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Mauro just won \$1,000,000 from the lottery! Despite his excitement in winning a tremendous amount of money, his brother (who is an accountant) warns him not to spend it all at once and hands him this tax rate schedule for single filers:




Taxable Income		Federal Tax

\$0 - \$7,825		10\% of amount

\$7,825.01 - \$31,850		\$725.50 plus 15\% of amount over \$7,825

\$31,850.01 - \$77,100		\$4,386.25 plus 25\% of amount over \$31,850

\$77,100.01 - \$160,850		\$15,698.75 plus 28\% of amount over \$77,100

\$160,850.01 - \$349,700		\$39,148.75 plus 33\% of the amount over \$160,850

\$349,700.01 and up		\$101,469.25 plus 35\% of amount over \$349,700






Using this chart, a taxpayer who makes \$58,000 annually (line 3) will have to pay \$4,386.25 plus 25\% of the difference of 58,000 and 31,850, or 4,386.25 + (0.25)(58,000 - 31,850) = \$10,923.75.



Before winning the lottery, Mauro's annual income was \$34,500. Use the chart to determine Mauro's federal tax before winning the lottery and after winning the lottery.

Verified Answer :

  • Identify the applicable tax bracket for Mauro's pre-lottery income of \(\$34,500\), which is the \(\$31,850.01 - \$77,100\) range, resulting in a tax of \(\boxed{\$5,048.75}\).
  • Determine the applicable tax bracket for Mauro's total income after the lottery win (\(\$1,000,000\)), which is the \(\$349,700.01\) and up bracket.
  • Compute the tax for the second scenario by applying the base fee of \(\$101,469.25\) plus \(35\%\) of the amount exceeding \(\$349,700\), yielding \(\boxed{\$329,074.25}\).

Explanation

  1. Analyzing the Problem and Data

To determine Mauro's federal tax, we must identify which tax bracket his annual income falls into based on the provided tax schedule. We have two scenarios: his income before winning the lottery (\$I_{pre} = \$34,500\$) and his total income after winning the lottery (\$I_{post} = \$1,000,000\$). Each tax bracket calculates the tax as a base amount plus a percentage of the income exceeding the bracket's lower limit.

  1. Calculating Tax Before Winning the Lottery

Mauro's pre-lottery income is \(\$34,500\). Looking at the tax schedule, this value falls into the third tax bracket: \(\$31,850.01 - \$77,100\). The rule for this bracket is \(\$4,386.25\) plus \(25\%\) of the amount over \(\$31,850\).
Calculation:
\[T_{pre} = 4,386.25 + 0.25 \times (34,500 - 31,850)\]
\[T_{pre} = 4,386.25 + 0.25 \times (2,650)\]
\[T_{pre} = 4,386.25 + 662.50 = \boxed{\$5,048.75}\]
So, Mauro's federal tax before winning the lottery was \(\$5,048.75\).

  1. Calculating Tax After Winning the Lottery

Mauro's total income after winning the lottery is \(\$1,000,000\). This value falls into the final tax bracket: \(\$349,700.01\) and up. The rule for this bracket is \(\$101,469.25\) plus \(35\%\) of the amount over \(\$349,700\).
Calculation:
\[T_{post} = 101,469.25 + 0.35 \times (1,000,000 - 349,700)\]
\[T_{post} = 101,469.25 + 0.35 \times (650,300)\]
\[T_{post} = 101,469.25 + 227,605.00 = \boxed{\$329,074.25}\]
Thus, Mauro's federal tax after winning the lottery would be \(\$329,074.25\).

Examples

Understanding progressive tax brackets is a vital skill for anyone managing personal finances. For instance, when planning for salary increases, investments, or bonuses, it helps to know that moving into a higher income bracket usually means paying a higher percentage on the additional income, not on the entire amount. Applying these calculations ensures individuals can accurately estimate their net take-home pay and manage their budgets effectively.

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