Answered

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 taxpayers.




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.



How much extra does he have to pay in federal taxes because he won the lottery?

Verified Answer :

  • Calculate pre-lottery tax (\(\$34,500\)): \(\$4,386.25 + 0.25 \times (\$34,500 - \$31,850) = \$5,048.75\).
  • Calculate post-lottery tax (\(\$1,034,500\)): \(\$101,469.25 + 0.35 \times (\$1,034,500 - \$349,700) = \$341,149.25\).
  • Determine the difference: \(\$341,149.25 - \$5,048.75 = \boxed{\$336,100.50}\).

Explanation

  1. Analysis of Income and Tax Brackets

To determine how much extra federal tax Mauro has to pay, we first need to calculate his tax liability before and after winning the lottery. His annual income before winning was \(\$34,500\), and after winning \(\$1,000,000\), his total income became \(\$34,500 + \$1,000,000 = \$1,034,500\). We use the provided tax table for single taxpayers to find the respective tax amounts.

  1. Calculating Pre-Lottery Tax

Mauro's pre-lottery income of \(\$34,500\) falls into the tax bracket of \(\$31,850.01 - \$77,100\). The tax for this bracket is calculated as \(\$4,386.25\) plus \(25\%\) of the amount exceeding \(\$31,850\).
The tax is:
\[T_1 = 4,386.25 + 0.25 \times (34,500 - 31,850)\]
\[T_1 = 4,386.25 + 0.25 \times (2,650)\]
\[T_1 = 4,386.25 + 662.50 = \$5,048.75\]
Thus, Mauro's federal tax before winning the lottery was \(\$5,048.75\).

  1. Calculating Post-Lottery Tax

Mauro's post-lottery income of \(\$1,034,500\) falls into the top tax bracket of \(\$349,700.01\) and up. The tax for this bracket is \(\$101,469.25\) plus \(35\%\) of the amount exceeding \(\$349,700\).
The tax is:
\[T_2 = 101,469.25 + 0.35 \times (1,034,500 - 349,700)\]
\[T_2 = 101,469.25 + 0.35 \times (684,800)\]
\[T_2 = 101,469.25 + 239,680 = \$341,149.25\]
Thus, Mauro's federal tax after winning the lottery is \(\$341,149.25\).

  1. Calculating the Additional Tax Liability

The extra tax Mauro must pay due to his lottery winnings is the difference between his post-lottery tax and his pre-lottery tax:
\[\Delta T = T_2 - T_1\]
\[\Delta T = 341,149.25 - 5,048.75 = \$336,100.50\]
Therefore, Mauro has to pay an additional \(\$336,100.50\) in federal taxes because he won the lottery. Final answer: \(\boxed{\$336,100.50}\).

Examples

Understanding tax brackets is vital for financial planning, especially when handling significant income fluctuations like bonuses, investments, or lottery winnings. By calculating marginal tax rates, individuals can better anticipate the actual amount they will take home, helping them make informed decisions about savings, investments, or large purchases. This approach is fundamental in personal finance to ensure one meets legal tax obligations without unnecessary financial surprises.