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Mauro just won [tex]\$1,000,000[/tex] 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.

\begin{tabular}{|c|c|}
\hline
Taxable Income & Federal Tax \\
\hline
\$0 - \[tex]$7,825 & 10\% of amount \\
\hline
\$[/tex]7,825.01 - \[tex]$31,850 & \$[/tex]725.50 plus 15\% of amount over \[tex]$7,825 \\
\hline
\$[/tex]31,850.01 - \[tex]$77,100 & \$[/tex]4,386.25 plus 25\% of amount over \[tex]$31,850 \\
\hline
\$[/tex]77,100.01 - \[tex]$160,850 & \$[/tex]15,698.75 plus 28\% of amount over \[tex]$77,100 \\
\hline
\$[/tex]160,850.01 - \[tex]$349,700 & \$[/tex]39,148.75 plus 33\% of amount over \[tex]$160,850 \\
\hline
\$[/tex]349,700.01 and up & \[tex]$101,469.25 plus 35\% of amount over \$[/tex]349,700 \\
\hline
\end{tabular}

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

Before winning the lottery, Mauro's annual income was [tex]\$34,500[/tex]. 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?

A. [tex]\$5,048.75[/tex]

B. [tex]\$336,100.50[/tex]

C. [tex]\$341,149.25[/tex]

Sagot :

GinnyAnsweridn
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]
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