Internship is always possible if you have got the right package.

What is your background? Finance is quite broad- in which area do you think you fit in?

One way to really impress your recruiter is to run them through a scenario that involves a current event. To that end, please tell me an issue or a case study in finance where it clearly shows that you are passionate, articulate, thorough, and have convictions toward the end result. 

This doesn't have to be very long by the way- I can try to give you some feedback on your readiness if you wish...

JB