Do "capital gains" add to your total income for the purpose of determining your tax bracket or are they taxed at the rate of your income-only tax bracket?
I do not believe capital gains adds to your total income for determining your tax rate.
So what about students and the like, who perhaps have no income or have income so low as to qualify as exempt? I would assume they'd pay at the lowest bracket, right?
This is correct. In 2011 for a non-married individual, if you make less than $34,500 you would pay 0% capital gains taxes. So, before you sell your bitcoin, ask for a reduction in your salary, then wait a year
