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Let's say I use my $10k saving to trade stocks and earn $10k (not paying tax yet)
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Have you already doubled your money trading stock? Or you are planning on doubling your money?
If you've already doubled your money, congratulations, you should drop out and trade for a living, you are 1 in a million. Only half kidding.
If this is your plan to put yourself through college by doubling your money, I would say you much a much greater chance of losing it all than doubling it, and maybe you should rethink it.
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will they find out that I have $10k?
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Only if you fill out the forms honestly. Or if they examine your tax return, where they might wonder how you made $10K in STCG with no reported assets.