Answer :
Let's break this down step-by-step.
### 1. Mauro's Federal Tax Before Winning the Lottery
Mauro's income before winning the lottery was [tex]$34,500. Using the tax rate schedule for single taxpayers: 1. Taxable Income: $[/tex]0 - [tex]$7,825 - Tax for this portion: \( 10\% \times 7,825 = 782.50 \) 2. Taxable Income: $[/tex]7,825.01 - [tex]$31,850 - Tax for this portion: \( \$[/tex] 725.50 \) plus [tex]\( 15\% \)[/tex] of the amount over [tex]\( 7,825 \)[/tex]
- [tex]\( 31,850 - 7,825 = 24,025 \)[/tex]
- [tex]\( 0.15 \times 24,025 = 3,603.75 \)[/tex]
- Tax for this portion: [tex]\( 725.50 + 3,603.75 = 4,329.25 \)[/tex]
3. Taxable Income: [tex]$31,850.01 - $[/tex]34,500
- Tax for this portion: [tex]\( \$ 4,386.25 \)[/tex] plus [tex]\( 25\% \)[/tex] of the amount over [tex]\( 31,850 \)[/tex]
- [tex]\( 34,500 - 31,850 = 2,650 \)[/tex]
- [tex]\( 0.25 \times 2,650 = 662.50 \)[/tex]
- Tax for this portion: [tex]\( 4,386.25 + 662.50 = 5,048.75 \)[/tex]
So, Mauro’s federal tax before winning the lottery is [tex]\( \$ 5,048.75 \)[/tex].
### 2. Mauro's Federal Tax After Winning the Lottery
After winning the lottery, Mauro's income is [tex]$1,000,000 + $[/tex]34,500 = [tex]$1,034,500. Using the tax rate schedule: 1. Taxable Income: $[/tex]0 - [tex]$7,825 - Tax for this portion: \( 10\% \times 7,825 = 782.50 \) 2. Taxable Income: $[/tex]7,825.01 - [tex]$31,850 - Tax for this portion: \( \$[/tex] 725.50 \) plus [tex]\( 15\% \)[/tex] of the amount over [tex]\( 7,825 \)[/tex]
- [tex]\( 31,850 - 7,825 = 24,025 \)[/tex]
- [tex]\( 0.15 \times 24,025 = 3,603.75 \)[/tex]
- Tax for this portion: [tex]\( 725.50 + 3,603.75 = 4,329.25 \)[/tex]
3. Taxable Income: [tex]$31,850.01 - $[/tex]77,100
- Tax for this portion: [tex]\( \$ 4,386.25 \)[/tex] plus [tex]\( 25\% \)[/tex] of the amount over [tex]\( 31,850 \)[/tex]
- [tex]\( 77,100 - 31,850 = 45,250 \)[/tex]
- [tex]\( 0.25 \times 45,250 = 11,312.50 \)[/tex]
- Tax for this portion: [tex]\( 4,386.25 + 11,312.50 = 15,698.75 \)[/tex]
4. Taxable Income: [tex]$77,100.01 - $[/tex]160,850
- Tax for this portion: [tex]\( \$ 15,698.75 \)[/tex] plus [tex]\( 28\% \)[/tex] of the amount over [tex]\( 77,100 \)[/tex]
- [tex]\( 160,850 - 77,100 = 83,750 \)[/tex]
- [tex]\( 0.28 \times 83,750 = 23,450 \)[/tex]
- Tax for this portion: [tex]\( 15,698.75 + 23,450 = 39,148.75 \)[/tex]
5. Taxable Income: [tex]$160,850.01 - $[/tex]349,700
- Tax for this portion: [tex]\( \$ 39,148.75 \)[/tex] plus [tex]\( 33\% \)[/tex] of the amount over [tex]\( 160,850 \)[/tex]
- [tex]\( 349,700 - 160,850 = 188,850 \)[/tex]
- [tex]\( 0.33 \times 188,850 = 62,320.50 \)[/tex]
- Tax for this portion: [tex]\( 39,148.75 + 62,320.50 = 101,469.25 \)[/tex]
6. Taxable Income: [tex]$349,700.01 and up - Tax for this portion: \( \$[/tex] 101,469.25 \) plus [tex]\( 35\% \)[/tex] of the amount over [tex]\( 349,700 \)[/tex]
- [tex]\( 1,034,500 - 349,700 = 684,800 \)[/tex]
- [tex]\( 0.35 \times 684,800 = 239,680 \)[/tex]
- Tax for this portion: [tex]\( 101,469.25 + 239,680 = 341,149.25 \)[/tex]
So, Mauro's federal tax after winning the lottery is [tex]\( \$ 341,149.25 \)[/tex].
### 3. Additional Tax Due to Lottery Win
[tex]\[ \text{Additional Tax} = \text{Tax After Winning} - \text{Tax Before Winning} \][/tex]
[tex]\[ \text{Additional Tax} = 341,149.25 - 5,048.75 = 336,100.50 \][/tex]
Thus, Mauro has to pay an additional [tex]\( \$ 336,100.50 \)[/tex] in federal taxes because he won the lottery.
