To calculate the federal income tax owed on a \[tex]$57,600 salary given the progressive tax rates and standard deduction, we need to follow these steps:
1. Determine the Taxable Income:
Subtract the standard deduction from the salary to find the taxable income.
\[
\text{Taxable Income} = \$[/tex]57,600 - \[tex]$12,200 = \$[/tex]45,400
\]
2. Apply the Progressive Tax Rates:
The taxable income of \[tex]$45,400 falls into multiple tax brackets. We need to calculate the tax for each portion of the income within those brackets.
- First Bracket (\$[/tex]0 - \[tex]$9,700):
\[
\$[/tex]9,700 \times 10\% = \[tex]$970
\]
- Second Bracket (\$[/tex]9,701 - \[tex]$39,475):
\[
(\$[/tex]39,475 - \[tex]$9,700) \times 12\% = \$[/tex]29,775 \times 12\% = \[tex]$3,573
\]
- Third Bracket (\$[/tex]39,476 - \[tex]$84,200):
Since \$[/tex]45,400 is within this bracket, we only need to calculate the tax for the portion of the income that falls within this range.
[tex]\[
(\$45,400 - \$39,475) \times 22\% = \$5,925 \times 22\% = \$1,303.50
\][/tex]
3. Sum the Tax Amounts:
Add the tax amounts from each bracket.
[tex]\[
\$970 + \$3,573 + \$1,303.50 = \$5,846.50
\][/tex]
So, the federal income tax owed on a \$57,600 salary is calculated to be:
[tex]\[
\boxed{5,846.5}
\][/tex]
