Let's go through the problem step by step to determine the taxable income, the federal income tax owed, and the marginal tax rate applied to the last dollar of taxable income.
### Step A: Calculating Taxable Income
1. Initial taxable income: \[tex]$36,850.
2. Standard deduction: As head of household, you are allowed to exempt \$[/tex]18,000 from your taxable income.
3. New taxable income: Subtract the standard deduction from the initial taxable income.
[tex]\[ \text{New taxable income} = \text{Initial taxable income} - \text{Standard deduction} \][/tex]
[tex]\[ \text{New taxable income} = 36,850 - 18,000 \][/tex]
[tex]\[ \text{New taxable income} = 18,850 \][/tex]
The taxable income after accounting for the standard deduction is \[tex]$18,850.
### Step B: Applying the Tax Rates
Using the tax brackets provided, we calculate the federal tax owed:
\[
\begin{array}{|c|c|}
\hline
\text{Total Taxable Income} & \text{Marginal Tax Rate (\%)} \\
\hline
\$[/tex]0 - \[tex]$19,400 & 10\% \\
\hline
\$[/tex]19,401 - \[tex]$78,950 & 12\% \\
\hline
\$[/tex]78,951 - \[tex]$168,400 & 22\% \\
\hline
\$[/tex]168,401 - \[tex]$321,450 & 24\% \\
\hline
\$[/tex]321,451 - \[tex]$408,200 & 32\% \\
\hline
\$[/tex]612,351 \text{ and above} & 35\% \\
\hline
\end{array}
\]
Since our taxable income of \[tex]$18,850 falls within the first bracket (\$[/tex]0 - \[tex]$19,400) at a rate of 10%, we calculate the tax as follows:
\[
\text{Federal tax} = \text{Taxable income} \times \text{Tax rate} \\
= 18,850 \times 0.10 \\
= 1,885.00
\]
### Step C: Finding the Marginal Tax Rate
The marginal tax rate is the rate applied to the last dollar of taxable income. Since our taxable income (\$[/tex]18,850) falls within the \[tex]$0 - \$[/tex]19,400 bracket, the marginal tax rate for this income is 10%.
### Final Results
1. Federal income tax owed: \[tex]$1,885.00
2. Marginal tax rate: 10.0%
Therefore, the answers are:
- Federal income tax owed: $[/tex]\[tex]$1885.00$[/tex]
- Marginal tax rate: [tex]$10.0$[/tex] percent
