To correctly compute Sue's tax liability based on her taxable income of \[tex]$30,000, we need to consider the tax brackets and the corresponding tax rates.
Here is a step-by-step breakdown:
1. Identify the applicable tax brackets and rates:
- For the first \$[/tex]9,875 of income, the tax rate is 10%.
- For income from \[tex]$9,876 to \$[/tex]30,000, the tax rate is 12%.
2. Compute the tax for income in each bracket:
- First bracket (\[tex]$0 - \$[/tex]9,875) at 10%:
[tex]\[
\text{Tax for first bracket} = 10\% \times \$9,875 = 0.10 \times \$9,875 = \$987.50
\][/tex]
- Second bracket (\[tex]$9,876 - \$[/tex]30,000) at 12%:
- Income in this bracket: [tex]\(\$30,000 - \$9,875 = \$20,125\)[/tex]
[tex]\[
\text{Tax for second bracket} = 12\% \times \$20,125 = 0.12 \times \$20,125 = \$2,415.00
\][/tex]
3. Sum the taxes from both brackets to get the total tax:
[tex]\[
\text{Total tax} = \$987.50 + \$2,415.00 = \$3,402.50
\][/tex]
Now, let's choose the correct answer from the given options.
- Option A:
[tex]\[
12\% \times \$30,000 = 0.12 \times \$30,000 = \$3,600
\][/tex]
This does not account for the 10% tax rate for the first \[tex]$9,875 of income.
- Option B:
\[
1246 \times (\$[/tex]40,125 - \[tex]$30,000) = \text{Not applicable and incorrect}
\]
- Option C:
\[
10\% \times \$[/tex]9,875 + 12\% \times (\[tex]$40,125 - \$[/tex]30,000) = \text{Misinterpretation of brackets and incorrect}
\]
- Option D:
[tex]\[
10\% \times \$9,875 + 12\% \times (\$30,000 - \$9,875) = 0.10 \times \$9,875 + 0.12 \times (\$30,000 - \$9,875)
\][/tex]
[tex]\[
= \text{Correct calculation:} \ \text{10\%} \times \$9,875 + \text{12\%} \times \$20,125
\][/tex]
- Option E:
[tex]\[
10\% \times \$9,875 + 12\% \times \$30,000 = \text{Incorrect breakdown as the entire amount of \$30,000 is not taxed at 12\%}
\][/tex]
Therefore, Option D is the correct and detailed way to compute the tax Sue owes:
[tex]\[
\boxed{D}
\][/tex]
