A bank was a financial institution.
In the 1890s, Henry Gordon Jago owed 500 guineas to the bank. (AUDIO: The Ruthven Inheritance)
In 1968, the Monk deposited money in a London bank. He then went to 2168 and capitalised on 200 years of accumulated compound interest. (TV: "Checkmate")
Countess Heidi Scarlioni met her future husband Count Carlos whilst she was working for her father in a Swiss bank. (PROSE: City of Death)
On a trip to 1920s London, the Sixth Doctor had made Melanie Bush a cosignatory on his Coutts bank account. (PROSE: Instruments of Darkness)
In 2007, the Tenth Doctor used his sonic screwdriver to get money out of a London Credit Bank cashpoint. (TV: The Runaway Bride)
The Bank of Karabraxos. (TV: Time Heist)
The Bank of Silence was run by the Silence. Individuals made deposits at the bank and then forgot they made them, allowing the Silence full control of the funds. (COMIC: Service with a Shhhh)
The Bank of Karabraxos was the most secure bank in the galaxy. This was in part due to the security provided by the Teller, which could detect guilt and liquefy the brain of the potential criminal. (TV: Time Heist)