Any Prospectors citizen can open their own Private Bank as long as they own a Banking license. The main task of the Central Bank is to issue Banking licenses to the people who want to start their own Bank. Once a resident owns a Banking License, they have the right to construct a private Bank and provide different banking services there. For example, they may convert mined gold into gold on their accounts with a chosen commission. Each Bank, which is a private enterprise, can choose the commission it will charge from every transaction within limits provided by State (you can see the list of Private Banks below). If the owner of the Bank decides to go out of business, he will be able to sell this license together with the building through the auction or sell it separately after he destroys the building.
In the screenshot below you can see a list of private banks and the amount of their commissions.