The word "accountable" comes from Old French "acontable", meaning "liable to be called to account," derived from "aconter" ("to count, reckon") and the Latin computare ("to calculate").   It entered English around the 14th century, initially for financial matters (giving a count of money/debts) but soon expanded to mean being able to explain or justify one's actions, combining the core idea of "counting" or "answering for" with the suffix "-able," meaning "capable of being". 

According to the Oxford English Dictionary (OED), the adjective "accountable" first appeared in Middle English around c. 1400, with its earliest documented use found in the writings of poet William Langland in "Piers Plowman" (around 1387-1399), meaning "answerable," or "able to be counted or explained".