To calculate the federal income tax owed on a salary of [tex]$52,800 using the provided progressive tax rates, follow these steps:
### Step 1: Calculate Taxable Income
First, we need to subtract the standard deduction from the gross salary to find the taxable income:
\[ \text{Taxable Income} = \text{Salary} - \text{Standard Deduction} \]
\[ \text{Taxable Income} = \$[/tex]52,800 - \[tex]$12,200 \]
\[ \text{Taxable Income} = \$[/tex]40,600 \]
### Step 2: Apply Progressive Tax Rates
Next, apply the appropriate tax rates to each portion of the taxable income based on the given brackets:
#### Bracket 1: [tex]$0 - $[/tex]9,700:
Tax rate is 10%.
[tex]\[ \text{Tax for Bracket 1} = \$9,700 \times 0.10 \][/tex]
[tex]\[ \text{Tax for Bracket 1} = \$970 \][/tex]
#### Bracket 2: [tex]$9,701 - $[/tex]39,475:
Tax rate is 12%.
[tex]\[ \text{Tax for Bracket 2} = (\$39,475 - \$9,700) \times 0.12 \][/tex]
[tex]\[ \text{Tax for Bracket 2} = \$29,775 \times 0.12 \][/tex]
[tex]\[ \text{Tax for Bracket 2} = \$3,573 \][/tex]
#### Bracket 3: [tex]$39,476 - $[/tex]84,200:
Tax rate is 22%. Since our taxable income extends into but does not exceed this bracket, we will calculate the tax only on the portion within this bracket.
[tex]\[ \text{Tax for Bracket 3} = (\$40,600 - \$39,476) \times 0.22 \][/tex]
[tex]\[ \text{Tax for Bracket 3} = \$1,124 \times 0.22 \][/tex]
[tex]\[ \text{Tax for Bracket 3} = \$247.28 \][/tex]
### Step 3: Sum Up Taxes from All Brackets
Finally, we add up the taxes calculated for each bracket to determine the total tax owed.
[tex]\[ \text{Total Tax Owed} = \text{Tax for Bracket 1} + \text{Tax for Bracket 2} + \text{Tax for Bracket 3} \][/tex]
[tex]\[ \text{Total Tax Owed} = \$970 + \$3,573 + \$247.28 \][/tex]
[tex]\[ \text{Total Tax Owed} = \$4,790.28 \][/tex]
Therefore, the federal income tax owed on a salary of [tex]$52,800 is \(\$[/tex]4,790.28\).
