account (n.)
c.1300, "reckoning of money received and paid," from Old French acont "account, reckoning, terminal payment," from a "to" (see ad-) + cont "counting, reckoning of money to be paid," from Late Latin computus "a calculation," from Latin computare "calculate" (see compute).

Meaning "sum of (one's) money in a bank" is from 1833. Sense of "narration" is first attested 1610s. Plural accounts used as a collective or singular in phrases such as to give accounts (of something), is from mid-13c. Phrase by all accounts is attested from 1798.
account (v.)
c.1300, "to count, enumerate," from Old French aconter "to count, render account" (Modern French conter), from a "to" (see ad-) + conter "to count, tell" (see count (v.)). Meaning "to reckon for money given or received, render a reckoning," is from late 14c.; sense of "to explain" (c.1710) is from notion of "answer for money held in trust." Transferred sense of "value" is from late 14c. Related: Accounted; accounting.