Banking has actually been around for a very long time. The first examples were merchants from ca. 2000 BCE who made grain loans to farmers and traders carrying good between cities.
Money lending was common in the Roman empire, with common interest rates of 4-12 percent, but they could be as high as 48 percent. The first Council of Nicea (AD 325) forbade the clergy from lending money at interest (usury).
Merchant banks emerged in the Middle Ages from the Italian grain and cloth merchants community and started to develop in the 11th century during the large European fair of St. Giles in England.
In medieval Europe, an early example of banking was during the Crusades. Henry II levied a tax in 1167 to finance his crusade, and the Knights Templar functioned as his bankers in the Holy Land. According to Wikipedia,
The Templars' wide flung, large land holdings across Europe also emerged in the 1100–1300 time frame as the beginning of Europe-wide banking, as their practice was to take in local currency, for which a demand note would be given that would be good at any of their castles across Europe, allowing movement of money without the usual risk of robbery while traveling.
The answer to your question then seems obvious: Banking establishments in early medieval times did, in fact, make money from charging interest on loans, and from making promisory demand notes, and hence, your banking establishment could do the same.
You could also introduce the more modern banking practice of borrowing and lending: Banks keep people's money safe while giving a small interest, and then lend the money out to others at higher interest rates. Trust in banks might be an issue, and banking crises have been known since the 13th century.