To calculate the federal income tax owed on a \[tex]$53,600 salary using the given progressive tax rates, let's break it down step-by-step:
1. Calculate Taxable Income:
The standard deduction for an individual is \$[/tex]12,200.
[tex]\[
\text{Taxable Income} = \text{Salary} - \text{Standard Deduction} = 53,600 - 12,200 = 41,400
\][/tex]
2. Apply the Progressive Tax Rates:
We need to apply the given tax rates to the different portions of the taxable income within the specified brackets.
- First Bracket:
[tex]\[
0 - 9,700 \text{ at } 10\%
\][/tex]
The tax for this portion of the income:
[tex]\[
9,700 \times 0.10 = 970
\][/tex]
- Second Bracket:
[tex]\[
9,701 - 39,475 \text{ at } 12\%
\][/tex]
The tax for this portion of the income:
[tex]\[
\left(39,475 - 9,700\right) \times 0.12 = 29,775 \times 0.12 = 3,573
\][/tex]
- Third Bracket:
[tex]\[
39,476 - 84,200 \text{ at } 22\%
\][/tex]
The taxable income within this bracket is the amount in excess of 39,475 up to 41,400. Since 41,400 is within this bracket:
[tex]\[
\left(41,400 - 39,475\right) \times 0.22 = 1,925 \times 0.22 = 423.5
\][/tex]
3. Sum the Taxes:
Adding the tax from all brackets:
[tex]\[
970 \, (\text{first bracket}) + 3,573 \, (\text{second bracket}) + 423.5 \, (\text{third bracket}) = 4,966.5
\][/tex]
Therefore, the total federal income tax owed on a \[tex]$53,600 salary is \(\$[/tex]4,966.5\).
