In English, of sounds from 1630s. Financial sense of "capable of being converted to cash" is first recorded 1818, from earlier use in Scots Law (17c.) in reference to debts that had been proved (in court, etc.).
mid-14c., "a plentiful flowing, an abundant supply," from Old French affluence, from Latin affluentia "affluence, abundance," literally "a flowing to," abstract noun from affluentem (nominative affluens) "flowing toward; abounding, rich, copious" (see affluent). The notion in the figurative Latin sense is of "a plentiful flow" of the gifts of fortune, hence "wealth, abundance of earthly goods," a sense attested in English from c. 1600. Latin affluentia is glossed in Ælfric's vocabulary (late Old English) by oferflowendnys.
1650s, "condition of flowing," a sense now rare or obsolete, from Latin currens, present participle of currere "to run" (from PIE root *kers- "to run"). The notion of "state or fact of flowing from person to person" led to the senses "continuity in public knowledge" (1722) and "that which is current as a medium of exchange, money" (1729).
late 14c., curraunt, "that which runs or flows," from Old French corant (Modern French courant), from Old French corant (see current (adj.)). Meaning "a flowing," especially "portion of a large body of water or air moving in a certain direction," is from 1550s. Applied from 1747 to the flowing of electrical force through a conducting body (electricity formerly was regarded as a sort of fluid).
Canadian province, named for the river running through it, which is from Cree (Algonquian) kis-si-ska-tches-wani-sipi "rapid flowing river."