How Loan Amortization Works: Principal, Interest and Schedules
Understand fixed-rate amortization, the monthly payment formula, payment schedules and extra principal contributions.
What does amortization mean?
Amortization is the process of gradually repaying borrowed principal through scheduled payments. A standard fully amortizing fixed-rate installment loan has a consistent scheduled principal-and-interest payment. The amount going toward principal and interest changes over the life of the loan.
Why interest is largest early in the term
Interest depends on the unpaid balance. When you first borrow, that balance is at its maximum, so interest is high. Each payment reduces principal, leaving less balance on which to calculate next month’s interest.
Calculate the fixed monthly payment
For principal P, monthly rate r, and number of payments n, the formula is:
Payment = P × r ÷ [1 − (1 + r)^(-n)]
Convert a percentage APR to a monthly decimal with r = APR ÷ 1200, and multiply loan years by 12 for the number of installments. With zero interest, the required payment is simply P ÷ n.
Worked example: $200,000 loan at 6%
For a 30-year term, n = 360 and r = 0.005. The scheduled monthly payment is approximately $1,199.10. First-month interest is $200,000 × 0.005 = $1,000, so about $199.10 of the first payment reduces principal.
This example includes only principal and interest; a mortgage payment can also include insurance and property taxes.
How an amortization schedule is read
A schedule usually lists the payment number, total payment, interest paid, principal paid and remaining balance. Check whether your lender uses daily interest, exact due dates, different rounding conventions or fees; these can change statement values.
Extra principal payments and early payoff
Paying extra toward principal reduces the balance earlier and therefore decreases future modeled interest. The regular scheduled payment need not change, but the loan may finish before its original maturity date. Be sure extra amounts are actually applied to principal and that no prepayment restrictions apply.
Interest rate versus APR
A quoted APR can include costs beyond the periodic interest rate in some loan products. The Amortization Calculator treats the entered percentage as the periodic-interest basis for the schedule. For real financial products, examine the lender’s stated nominal interest rate and APR definitions.
Common mistakes
Do not mistake your initial loan amount for the current outstanding principal, use an annual rate directly as a monthly rate, or assume that your last payment always equals the scheduled payment after extra repayments.
Model your own loan
Try the Amortization Calculator to compare the standard payment, extra principal, total interest and first 12 rows of a simulated payment schedule.