account (n.) Look up account at Dictionary.com
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.) Look up account at Dictionary.com
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.