Put more specificaly, if you want to add two numbers, make sure that there is no way the result could be out of the range of its data type. If you want someone to enter a name for something, define what that string can contain - maybe only a to z, A to Z, 0 to 9, and it must have a length from 1 to 20 bytes.
Write every function of your program so that it has deterministic behavior, and that it has a clearly defined result for every possible input.
By the way, I doubt that banking account management systems are as secure as people might feel comfortable to think they are. Most commercial systems have poor security, because companies prefer cheap but insecure mainstream IT systems over expensive but secure custom IT systems.