To determine the federal income tax owed on a salary of [tex]$53,600, we will follow these steps through careful calculations according to the progressive tax rate system:
1. Calculate Taxable Income:
- First, we subtract the standard deduction from the salary to find the taxable income.
\[
\text{Taxable Income} = \$[/tex]53,600 - \[tex]$12,200 = \$[/tex]41,400
\]
2. Determine Tax Owed Based on Income Brackets:
- Next, we will evaluate the taxable income against the given tax brackets and apply the respective tax rates to different portions of the taxable income.
3. Calculate Tax for Each Bracket:
- First Bracket: \[tex]$0 - \$[/tex]9,700
- The amount in this bracket: \[tex]$9,700
- Tax rate: 10%
- Tax for this bracket: \( 9,700 \times 0.10 = \$[/tex]970 \)
- Second Bracket: \[tex]$9,701 - \$[/tex]39,475
- The amount in this bracket: [tex]\( 39,475 - 9,700 = \$29,775 \)[/tex]
- Tax rate: 12%
- Tax for this bracket: [tex]\( 29,775 \times 0.12 = \$3,573 \)[/tex]
- Third Bracket: \[tex]$39,476 - \$[/tex]84,200
- The amount in this bracket: [tex]\( 41,400 - 39,475 = \$1,925 \)[/tex]
- Tax rate: 22%
- Tax for this bracket: [tex]\( 1,925 \times 0.22 = \$423.50 \)[/tex]
4. Sum of Taxes Owed in All Brackets:
- Finally, we sum the taxes calculated for each bracket to find the total tax owed.
[tex]\[
\text{Total Tax Owed} = \$970 + \$3,573 + \$423.50 = \$4,966.50
\][/tex]
Therefore, on a salary of $53,600, the federal income tax owed would be:
[tex]\[
\boxed{4,966.50}
\][/tex]
