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What percentage of federal income tax is paid by the wealthy?

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Well, I'm not sure where you define wealthy...but the upper 50% of the wage earners pay @97% of all tax collections, and the lower ones only @3%. The upper of the upper pay a disproportionate share of that too, the Top 1% of earners = 37% of taxes paid, the next bracket 2-5% accounts for another 20%. So about 57% paid by the top 5%. Especially as this is for Personal Income Tax only, and many of the more wealthy have much of the income taxed (some would say double taxed) by in the Corporate returns of those corporations they control/own.

Also, this is of those filing returns. The percentage of people whose income is, because of deductions/exemptions below where they have to file returns, and with things like Earned Income tax credits, actually get more back than they might pay, is huge...something like 40% of the populace. And of course, the lower earners pay at much reduced rate anyway.
Some quick statistics: The top 1% of earners pay 21.20% of all taxes paid at an average rate of 24%, the top 2 - 5% of earners pay 14.55% of all taxes at an average of 18% (Top 5% pay @36% of all tax) The bottom 50% pay 3% of all tax collected at an average rate of 2.98%.

See link for full discussion, and chart that holds format.

Number of Returns with Positive AGI AGI ($ millions) Income Taxes Paid ($ millions) Group's Share of Total AGI Group's Share of Income Taxes Income Split Point Average Tax Rate All Taxpayers 130,371,156 $6,875,123 $831,890 100.00% 100.00% - 12.10% Top 1% 1,303,712 $1,306,417 $306,902 19.00% 36.89% > $328,049 23.49% Top 2-5% 5,214,846 $993,178 $168,322 14.45% 20.23% 16.95% Top 5% 6,518,558 $2,299,595 $475,224 33.45% 57.13% > $137,056 20.67% Top 6-10% 6,518,558 $749,680 $92,049 10.90% 11.07% 12.28% Top 10% 13,037,116 $3,049,275 $567,273 44.35% 68.19% > $99,112 18.60% Top 11-25% 19,555,673 $1,497,126 $138,642 21.78% 16.67% 9.26% Top 25% 32,592,789 $4,546,401 $705,915 66.13% 84.86% > $60,041 15.53% Top 26-50% 32,592,789 $1,406,380 $98,556 20.46% 11.85% 7.01% Top 50% 65,185,578 $5,952,781 $804,471 86.58% 96.70% > $30,122 13.51% Bottom 50% 65,185,578 922,342 27,419 13.42% 3.30% > $30,122 2.97%
See Related Links See the Related Links for "http://www.taxfoundation.org/taxdata/show/250.html" to the bottom for the answer.
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