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Follow the steps to calculate the federal income tax owed on a [tex]$\$[/tex]30,000$ salary using the given tax rates.

1. Calculate the amount of taxable income by subtracting the standard deduction from the salary.
[tex]\[
\text{Taxable Income} = \[tex]$30,000 - \$[/tex]12,200 = \$17,800
\][/tex]

2. Apply the progressive tax rates to the taxable income:
[tex]\[
\begin{array}{|r|c|}
\hline
\text{Income Range (\$)} & \text{Tax Rate} \\
\hline
0-9,700 & 10\% \\
\hline
9,701-39,475 & 12\% \\
\hline
39,476-84,200 & 22\% \\
\hline
84,201-160,275 & 24\% \\
\hline
160,276+ & 32\% \\
\hline
\end{array}
\][/tex]

3. Calculate the tax for each bracket up to \$17,800:
[tex]\[
\text{Tax} = (\[tex]$9,700 \times 0.10) + (\$[/tex]8,100 \times 0.12)
\][/tex]

4. Sum the tax amounts to find the total tax owed:
[tex]\[
\text{Total Tax} = \[tex]$970 + \$[/tex]972 = \$1,942
\][/tex]

So, the federal income tax owed on a \[tex]$30,000 salary is \$[/tex]1,942.

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step:

Step 1: Calculate Taxable Income
Subtract the standard deduction from the salary to get the taxable income.

Given:
- Salary: \$30,000
- Standard Deduction: \$12,200

Taxable Income \(= \[tex]$30,000 - \$[/tex]12,200 = \$17,800\).

So, the taxable income is \$17,800.

Step 2: Calculate Tax for Each Bracket
We need to apply the progressive tax rates to the taxable income.

- For the first \$9,700 at 10%:
[tex]\[ \text{Tax for the first \[tex]$9,700} = \$[/tex]9,700 \times 0.10 = \$970
\][/tex]

- For the amount over \[tex]$9,700 but less than or equal to \$[/tex]39,475 at 12%:
[tex]\[ \text{Remaining Taxable Income} = \[tex]$17,800 - \$[/tex]9,700 = \$8,100
\][/tex]
[tex]\[ \text{Tax for the remaining \[tex]$8,100} = \$[/tex]8,100 \times 0.12 = \$972
\][/tex]

Step 3: Calculate the Total Tax Owed
Add the tax amounts from each bracket.

[tex]\[ \text{Total Tax} = \[tex]$970 + \$[/tex]972 = \$1,942
\][/tex]

### Summary:
- Taxable Income: \$17,800
- Tax for \[tex]$0 to \$[/tex]9,700: \$970
- Tax for \[tex]$9,701 to \$[/tex]17,800: \$972
- Total Tax Owed: \$1,942
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