calculated on a smaller balance, compounding the effect (see Compound Interest) in the borrower's favor instead of the lender's.
Formula & mechanics
The fixed payment amount is given by:
Payment = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]
P— the principal, the amount borrowedr— the interest rate per payment period (the annual rate divided by the number of payments per year)n— the total number of payments over the life of the loan
Each period, that fixed payment splits into interest (the remaining balance × r) and principal (the rest of the payment) — and the remaining balance shrinks accordingly for the next period's calculation.
Worked example
A $200,000 loan at a 6% annual rate, paid monthly over 30 years (360 payments), works out to a fixed payment of about $1,199 a month.
Payment 1: $1,000 interest + $199 principal (balance: $200,000) Payment 181: $711 interest + $489 principal (balance: ~$142,000)
The payment amount never changes, but by payment 181 — roughly halfway through the loan — more than twice as much of it is going toward principal compared to payment 1, purely because the balance interest is calculated on has shrunk. Try the Amortization Calculator to see how the rate, term, or loan amount changes this split. For a full mortgage payment — including property tax and insurance collected alongside it — try the Mortgage Calculator.
Try it yourself
Payment per month
$1,199.10
Total paid over the loan
$431,676.38
Total interest paid
$231,676.38
How the math works
Every payment is the same size — $1,199.10 — but how much of it goes toward interest versus principal shifts as the loan balance shrinks:
First payment: $1,000.00 interest + $199.10 principal Last payment: $5.97 interest + $1,193.14 principal
Over 360 payments, this loan costs $231,676.38 in interest on top of the $200,000.00 borrowed — because early payments are mostly interest, paying extra toward principal early in the loan has an outsized effect on the total interest paid.
Common misconceptions
“Each loan payment reduces the balance by the same amount.”
The payment amount is fixed, but the split between interest and principal changes every period — early payments barely touch the balance, later payments pay it down much faster.
“Paying a little extra each month has only a small effect on how quickly you pay off a loan.”
Because interest is calculated on the remaining balance, extra principal payments made early in the loan compound in the borrower's favor and can shave years — and a disproportionate amount of interest — off a long loan.
“A lower monthly payment always means you're paying less for the loan overall.”
A lower payment often comes from stretching the loan over more periods, which usually means more total interest paid over the life of the loan, even though each individual payment is smaller.
Also in the Glossary: Amortization (Loans & Mortgages)