Let P be the starting principal, r the monthly interest rate as a decimal, and n the number of months. For a positive interest rate, the unrounded regular payment is:
Payment = P × r ÷ [1 − (1 + r)−n]
Here, r = entered annual percentage ÷ 1,200. At 0% interest, the payment is P ÷ n. This formula assumes a fixed rate and the first payment one month after the loan begins, followed by payments at the end of each monthly period.
- Calculate the regular payment and round it to two decimal places, with exact half-cent values rounded up.
- Each month, multiply the opening balance by the monthly rate and round that interest to cents using the same rule.
- Subtract interest from the payment to find principal repaid, then subtract that principal from the balance.
- In the final month, collect the remaining balance plus that month's rounded interest. If the regular payment clears the balance sooner, stop there and show the actual number of months.
The formula and schedule use exact integer fractions before rounding; no binary floating-point approximation is used for money or interest. The principal portions add up exactly to the starting loan amount, total paid equals principal plus total interest, and the final balance is 0.00.
Rounding can matter for unusual inputs. A very small payment may round to 0.00, leaving the balance for the final month. With a high rate and long term, the rounded regular payment may only cover interest, creating a much larger final payment. The result flags these cases. This model does not add unpaid interest to the balance.
The entered loan amount must be positive, with up to 15 integer digits and 2 decimal digits. The nominal annual rate accepts 0–100%, with up to 10 decimal digits. Both fields accept correctly grouped thousands commas and at most 64 characters. Enter a whole-number term from 1 to 600 months without commas. Currency symbols, percent signs, expressions, and scientific notation are not accepted.
These are estimates under the stated monthly rounding policy. Fees, taxes, insurance, daily accrual, changing rates, and extra, missed, or early payments are outside this calculator's scope. It does not calculate APR or compare loan offers.
References: OpenStax — Loan Amortization explains the payment formula and monthly periods. The CFPB explanation of interest rate and APR describes how APR also includes certain borrowing fees.