Tax Conundrum

 red pin and a sticky note with text: taxes *Submitted by Dr. Ted Stanford, NMSU Mathematician.

  1. In 2009, Mark was a college student. When it came time to fill out his tax forms, his taxable income was $7228. This means he was in the bracket where he pays 10% in federal income tax. What was Mark’s federal tax for 2009?
  2. Then Mark graduated and got a job. On his 2010 tax forms, his taxable income is $38,754, which puts him in the 25% tax bracket.  Mark is pretty good at estimating with percentages, so he figures he’ll owe a quarter of $38,754 in tax, which he knows will number somewhere between $9,000 and $10,000. When he looks up $38,754 in the table, how ever, he finds that he needs to pay only $5,875 in federal tax. Can you explain to Mark what his mistake is? (Mark tries to make sense of the situation by looking up some other numbers, shown in the following tax table, but he only gets more confused.)
Taxable Income Tax
$  5,000 $   503
$10,000 $1,085
$15,000 $1,835
$20,000 $2,585
$25,000 $3,335
$30,000 $4,085
$35,000 $4,938
$40,000 $6,188
$45,000 $7,438

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