Old English andswaru "an answer, a reply," from and- "against" (see ante) + -swaru "affirmation," from swerian "to swear" (see swear), suggesting an original sense of "make a sworn statement rebutting a charge." A common Germanic compound (cf. Old Saxon antswor, Old Norse andsvar, Old Frisian ondser, Danish and Swedish ansvar), implying a Proto-Germanic *andswara-. Meaning "a reply to a question," the main modern sense, was present in Old English. Meaning "solution of a problem" is from c.1300.
Old English answarian "to answer;" see answer (n.). Meaning "to respond in antiphony" is from early 15c.; that of "to be responsible for" is early 13c. Related: Answered; answering. The telephone answering machine is from 1961.