amortize (v.) Look up amortize at Dictionary.com
late 14c., from Old French amortiss-, present participle stem of amortir "deaden, kill, destroy; give up by right" (12c.), from Vulgar Latin *admortire "to extinguish," from ad "to" (see ad-) + mortus "dead," from Latin mors "death" (see mortal (adj.)).

Originally in English in the literal sense "make dead," also a legal term for an act of alienating lands. In reference to extinguishing a debt from early 19c. Related: Amortized; amortizing.