amortize (v.)

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," from PIE root *mer- "to rub away, harm" (also "to die" and forming words referring to death and to beings subject to death).

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.