To calculate the federal income tax owed on a \[tex]$49,500 salary using the given progressive tax rates, follow these steps:
1. Calculate Taxable Income:
\[
\text{Gross salary} = 49,500
\]
\[
\text{Standard deduction} = 12,200
\]
\[
\text{Taxable income} = \text{Gross salary} - \text{Standard deduction} = 49,500 - 12,200 = 37,300
\]
2. Apply Progressive Tax Rates:
The taxable income of \$[/tex]37,300 falls into different segments of the tax brackets provided. We need to break down the taxable income within each range and apply corresponding tax rates.
- First Bracket (up to \[tex]$9,700):
\[
\text{Tax} = 9,700 \times 10\% = 9,700 \times 0.10 = 970
\]
- Second Bracket (\$[/tex]9,701 to \[tex]$39,475):
Since \$[/tex]37,300 is within this range but below the upper limit (\[tex]$39,475), we should calculate the tax only for the portion that exceeds \$[/tex]9,700:
[tex]\[
\text{Amount in this bracket} = 37,300 - 9,700 = 27,600
\][/tex]
[tex]\[
\text{Tax} = 27,600 \times 12\% = 27,600 \times 0.12 = 3,312
\][/tex]
3. Total Tax Calculation:
Add up the tax amounts from each bracket:
[tex]\[
\text{Total tax} = 970 + 3,312 = 4,282
\][/tex]
Therefore, the federal income tax owed on a \[tex]$49,500 salary is \$[/tex]4,282.
