What are you looking to get out of this internship?
What are your strengths?
What is your weakness?
Talk me through your CV/skills/experience
What can you tell us about BNY?
I think the key here, is really understanding: (a) what they do as a business, and (b) what that particular division you are applying for does. I had a very brief job spec so I used that to work out what that division did, what services it covered and I also made sure I understood the organisation.
Know where they are positioned in the market, what do they actually do and demonstrate that you understand it, demonstrate and understanding of the differences between investment services and investment management. IF you can show them that your research extended beyond the first page of their site/wiki it speaks a lot. Try to demonstrate what a "useful" intern you will be. If you're the type of intern who can demonstrate some knowledge and transferable skills you can pretty much hit the ground running with the coaching and support given to you on the programme and learn so much more about the organisation and the person supervising you will actually get a young pair of hands that is useful and not someone to babysit for 9 weeks and keep having to explain what asset servicing really means.
Overall- I got a really good impression of the bank. The interviewers were very nice- don't take this to mean it is an easy interview- they are intelligent and are looking to challenge you. However it felt more natural and like they actually wanted to know me compared to previous interviews where I felt like they had already made up their mind about their ideal candidate and just weren't bothered to give me a real chance to prove myself.