There are lots of ways that mathematics is used in banking, so it is quite complex really obviously as it is an institution that deals with money and lending money to others. Here are a few ideas which should help you to get started.
Interest rates are added to money which is loaned to a customer by a bank. The bank needs to make the initial outlay back and gain some more on top, so a percentage is worked out and agreed with the customer.
Whilst that sounds easy enough on the surface it can get quite involved when factors like a change in interest rate or if the customer defaults on the agreement
Talking of customer defaults, this has to be factored into as do things like stocks and shares. The bank needs to cover itself in the event that the money paid out for any of these things fails to be repaid, so profit and loss figures heavily in the banking role.
On a daily basis simple maths is used - addition, subtraction, multiplication and division. These are used in the same way that accountants work really, to work out debit and credit.
However for investment banks the amount of math used is huge. It involves solving partial differential calculus, stochastics calculus, probability etc.
To be honest, there isn't a business in the world that doesn't use some kind of mathematics but obviously banks deal with this more than any other.