To find out the extra amount of federal taxes Mauro has to pay due to winning the lottery, we need to calculate the federal tax he paid before and after winning the lottery.
First, let's determine Mauro's annual federal tax before winning the lottery with an income of \[tex]$34,500:
Using the tax rate structure:
- For income up to $[/tex]31,850: The tax is a fixed amount + 25% for the excess of [tex]$31,850:
\[
\text{Initial Tax} = \$[/tex]4,386.25 + 0.25 \times (\[tex]$34,500 - \$[/tex]31,850)
\]
Calculate the excess earnings:
[tex]\[
\$34,500 - \$31,850 = \$2,650
\][/tex]
Calculate 25% of the excess amount:
[tex]\[
0.25 \times \$2,650 = \$662.50
\][/tex]
Now, add this to the base tax:
[tex]\[
\text{Initial Tax} = \$4,386.25 + \$662.50 = \$5,048.75
\][/tex]
Therefore, Mauro's tax before winning the lottery was \[tex]$5,048.75.
Next, let's determine Mauro's annual federal tax after winning the lottery with an income of \$[/tex]349,700.01:
Using the tax rate structure:
- For income of [tex]$349,700.01 and up: The tax is calculated as \$[/tex]101,469.25 plus 35% of the amount over \[tex]$349,700:
\[
\text{Tax After Winning} = \$[/tex]101,469.25 + 0.35 \times (\[tex]$349,700.01 - \$[/tex]349,700)
\]
Calculate the excess amount:
[tex]\[
\$349,700.01 - \$349,700 = \$0.01
\][/tex]
Calculate 35% of the excess amount:
[tex]\[
0.35 \times \$0.01 = \$0.0035
\][/tex]
Add the excess amount to the base tax:
[tex]\[
\text{Tax After Winning} = \$101,469.25 + \$0.0035 = \$101,469.2535 \approx \$101,469.25
\][/tex]
Therefore, Mauro's tax after winning the lottery is \[tex]$101,469.25.
Finally, let's calculate the extra amount Mauro has to pay in federal taxes because he won the lottery. Subtract his tax before winning the lottery from his tax after winning the lottery:
\[
\text{Extra Tax} = \$[/tex]101,469.25 - \[tex]$5,048.75 = \$[/tex]96,420.50
\]
Therefore, the calculations above show Mauro's federal tax would change from \[tex]$5,048.75 to \$[/tex]101,469.25, resulting in an additional tax due of:
[tex]\[
\boxed{\$96,420.50}
\][/tex]
Notice that none of the answer choices provided (a. \[tex]$5,048.75, b. \$[/tex]336,100.50, c. \[tex]$341,149.25, d. \$[/tex]676,260.76) matches \[tex]$96,420.50, which could be a mistake in the problem formulation. Based on the steps and provided rates, the answer to the task is that Mauro would have to pay an additional \$[/tex]96,420.50 due to winning the lottery.
