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If I purchased a stock ten years ago in a regular brokerage account for $10 per share and sold it today for $60 I would have long term capital gains of $50 per share. How would I calculate the total tax owed, is it just $7.50 (15% of $50), is that $50 added to my income or is it some combination of both?

All of the above. Your capital gain is added to your other income in determining AGI and, ultimated, taxable income. When it gets time to compute tax, your net long-term capital gain is treated differently. See the instructions for the "tax" line of Form 1040.

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