How to Improve Chances of Getting Internship

I'm a senior graduating January 2016 and I have no internship experience yet. I have managed to get a few interviews so far and even made it to second rounds but unfortunately I have not made the cut so far. I feel like I have derived as much experience as I can short of interning (Two student leader positions, I tutor at the learning center, I volunteer at a non-profit, placed 2nd in a stock valuation case study), and in terms of interviewing I can answer most questions with ease and confidently, although I still make small mistakes that probably affect my standings (Ex: Failing to bring up usage of analysis in stock case study when interviewer brought up how much P&L analysis is used in the internship).

I'm afraid that if I graduate without any internships, my life is screwed as firms won't hire anyone without internship experience. What can I do to help increase my shots? I'm not selective about where I intern as long as it's relevant to Finance or Economics in some sense and I have been sending out 3-5 applications every day or at least every other day on Indeed and my college's Career site.