The correct answers are:
a. [tex]\( \$ 5,048.75 \)[/tex]
b. [tex]\( \$ 336,100.50 \)[/tex]
c. [tex]\( \$ 341,149.25 \)[/tex]
### 1. Mauro's Federal Tax Before Winning the Lottery
Mauro's income before winning the lottery was [tex]$34,500. Using the tax rate schedule for single taxpayers: 1. Taxable Income: $[/tex]0 - [tex]$7,825 - Tax for this portion: \( 10\% \times 7,825 = 782.50 \) 2. Taxable Income: $[/tex]7,825.01 - [tex]$31,850 - Tax for this portion: \( \$[/tex] 725.50 \) plus [tex]\( 15\% \)[/tex] of the amount over [tex]\( 7,825 \)[/tex]
- [tex]\( 31,850 - 7,825 = 24,025 \)[/tex]
- [tex]\( 0.15 \times 24,025 = 3,603.75 \)[/tex]
- Tax for this portion: [tex]\( 725.50 + 3,603.75 = 4,329.25 \)[/tex]
3. Taxable Income: [tex]$31,850.01 - $[/tex]34,500
- Tax for this portion: [tex]\( \$ 4,386.25 \)[/tex] plus [tex]\( 25\% \)[/tex] of the amount over [tex]\( 31,850 \)[/tex]
- [tex]\( 34,500 - 31,850 = 2,650 \)[/tex]
- [tex]\( 0.25 \times 2,650 = 662.50 \)[/tex]
- Tax for this portion: [tex]\( 4,386.25 + 662.50 = 5,048.75 \)[/tex]
So, Mauro’s federal tax before winning the lottery is [tex]\( \$ 5,048.75 \)[/tex].
### 2. Mauro's Federal Tax After Winning the Lottery
After winning the lottery, Mauro's income is [tex]$1,000,000 + $[/tex]34,500 = [tex]$1,034,500. Using the tax rate schedule: 1. Taxable Income: $[/tex]0 - [tex]$7,825 - Tax for this portion: \( 10\% \times 7,825 = 782.50 \) 2. Taxable Income: $[/tex]7,825.01 - [tex]$31,850 - Tax for this portion: \( \$[/tex] 725.50 \) plus [tex]\( 15\% \)[/tex] of the amount over [tex]\( 7,825 \)[/tex]
- [tex]\( 31,850 - 7,825 = 24,025 \)[/tex]
- [tex]\( 0.15 \times 24,025 = 3,603.75 \)[/tex]
- Tax for this portion: [tex]\( 725.50 + 3,603.75 = 4,329.25 \)[/tex]
3. Taxable Income: [tex]$31,850.01 - $[/tex]77,100
- Tax for this portion: [tex]\( \$ 4,386.25 \)[/tex] plus [tex]\( 25\% \)[/tex] of the amount over [tex]\( 31,850 \)[/tex]
- [tex]\( 77,100 - 31,850 = 45,250 \)[/tex]
- [tex]\( 0.25 \times 45,250 = 11,312.50 \)[/tex]
- Tax for this portion: [tex]\( 4,386.25 + 11,312.50 = 15,698.75 \)[/tex]
4. Taxable Income: [tex]$77,100.01 - $[/tex]160,850
- Tax for this portion: [tex]\( \$ 15,698.75 \)[/tex] plus [tex]\( 28\% \)[/tex] of the amount over [tex]\( 77,100 \)[/tex]
- [tex]\( 160,850 - 77,100 = 83,750 \)[/tex]
- [tex]\( 0.28 \times 83,750 = 23,450 \)[/tex]
- Tax for this portion: [tex]\( 15,698.75 + 23,450 = 39,148.75 \)[/tex]
5. Taxable Income: [tex]$160,850.01 - $[/tex]349,700
- Tax for this portion: [tex]\( \$ 39,148.75 \)[/tex] plus [tex]\( 33\% \)[/tex] of the amount over [tex]\( 160,850 \)[/tex]
- [tex]\( 349,700 - 160,850 = 188,850 \)[/tex]
- [tex]\( 0.33 \times 188,850 = 62,320.50 \)[/tex]
- Tax for this portion: [tex]\( 39,148.75 + 62,320.50 = 101,469.25 \)[/tex]
6. Taxable Income: [tex]$349,700.01 and up - Tax for this portion: \( \$[/tex] 101,469.25 \) plus [tex]\( 35\% \)[/tex] of the amount over [tex]\( 349,700 \)[/tex]
- [tex]\( 1,034,500 - 349,700 = 684,800 \)[/tex]
- [tex]\( 0.35 \times 684,800 = 239,680 \)[/tex]
- Tax for this portion: [tex]\( 101,469.25 + 239,680 = 341,149.25 \)[/tex]
So, Mauro's federal tax after winning the lottery is [tex]\( \$ 341,149.25 \)[/tex].
### 3. Additional Tax Due to Lottery Win
[tex]\[ \text{Additional Tax} = \text{Tax After Winning} - \text{Tax Before Winning} \][/tex]
[tex]\[ \text{Additional Tax} = 341,149.25 - 5,048.75 = 336,100.50 \][/tex]
Thus, Mauro has to pay an additional [tex]\( \$ 336,100.50 \)[/tex] in federal taxes because he won the lottery.
The correct answers are:
a. [tex]\( \$ 5,048.75 \)[/tex]
b. [tex]\( \$ 336,100.50 \)[/tex]
c. [tex]\( \$ 341,149.25 \)[/tex]