Let's calculate the federal income tax owed on a [tex]$55,000 salary using the given progressive tax rates and the standard deduction.
### Step-by-Step Solution
1. Calculate the Taxable Income:
- Salary: $[/tex]55,000
- Standard Deduction: [tex]$12,200
To find the taxable income:
\[
\text{Taxable Income} = \text{Salary} - \text{Standard Deduction}
\]
\[
\text{Taxable Income} = 55,000 - 12,200 = 42,800
\]
2. Determine the Income in Each Tax Bracket:
- Since the taxable income is $[/tex]42,800, we need to find out how much of this falls into each tax bracket:
- First bracket: [tex]$0 - $[/tex]9,700 at 10%
- Second bracket: [tex]$9,701 - $[/tex]39,475 at 12%
- Third bracket: [tex]$39,476 - $[/tex]84,200 at 22%
3. Calculate the Tax for Each Bracket:
- First Bracket:
[tex]\[
\text{Tax for the first bracket} = 9,700 \times 0.10 = 970
\][/tex]
- Second Bracket:
The second bracket covers the range from [tex]$9,701 to $[/tex]39,475. The amount from the taxable income that falls into this bracket is [tex]$39,475 - $[/tex]9,700 = [tex]$29,775.
\[
\text{Tax for the second bracket} = 29,775 \times 0.12 = 3,573
\]
- Third Bracket:
The amount from the taxable income that falls into this bracket is $[/tex]42,800 - [tex]$39,475 = $[/tex]3,325.
[tex]\[
\text{Tax for the third bracket} = 3,325 \times 0.22 = 731.5
\][/tex]
4. Sum Up the Taxes Owed from Each Bracket:
- Summing up the tax from all three brackets:
[tex]\[
\text{Total Tax Owed} = 970 + 3,573 + 731.5 = 5,274.5
\][/tex]
Hence, the federal income tax owed on a $55,000 salary is:
[tex]\[
\boxed{5,274.5}
\][/tex]
