Answer :
To determine the correct answer, we need to calculate the total tax payable on a taxable income of \[tex]$64,000 using the provided tax brackets. We will apply the tax rate to the portion of the income that falls within each bracket.
1. First Bracket (\$[/tex]0 to \[tex]$9,875):
- This portion of the income (\$[/tex]0 to \[tex]$9,875) is taxed at 10%.
- Tax: \( \$[/tex]9,875 \times 10\% = \[tex]$9,875 \times 0.10 = \$[/tex]987.50 \)
2. Second Bracket (\[tex]$9,876 to \$[/tex]40,125):
- The next portion of the income (\[tex]$9,876 to \$[/tex]40,125) is taxed at 12%.
- Amount in this bracket: [tex]\( \$40,125 - \$9,875 = \$30,250 \)[/tex]
- Tax: [tex]\( \$30,250 \times 12\% = \$30,250 \times 0.12 = \$3,630 \)[/tex]
3. Third Bracket (\[tex]$40,126 to \$[/tex]85,525):
- The remaining portion of the income up to \[tex]$64,000 falls within this bracket (\$[/tex]40,126 to \[tex]$64,000) and is taxed at 22%. - Amount in this bracket: \( \$[/tex]64,000 - \[tex]$40,125 = \$[/tex]23,875 \)
- Tax: [tex]\( \$23,875 \times 22\% = \$23,875 \times 0.22 = \$5,252.50 \)[/tex]
4. Total Tax Calculation:
- We sum the taxes calculated for each bracket.
- Total Tax: [tex]\( \$987.50 + \$3,630 + \$5,252.50 = \$9,870 \)[/tex]
Therefore, the tax is calculated as:
[tex]\[ 10\% \times \$9,875 + 12\% \times (\$40,125 - \$9,875) + 22\% \times (\$64,000 - \$40,125) \][/tex]
This corresponds to option D:
[tex]\[ \boxed{10\% \times \$9,875 + 12\% \times (\$40,125 - \$9,875) + 22\% \times (\$64,000 - \$40,125)} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
2. Second Bracket (\[tex]$9,876 to \$[/tex]40,125):
- The next portion of the income (\[tex]$9,876 to \$[/tex]40,125) is taxed at 12%.
- Amount in this bracket: [tex]\( \$40,125 - \$9,875 = \$30,250 \)[/tex]
- Tax: [tex]\( \$30,250 \times 12\% = \$30,250 \times 0.12 = \$3,630 \)[/tex]
3. Third Bracket (\[tex]$40,126 to \$[/tex]85,525):
- The remaining portion of the income up to \[tex]$64,000 falls within this bracket (\$[/tex]40,126 to \[tex]$64,000) and is taxed at 22%. - Amount in this bracket: \( \$[/tex]64,000 - \[tex]$40,125 = \$[/tex]23,875 \)
- Tax: [tex]\( \$23,875 \times 22\% = \$23,875 \times 0.22 = \$5,252.50 \)[/tex]
4. Total Tax Calculation:
- We sum the taxes calculated for each bracket.
- Total Tax: [tex]\( \$987.50 + \$3,630 + \$5,252.50 = \$9,870 \)[/tex]
Therefore, the tax is calculated as:
[tex]\[ 10\% \times \$9,875 + 12\% \times (\$40,125 - \$9,875) + 22\% \times (\$64,000 - \$40,125) \][/tex]
This corresponds to option D:
[tex]\[ \boxed{10\% \times \$9,875 + 12\% \times (\$40,125 - \$9,875) + 22\% \times (\$64,000 - \$40,125)} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
