To determine the federal income tax owed on a [tex]\( \$55,400 \)[/tex] salary, given the tax brackets and the standard deduction, follow these steps:
1. Calculate the Taxable Income:
[tex]\[
\text{Taxable Income} = \text{Gross Salary} - \text{Standard Deduction}
\][/tex]
Given:
[tex]\[
\text{Gross Salary} = \$55,400
\][/tex]
[tex]\[
\text{Standard Deduction} = \$12,200
\][/tex]
[tex]\[
\text{Taxable Income} = \$55,400 - \$12,200 = \$43,200
\][/tex]
2. Determine the Tax Owed in Each Bracket:
[tex]\[
\text{Tax Brackets} \text{ and corresponding } \text{Rates:}
\][/tex]
- [tex]\(0 - 9,700\)[/tex] at [tex]\(10\% \)[/tex]
- [tex]\(9,701 - 39,475\)[/tex] at [tex]\(12\% \)[/tex]
- [tex]\(39,476 - 84,200\)[/tex] at [tex]\(22\% \)[/tex]
- [tex]\(84,201 - 160,275\)[/tex] at [tex]\(24\% \)[/tex]
- [tex]\(160,276+\)[/tex] at [tex]\(32\% \)[/tex]
[tex]\[
\text{Taxable Income} = \$43,200
\][/tex]
3. Calculate Tax for Each Bracket:
- For the first bracket ([tex]\(0 - 9,700\)[/tex]):
[tex]\[
\text{Tax} = 9,700 \times 0.10 = \$970
\][/tex]
- For the second bracket ([tex]\(9,701 - 39,475\)[/tex]):
[tex]\[
\text{Tax} = (39,475 - 9,700) \times 0.12 = 29,775 \times 0.12 = \$3,573
\][/tex]
- For the third bracket ([tex]\(39,476 - 84,200\)[/tex]):
[tex]\[
\text{The amount within this bracket is} \text{ from } 39,476 \text{ to } 43,200
\][/tex]
[tex]\[
\text{Tax} = (43,200 - 39,476) \times 0.22 = 3,724 \times 0.22 = \$819.28
\][/tex]
4. Summing Up the Taxes:
[tex]\[
\text{Total Tax} = \$970 + \$3,573 + \$819.28 = \$5,362.28
\][/tex]
Thus, the total federal income tax owed on a [tex]\( \$55,400 \)[/tex] salary, after accounting for the standard deduction, is approximately [tex]\( \$5,362.16 \)[/tex] when rounded to two decimal places.
In summary:
[tex]\[
\text{Tax Owed} = \$5,362.16
\][/tex]
[tex]\[
\text{Taxable Income} = \$43,200
\][/tex]
