Level payment

A level payment is not simply principal divided by periods when the periodic rate is positive. Each payment must cover that period's interest and reduce principal enough to reach zero after the final scheduled payment.

For zero interest, the limiting case is principal divided by payment count. For positive interest, solve the ordinary-annuity present-value equation for PMT. Preserve the end-of-period timing assumption; beginning-of-period payments require a different factor.

Check the solution with a schedule rather than trusting the payment formula alone. Each row begins with the prior closing balance, applies the periodic rate to that opening balance, and treats the rest of the payment as principal. Under an unrounded analytical schedule, the last row should close the balance to zero within the declared tolerance.

“Level” describes the total scheduled payment in this bounded model. The interest component generally falls as principal declines, while the principal component rises. Real payments may include fees, taxes, insurance, escrow, balloons, variable rates, or contractual cent-rounding outside this definition.