How the loan payment formula works
Most installment loans — personal, auto, student and home loans — are fixed-rate and fully amortizing, so they all use the same loan payment formula. Your monthly payment is:
M = P × r(1 + r)n / ((1 + r)n − 1)
where P is the loan amount (the principal), r is the monthly interest rate (your annual APR ÷ 12), and n is the loan term in months. For a $25,000 loan at 9.5% APR over 5 years (60 months) that works out to about $525 per month, with roughly $6,500 of total interest over the life of the loan.
Each month interest is charged on the remaining balance and the rest of your payment reduces the principal. Early payments are mostly interest, later ones almost all principal — the amortization schedule above shows the exact split for every single payment, so you can see precisely where your money goes.
Personal, auto, student and home loans
This calculator works for any fully amortizing fixed-rate loan — just enter the amount, APR and term. The math is identical; only the typical numbers differ:
- Personal loans usually run 1–7 years with higher APRs (often 7–20%) because they are unsecured. Use the years/months toggle and try a shorter term to see how much interest you can cut.
- Auto loans are typically 36–84 months and secured by the car, so APRs are lower. For trade-in, sales tax and fees, use our dedicated car loan calculator.
- Student loans often use a 10-year standard term. Model extra payments to see how fast you can clear them after graduation.
- Home and home-improvement loans can run 15–30 years. For escrow, PMI and property tax, try our mortgage calculator.
Because all of the math runs locally in your browser, you can test scenarios freely — a bigger down payment, a shorter term, a different APR from your bank or credit union — without creating an account or getting sales calls. Nothing you type is uploaded, stored or shared.
Loan calculator FAQ
How is a monthly loan payment calculated?
It uses the amortization formula M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is the loan amount, r the monthly rate (APR ÷ 12) and n the term in months. The calculator then splits every payment into interest and principal in the schedule above.
What is a loan amortization schedule?
A payment-by-payment table showing how each payment splits between interest and principal and what balance remains. Early payments carry more interest; later ones are mostly principal. View it yearly or monthly above and download the full schedule as a CSV for Excel or Google Sheets.
Do extra payments pay off a loan faster?
Yes. On a fixed-rate loan extra money goes straight to principal, so the balance drops faster, less interest accrues and the loan ends before the term is up. The green panel above shows exactly how much time and interest you save.
Does this work for personal, auto, student and home loans?
Yes. Any fixed-rate amortizing loan uses the same math — enter the amount, APR and term. For car-specific trade-in and tax use our car loan calculator; for escrow and PMI use our mortgage calculator.
Is this loan calculator free and private?
Yes — completely free, no sign-up and no lead forms. Every calculation runs locally in your browser with JavaScript; the numbers you enter are never sent to a server.
What APR should I enter?
Use the APR your lender quotes, since it includes most loan fees and gives the most accurate payment. If you only have an interest rate, enter that — it will be very close. Try several rates to compare lenders instantly.