Loans guide · Reviewed 28 August 2026

A loan payment is one formula solved for a constant number.

Every fixed-rate installment loan — auto, personal, student — uses the same amortization formula. Understanding it explains why term length moves your payment more than most borrowers expect.

The amortization formula, term by term

A fixed loan payment is: payment = P × r × (1+r)^n ÷ ((1+r)^n − 1). P is the principal you borrow, r is the monthly interest rate (your annual rate divided by 12), and n is the number of monthly payments over the loan's term. The formula finds the single constant payment that, applied every month against a shrinking balance, brings that balance to exactly zero on the final payment.

Each payment is split between interest — charged on whatever balance remains — and principal, which reduces the balance. Early in the loan the balance is largest, so more of each payment goes to interest; later payments are increasingly principal. The payment amount itself never changes; only the split between the two does.

Why term length has an outsized effect

Because interest compounds against the outstanding balance every period, extending n doesn't just add more payments — it changes the shape of the whole formula. A longer term lowers the monthly payment (each payment covers less), but the total interest paid over the life of the loan rises, sometimes substantially, because the balance stays higher for longer and accrues interest for more months.

This is why comparing loans by monthly payment alone can be misleading. A lower payment from a longer term isn't a cheaper loan — it's the same principal and rate spread over more interest-accruing months.

What the loan payment calculator computes

Enter the amount borrowed, the annual interest rate, and the term in months. The calculator applies the amortization formula directly to return the fixed monthly payment, the total amount repaid over the full term, and the total interest — the gap between what you borrow and what you repay.

Calculate a loan payment ↗ See the full amortization schedule ↗

Frequently asked questions

How is a monthly loan payment calculated?

A fixed-rate installment loan uses the standard amortization formula: payment = P × r × (1+r)^n ÷ ((1+r)^n − 1), where P is the amount borrowed, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. The formula solves for one constant payment that fully repays the loan, principal and interest, over the term.

Why does a small rate change move the payment so much on long loans?

Interest compounds against the outstanding balance every month, so the (1+r)^n term grows faster as either the rate or the term increases. On a short personal loan a rate change barely moves the payment; on a 30-year loan the same rate change compounds over 360 months and can shift the payment substantially.

Does the payment amount tell me the total cost of the loan?

No. The payment tells you the monthly cash outflow. Total cost is payment × number of payments, and the interest portion of that is total cost minus the amount borrowed. Two loans with identical payments but different terms can have very different total interest.

What does this calculation leave out?

It assumes a fixed rate, no missed or extra payments, and no fees rolled into the balance. Origination fees, insurance add-ons, variable rates, and early payoff all change the real cost — none of which a basic payment formula captures.

Why is my actual lender's payment slightly different from the calculator?

Lenders may round differently, charge fees that change the effective principal, use a different day-count convention, or add escrowed items like insurance. Treat this as a close estimate of the interest-and-principal payment, not a binding figure.

Source note: This guide describes the standard fixed-rate amortization formula as a general illustration. All calculations happen in your browser — nothing you enter is sent to a server or stored. This is educational information, not lending advice.