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I know that for U.S. Federal Personal Income Tax, the schedule is progressive, so for a single person filing for $60,000 (in 2011 for this example), the first $34,500 is taxed at 15% and then the rest is taxed at 25%.

What I don't understand is how the numbers in the "The Tax Is" column were calculated. For example, 15% of $34,500 is $5,175, not $4,750. How is the $4,750 calculated?

See the attached image here Tax Bracket Schedule

Thanks!

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Just to be clear, this is a 2011 tax table. No problem as an example, but I don't want you paying the wrong tax if you're actually using this now.

Beyond that, you've got the right idea, but you need to keep track of the progressive nature at each rung.

The first line your table is

Taxable    But not   Tax is  Plus   Of amount
Income     over                     over
$0         $8,500    $0.00   10%    $0

so if you're in the lowest bracket you just pay 10%.

The second line is 

8,550      34,500    850.00   15%   8,500

The third column contains 10% of the top of the first bracket, which is 10% of $8,500. So far so good.

Now the third line is

34,500     83,600    4,750.00  25%  34,500

Now to get the third column here, you take the $850 from the third column of the second line, and you add 15% of ($34,500 - $8,550). In other words, you're adding the marginal tax for the full width of the previous bracket only.

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  • Oh Okay, I understand now. Since that calculation comes to $4742.50, the author is simply rounding to $4750 for simplicity's sake, correct? As for the 2011 table, I'm just reviewing old concepts and I went blank at the progressive calculation, I don't know why. – Yistorian May 4 '16 at 2:14
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    Hmm. Yeah, I don't know what's going on with that "rounding." Is this a real tax table? Your comment about "the author" makes me think you got this from a textbook, in which case I wonder if it's just a mistake. – user32479 May 4 '16 at 2:21
  • Yes, it's from a textbook. It's a Barron's book, but still I think it's an errata, as well. That's really what threw me off because some of the numbers were off by just a few points each. I spent about 30min. crunching the numbers, but something just seemed off, lol. – Yistorian May 4 '16 at 2:23
  • I'm marking your response as the answer because I do think it's an errata. Thanks for your explanation, it solidified my understanding of the concept. – Yistorian May 4 '16 at 2:27

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