Honestly, that you have to ask that kind of question disqualifies you in my opinion to develop a banking (!) application were security is an extreme critical factor. I've already seen a payment provider (Neteller) failing in providing basic security features for their API (you could access any account data and do transactions AFAIR) when I had to implement it for a site ~2-3 years ago.
php is suitable for the frontend but php has quirks with floats. Shops like Magento and others have already suffered from bugs and problems with floats. It must be also ensured that the DB and possible type conversions in the app don't cause wrong calculations. Rounding might fail as well. See Real vs. Floating Point vs. Money You will have to put a serious amount of effort into testing the integrity of transactions and calculations.
On the backend side that does the actually processing of the data there is very like no php running at all for any banking application. Depending on the age of their infrastructure I guess it is most likely Java or something really ancient. Security, security and again security, good performance, and redundancy are as well critical when designing such an application. This is far more than just "What language should I pick?".
What Core modules (functions) can one use (implement) in further development of that sort of thing?
Seriously? This is so broad you could ask "What should I eat today?" as well. CakePHP is suitable for any kind of web application. No idea what exactly you mean. You should start with writing a clear and detailed specification and developing an architecture of the system even before worrying about the language or start writing code.
Good luck with the project and make sure you have a good lawyer and make sure your contracts keep as much responsibility for failure away from you. :)