Given a salary of \[tex]$74,300 and a standard deduction of \$[/tex]12,200, let's calculate the federal income tax owed step-by-step using the specified progressive tax rates.
1. Calculate the Taxable Income:
[tex]\[
\text{Taxable Income} = \$74,300 - \$12,200 = \$62,100
\][/tex]
2. Apply the Tax Rates by Income Brackets:
- First Bracket (\[tex]$0 - \$[/tex]9,700): 10%
[tex]\[
\text{Tax for this bracket} = \$9,700 \times 0.10 = \$970
\][/tex]
Subtracting this bracket from the taxable income:
[tex]\[
\$62,100 - \$9,700 = \$52,400
\][/tex]
- Second Bracket (\[tex]$9,701 - \$[/tex]39,475): 12%
[tex]\[
\text{Range for this bracket} = \$39,475 - \$9,700 = \$29,775
\][/tex]
[tex]\[
\text{Tax for this bracket} = \$29,775 \times 0.12 = \$3,573
\][/tex]
Subtracting this bracket from the remaining taxable income:
[tex]\[
\$52,400 - \$29,775 = \$22,625
\][/tex]
- Third Bracket (\[tex]$39,476 - \$[/tex]84,200): 22%
[tex]\[
\text{Remaining income fits entirely within this bracket} = \$22,625
\][/tex]
[tex]\[
\text{Tax for this bracket} = \$22,625 \times 0.22 = \$4,976.50
\][/tex]
3. Total Tax Calculation:
[tex]\[
\text{Total Tax Owed} = \$970 + \$3,573 + \$4,976.50 = \$9,519.50
\][/tex]
Thus, the federal income tax owed on a \[tex]$74,300 salary, after a \$[/tex]12,200 deduction, is [tex]\(\$9,519.50\)[/tex].
