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For 2021, the amount of U.S. federal tax owed T is a function of taxable income d:

 

\[T(d) = \begin{cases} 0.1d & \text{if}~d \le 9875, \\ 0.12(d-9875) + 987.5 & \text{if}~ 9876 \le d \le 40125, \\ 0.22(d-40125) + 4617.5 & \text{if}~ 40126 \le d \le 85525, \\ 0.24(d-85525) + 14605.5 & \text{if}~ 85526 \le d \le 163300, \\ 0.32(d-163300) + 33271.5 & \text{if}~ 163301 \le d \le 207350, \\ 0.35(d-207350) + 47367.5 & \text{if}~ 207351 \le d \le 518400, \\ 0.37(d-518400) + 156235 & \text{if}~ d > 518400. \end{cases}\]

 

Noam has $90,000 in taxable income, and Betty has $120,000. How much more tax does Betty pay?

 May 4, 2024

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Noam pays 13584.5 in tax, and Betty pays 18719.5 in tax.


The difference is 18719.5 - 13584.5 = 5135.

 May 4, 2024

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