Answer
The income tax owed by the household is \[\$1865\].
Work Step by Step
The adjusted gross income will be:
\[\begin{align}
& \text{Adjusted}\ \text{Gross}\ \text{Income}=\ \text{Gross}\ \text{Income}-\text{Adjustments} \\
& =\ \$50000-0\\&=\$50000\end{align}\]
The taxable income is the amount of income used to calculate how much tax an individual owes to the government in a given tax year.
The total deduction of \[\$6500\] is less than the standard deduction of \[\$8700\].
So, use \[\$8700\] for deduction.
Then, the taxable income will be:
\[\begin{align}
& \text{Taxable}\ \text{Income}=\ \text{Adjusted}\ \text{Gross}\ \text{Income}-\left( \text{Exemptions}+\text{Deductions} \right) \\
& =\ \$50000-\left(\$3800\cdot3+\$8700\right)\\&=\$29900\end{align}\]
For the head of household, tax rate is \[10%\] up to \[\$12400\], \[15%\] from \[\$12401\] to \[\$47350\].
Then, the tax computation will be:
\[\begin{align}
& \text{Tax computation}=\ 0.10\left( \$12400\right)+0.15\left(\$29900-\$12400\right)\\&=\$3865\end{align}\]
So, the income tax will be:
\[\begin{align}
& \text{Income tax}=\text{Tax computation}-\text{Tax credits} \\
& =\$3865-\$2000\\&=\$1865\end{align}\]
Therefore, the income tax owed by the household is \[\$1865\].
