bank (n.1)
"financial institution," late 15c., from either Old Italian banca or Middle French banque (itself from the Italian word), both meaning "table" (the notion is of the moneylender's exchange table), from a Germanic source (compare Old High German bank "bench"); see bank (n.2).

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 flamboyant pianist Liberace, after a Madison Square Garden concert that was packed with patrons but panned by critics.
bank (n.2)
"earthen incline, edge of a river," c.1200, probably in Old English but not attested in surviving documents, from a Scandinavian source such as Old Norse banki, Old Danish banke "sandbank," from Proto-Germanic *bangkon "slope," cognate with *bankiz "shelf" (see bench (n.)).
bank (v.)
"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. Meaning "to ascend," as of an incline, is from 1892. In aeronautics, from 1911. Related: Banked; banking.