Loan Amortization

Under a typical fixed-rate amortization schedule, the total principal-and-interest payment remains level while the interest portion generally declines and the principal portion generally increases over time.

For a fixed-rate loan with periodic rate i, n payment periods, and initial principal P, the level payment can be derived from the present value of an ordinary annuity: P = Payment × [1 − (1 + i)^−n] / i.

For a fully amortizing fixed-rate loan schedule, periodic interest is calculated using the beginning principal balance and the periodic interest rate; the principal portion equals the scheduled principal-and-interest payment minus that period’s interest.

A longer loan term generally lowers the scheduled periodic payment but increases the total interest paid over the life of the loan, assuming comparable principal and interest-rate terms.

A loan can have a payment or amortization schedule without being fully amortizing: interest-only payments can leave principal unpaid, negative amortization can increase the principal balance, and balloon structures can leave a large final principal payment due at maturity.