Amortized

Amortized is an adjective with two principal senses in finance and computer science.

In finance, amortization describes the gradual repayment of debt by making regular payments over time. Each payment typically includes both interest on the outstanding balance and a reduction of principal. An amortization schedule lists payment dates, amounts, interest, principal, and the remaining loan balance. The term also applies to spreading the cost of an intangible asset (such as a patent) or loan fees over its useful life for accounting and tax purposes, known as amortization expense.

In computer science, amortized analysis studies the average cost per operation over a worst-case sequence of operations. Rather than citing the cost of a single expensive step, amortized analysis assigns costs so that the total is distributed evenly across operations. Methods include the aggregate method, the accounting (or banker’s) method, and the potential method. A common illustration is a dynamic array that doubles its capacity when full: most insertions cost O(1), while occasional resizes cost O(n); the amortized cost per insertion remains O(1). Amortized costs provide guarantees for all sequences of operations, even if individual operations vary greatly in cost.

Amortization thus serves as a smoothing concept: in finance, to allocate expenditure over time; in algorithms, to analyze performance over a sequence, yielding more stable, representative bounds than worst-case per operation alone.