Let's go through the step-by-step solution to calculate the federal income tax owed on a [tex]$52,800 salary using the given progressive tax rates and a standard deduction.
### Step 1: Calculate the Taxable Income
First, subtract the standard deduction from the gross salary to find the taxable income.
\[
\text{Taxable Income} = \text{Gross Salary} - \text{Standard Deduction}
\]
Given:
\[
\text{Gross Salary} = \$[/tex]52,800
\]
[tex]\[
\text{Standard Deduction} = \$12,200
\][/tex]
So,
[tex]\[
\text{Taxable Income} = \$52,800 - \$12,200 = \$40,600
\][/tex]
### Step 2: Calculate Tax Owed Based on Progressive Tax Brackets
We will now calculate the tax owed using the progressive tax brackets provided.
1. Income from [tex]$0 to $[/tex]9,700 at 10%:
[tex]\[
\text{Tax for this range} = \$9,700 \times 0.10 = \$970
\][/tex]
2. Income from [tex]$9,701 to $[/tex]39,475 at 12%:
[tex]\[
\text{Income in this range} = \$39,475 - \$9,700 = \$29,775
\][/tex]
[tex]\[
\text{Tax for this range} = \$29,775 \times 0.12 = \$3,573
\][/tex]
3. Income from [tex]$39,476 to $[/tex]40,600 at 22%:
[tex]\[
\text{Income in this range} = \$40,600 - \$39,475 = \$1,125
\][/tex]
[tex]\[
\text{Tax for this range} = \$1,125 \times 0.22 = \$247.50
\][/tex]
### Step 3: Summing Up the Tax Owed
Now, add up the tax calculated for each income range to find the total tax owed.
[tex]\[
\text{Total Tax Owed} = \$970 + \$3,573 + \$247.50 = \$4,790.50
\][/tex]
### Summary
The taxable income is [tex]$40,600, and the total federal income tax owed on a $[/tex]52,800 salary using the provided progressive tax rates is:
[tex]\[
\$4,790.50
\][/tex]
Thus, the federal income tax owed is $4,790.50.
