To calculate the federal income tax owed on a \[tex]$62,900 salary given the progressive tax rates and standard deduction, we can follow these steps:
1. Calculate the Taxable Income:
- Start with the gross salary.
- Subtract the standard deduction from the gross salary.
\[
\text{Taxable Income} = \$[/tex]62,900 - \[tex]$12,200 = \$[/tex]50,700
\]
2. Apply the Tax Brackets:
- Break down the taxable income across the different tax brackets.
[tex]\[
\text{Tax Owed} = (\text{Amount in First Bracket}) \times (\text{Rate in First Bracket}) + (\text{Amount in Second Bracket}) \times (\text{Rate in Second Bracket}) + \ldots
\][/tex]
Let's apply each relevant tax bracket to the calculated taxable income of \[tex]$50,700.
- First Bracket: 0 to \$[/tex]9,700 taxed at 10%
[tex]\[
\$9,700 \times 0.10 = \$970
\][/tex]
- Second Bracket: \[tex]$9,701 to \$[/tex]39,475 taxed at 12%
[tex]\[
\left(\$39,475 - \$9,700\right) \times 0.12 = \$29,775 \times 0.12 = \$3,573
\][/tex]
- Third Bracket: \[tex]$39,476 to \$[/tex]84,200 taxed at 22%
[tex]\[
\left(\$50,700 - \$39,475\right) \times 0.22 = \$11,225 \times 0.22 = \$2,469.50
\][/tex]
3. Sum the Tax Amounts:
- Add up the calculated tax from each bracket to find the total tax owed.
[tex]\[
\text{Total Tax Owed} = \$970 + \$3,573 + \$2,469.50 = \$7,012.50
\][/tex]
So, the federal income tax owed on a \[tex]$62,900 salary, considering the standard deduction and progressive tax rates, is:
\[
\$[/tex]7,012.50
\]
