bank (n.1) Look up bank at
"financial institution," late 15c., originally "money-dealer's counter or shop," from either Old Italian banca or Middle French banque (itself from the Italian word), both meaning "table," from a Germanic source (such as Old High German bank "bench, moneylender's table"), from Proto-Germanic *bankiz- "shelf," *bankon- (see bank (n.2)). The etymonlogical notion is of the moneylender's exchange table.

As "institution for receiving and lending money" from 1620s. In games of chance, "the sum of money held by the proprietor or one who plays against the rest," by 1720. Bank holiday is from 1871, though the tradition is as old as the Bank of England. To cry all the way to the bank was coined 1956 by U.S. pianist Liberace (1919-1987), after a Madison Square Garden concert that was panned by critics but packed with patrons.
bank (v.3) Look up bank at
originally in billiards, "to make (the cue ball) touch the cushion (bank) of the table before touching another ball," from a specialized sense of bank (n.2); probably abstracted from bank-shot (n.), which is attested by 1889. Related: Banked; banking.
bank (v.1) Look up bank at
"to act as a banker," 1727, from bank (n.1). As "to deposit in a bank" from 1833. Figurative sense of "to rely on" (i.e. "to put money on") is from 1884, U.S. colloquial. Related: Banked; banking; bankable.
bank (v.2) Look up bank at
1580s, "to form a bank or slope or rise," from bank (n.2). Meaning "to rise in banks" is by 1870. That of "to ascend," as of an incline, is from 1892. In aeronautics, from 1911. Related: Banked; banking.
bank (n.2) Look up bank at
"natural earthen incline bordering a body of water," c. 1200, from a Scandinavian source such as Old Norse *banki, Old Danish banke "sandbank," from Proto-Germanic *bankon "slope," cognate with *bankiz "shelf" (see bench (n.)). As "rising ground in a sea or rover, shoal," from c. 1600. As "bench for rowers in an ancient galley," 1590s.

There probably was an Old English cognate but it is not attested in surviving documents. The nasalized form likely is a variant of Old Norse bakki "(river) bank, ridge, mound; cloud bank," cognate with Swedish backe, Danish bakke "hill, rising ground."