Formula
Payment = P x r(1 + r)^n / ((1 + r)^n - 1)
Variables
- P: loan principal, or amount borrowed.
- r: periodic interest rate. For monthly payments, annual rate / 12.
- n: total number of payments. For a 5-year monthly loan, n = 60.
Worked example
For a 10,000 loan at 6% annual interest over 5 years with monthly payments: r = 0.06 / 12 = 0.005 and n = 60. The formula gives a monthly payment of about 193.33 before any extra fees or insurance.
How to interpret the payment
The payment is the fixed amount that would fully pay off the principal and interest over the term if the rate stays fixed and every payment is made on schedule. Early payments contain more interest; later payments contain more principal.
Zero-rate case
If the interest rate is 0%, the amortization formula is not needed. Payment = principal / number of payments.
When the formula is not enough
- Origination fees, closing costs, insurance, taxes or account charges.
- Variable interest rates or promotional periods.
- Late fees, prepayment penalties or lender-specific rounding.
- APR disclosure rules, which can vary by country and product.
References
- Consumer Financial Protection Bureau: Loan Estimate - context on loan costs beyond principal and interest, accessed 2026-05-17.