To determine the federal income tax owed on a [tex]$49,500 salary, we will need to follow several steps. These steps include considering the standard deduction and applying the progressive tax rates to the remaining taxable income. Here is the detailed, step-by-step solution:
1. Calculate the Taxable Income:
- Start with the gross salary: $[/tex]49,500.
- Subtract the standard deduction: [tex]$12,200.
\[
\text{Taxable Income} = \$[/tex]49,500 - \[tex]$12,200 = \$[/tex]37,300
\]
2. Apply the Progressive Tax Rates:
- To calculate the tax, we need to apply the progressive tax rates to the taxable income.
- The tax brackets and their rates are:
- [tex]$0 - $[/tex]9,700 at 10%
- [tex]$9,701 - $[/tex]39,475 at 12%
- [tex]$39,476 - $[/tex]84,200 at 22%
Let's split the taxable income across these brackets and calculate the tax for each portion of the income that falls within them.
- First Bracket: [tex]$0 - $[/tex]9,700 at 10%
[tex]\[
\text{Tax for this bracket} = 9,700 \times 0.10 = \$970
\][/tex]
- Second Bracket: [tex]$9,701 - $[/tex]39,475 at 12%
The taxable income exceeding [tex]$9,700 within this bracket is:
\[
37,300 - 9,700 = 27,600
\]
Because $[/tex]27,600 is entirely within this bracket (since it's less than [tex]$39,475 - $[/tex]9,700), we calculate:
[tex]\[
\text{Tax for this bracket} = 27,600 \times 0.12 = \$3,312
\][/tex]
3. Total Federal Income Tax:
- Add the tax amounts from each bracket.
[tex]\[
\text{Total Federal Income Tax} = \$970 + \$3,312 = \$4,282
\][/tex]
Therefore, the federal income tax owed on a [tex]$49,500 salary, after accounting for a standard deduction of $[/tex]12,200 and applying the progressive tax rates, is $4,282.
