need help for career in trading

I am a junior majoring in applied math..minor economics at a state school..sure non target. I want to ultimately pursue a career in trading.

I want to attend a mfin think..nova or wustl, claremont. I know I will have the gpa and gmat scores, however I don't have any relevant experience. I have one summer research internship in high performance computing...and that's about it :(

I fear that even if I did get into a mfin I will be unemployable after graduating because of my lack of experience. Would getting an unpaid internship this summer before applying help my chances, or would I need a reputable, legit SA to be competitive after graduating. any help is appreciated.

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