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The progressive income tax divides your income into ranges, called brackets.
Income within a bracket is taxed at one rate. Income past a certain amount is taxed in a higher bracket at a higher rate. There may be multiple brackets. Consider the following example of tax brackets:
If you make $30,000, you are said to be in the highest tax bracket, paying 30% in taxes.
That doesn't mean you're paying 30% of your income (or $9,000) in taxes. Many people have that misunderstanding.
What it means is that the highest rate you're paying is 30%.
For your income from 10,001 to 20,000, you're paying 20%. For your income from 1 to 10,000, you're paying 10%. Let's do the actual math.
Add them up, and the total is $6,000. (Which works out to 20% in tax.)
Some people will say that "the first dollar you earn is taxed at the lowest rate" and "the last dollar you earn is taxed at the highest rate". This is factually true, but, tends to confuse beginners. So it's not much of a simplifcation.
Actual tax brackets
For actual tax brackets, see the Wikipedia article or the IRS.
The actual tax brackets are 10% all the way to 35%, and the 35% rate doesn't affect anyone earning less than $372,000 a year.
Most people are in the 25% bracket or below. The 25% bracket goes up into the $80,000 per year range.