finance · Browser tool
Loan Amortization Calculator
Enter the loan and see the payment, the interest total and every period of the schedule, including what an extra payment would change.
The loan
Summary
What the extra payment buys you
Leave the extra payment at zero to see the plain schedule.
Amortisation schedule
| # | Date | Payment | Interest | Principal | Balance |
|---|
What this does
An amortising loan keeps the payment constant and lets the split inside it drift. Each period the lender takes interest on whatever is still owed, and the rest of the payment reduces the balance. Early on the balance is large, so interest eats most of the payment; late on it is small and almost everything goes to principal. That is why a 30-year mortgage at 5.75% costs more in interest over its life than the house cost to buy, and why the first few years of overpayment matter far more than the last few.
The payment formula
For a rate i per period and n periods, the payment on principal P is P·i / (1 − (1+i)−n). At a rate of exactly zero that expression divides by zero, so this page handles it as a separate case and simply splits the principal evenly across the periods. The periodic rate here is the annual rate divided by the number of payments per year, which is how consumer loans in most of the world are quoted. Some lenders compound differently — Canadian mortgages compound semi-annually, for instance — and a schedule from such a lender will differ slightly from this one.
Rounding, and why the last payment is odd
Everything is computed in whole cents. Interest is rounded to the nearest cent each period, and because the constant payment rarely divides the balance evenly, a few cents of drift accumulate over hundreds of periods. The final payment absorbs whatever is left, so it is usually a little larger or smaller than the others and the closing balance is exactly zero rather than a stray fraction. A real lender does the same thing, though its rounding rule may differ by a cent or two.
Extra payments
An extra amount applied to principal shortens the loan rather than lowering the payment. The saving is not proportional: every unit of principal you remove early also removes all the interest that would have accrued on it for the remaining term, which is why a modest overpayment in year two can wipe out years at the end. The comparison shown here assumes the extra payment goes to principal immediately and never stops. Check your agreement — some lenders hold overpayments until the next scheduled date, and some charge a fee for early repayment, which this calculator does not model. Taxes, insurance, escrow and arrangement fees are also left out; this is the loan itself, not the total cost of owning the thing you borrowed for.