late 13c., "to go up, rise, mount (a horse)," from Old French amonter "rise, go up; mean, signify," from amont (adv.) "upward, uphill," literally "to the mountain" (12c.), a contraction of the prepositional phrase a mont, from a (from Latin ad "to;" see ad-) + Latin montem (nominative mons) "mountain" (from PIE root *men- (2) "to project"). Meaning "to rise in number or quality (so as to reach)" is from c. 1300. Simple mount (v.) is not used in the physical senses. Related: Amounted; amounting.
"quantity, sum," 1710, from amount (v.). As nouns, Middle English had amountance, amountment.