To calculate the federal income tax owed on a \[tex]$55,000 salary, we'll follow the progressive tax rate structure provided. Here's a detailed, step-by-step solution:
1. Calculate the Taxable Income:
\[
\text{Taxable Income} = \text{Gross Income} - \text{Standard Deduction}
\]
Given:
\[
\text{Gross Income} = \$[/tex]55,000
\]
[tex]\[
\text{Standard Deduction} = \$12,200
\][/tex]
Thus:
[tex]\[
\text{Taxable Income} = \$55,000 - \$12,200 = \$42,800
\][/tex]
2. Calculate the Tax Owed:
We will use the given tax brackets and apply each rate to the corresponding portion of the taxable income.
- First bracket (0 - \[tex]$9,700 at 10%):
\[
\text{Tax from first bracket} = \$[/tex]9,700 \times 0.10 = \[tex]$970
\]
- Second bracket (\$[/tex]9,701 - \[tex]$39,475 at 12%):
\[
\text{Amount in second bracket} = \$[/tex]39,475 - \[tex]$9,700 = \$[/tex]29,775
\]
[tex]\[
\text{Tax from second bracket} = \$29,775 \times 0.12 = \$3,573
\][/tex]
- Third bracket (\[tex]$39,476 - \$[/tex]84,200 at 22%):
The taxable income falls into the third bracket up to \[tex]$42,800:
\[
\text{Amount in third bracket} = \$[/tex]42,800 - \[tex]$39,475 = \$[/tex]3,325
\]
[tex]\[
\text{Tax from third bracket} = \$3,325 \times 0.22 = \$731.50
\][/tex]
3. Sum Up the Taxes from All Brackets:
[tex]\[
\text{Total Tax Owed} = \$970 + \$3,573 + \$731.50 = \$5,274.50
\][/tex]
Therefore, the federal income tax owed on a \[tex]$55,000 salary is approximately \(\$[/tex]5,274.16\).
The taxable income is [tex]\(\$42,800\)[/tex].
