To calculate the federal income tax owed on a [tex]$58,200 salary using the given progressive tax rates, we can follow these steps:
1. Determine Taxable Income:
- Start with the given salary.
- Subtract the standard deduction from the salary to find the taxable income.
\[
\text{Taxable Income} = \$[/tex]58,200 - \[tex]$12,200 = \$[/tex]46,000
\]
2. Calculate Tax on Each Bracket:
- The taxable income falls into multiple tax brackets, so we need to calculate the tax for each bracket up to our taxable income of [tex]$46,000.
3. First Bracket (0-9,700 at 10%):
- Calculate tax for income from $[/tex]0 to [tex]$9,700.
\[
\text{Tax}_{\text{first bracket}} = 9700 \times 0.10 = \$[/tex]970
\]
4. Second Bracket (9,701 - 39,475 at 12%):
- Calculate tax for income from [tex]$9,701 to $[/tex]39,475.
[tex]\[
\text{Tax}_{\text{second bracket}} = (39475 - 9700) \times 0.12 = 29775 \times 0.12 = \$3,573
\][/tex]
5. Third Bracket (39,476 - 84,200 at 22%):
- Calculate tax for the income up to [tex]$46,000, since it is less than $[/tex]84,200. We only need to tax the portion from [tex]$39,476 to $[/tex]46,000.
[tex]\[
\text{Tax}_{\text{third bracket}} = (46000 - 39475) \times 0.22 = 6525 \times 0.22 = \$1,435.5
\][/tex]
6. Total Tax:
- Add up the taxes from all brackets.
[tex]\[
\text{Total Tax} = \$970 + \$3,573 + \$1,435.5 = \$5,978.5
\][/tex]
So, the federal income tax owed on a $58,200 salary is:
[tex]\[
\boxed{5,978.5}
\][/tex]
