To determine the correct way to compute the tax Sue owes, let's analyze each option step by step:
#### Option A:
[tex]\[10\% \times \$9{,}875 + 12\% \times (\$30{,}000 - \$9{,}875)\][/tex]
1. Compute the tax for the first bracket:
[tex]\[0.10 \times \$9{,}875 = \$987.50\][/tex]
2. Compute the tax for the remaining income in the second bracket:
[tex]\[0.12 \times (\$30{,}000 - \$9{,}875) = 0.12 \times \$20{,}125 = \$2{,}415.00\][/tex]
3. Sum the taxes:
[tex]\[\$987.50 + \$2{,}415.00 = \$3{,}402.50\][/tex]
#### Option B:
[tex]\[12\% \times \$30{,}000\][/tex]
1. Compute the tax directly:
[tex]\[0.12 \times \$30{,}000 = \$3{,}600.00\][/tex]
#### Option C:
[tex]\[10\% \times \$9{,}875 + 12\% \times \$30{,}000\][/tex]
1. Compute the tax for the first bracket:
[tex]\[0.10 \times \$9{,}875 = \$987.50\][/tex]
2. Compute the tax for the entire taxable income in the second bracket:
[tex]\[0.12 \times \$30{,}000 = \$3{,}600.00\][/tex]
3. Sum the taxes:
[tex]\[\$987.50 + \$3{,}600.00 = \$4{,}587.50\][/tex]
#### Option D:
[tex]\[12\% \times (\$40{,}125 - \$30{,}000)\][/tex]
1. Compute the tax for the difference:
[tex]\[0.12 \times (\$40{,}125 - \$30{,}000) = 0.12 \times \$10{,}125 = \$1{,}215.00\][/tex]
#### Option E:
[tex]\[10\% \times \$9{,}875 + 12\% \times (\$40{,}125 - \$30{,}000)\][/tex]
1. Compute the tax for the first bracket:
[tex]\[0.10 \times \$9{,}875 = \$987.50\][/tex]
2. Compute the tax for the difference:
[tex]\[0.12 \times (\$40{,}125 - \$30{,}000) = 0.12 \times \$10{,}125 = \$1{,}215.00\][/tex]
3. Sum the taxes:
[tex]\[\$987.50 + \$1{,}215.00 = \$2{,}202.50\][/tex]
Comparing the computed values:
- Option A: \[tex]$3{,}402.50
- Option B: \$[/tex]3{,}600.00
- Option C: \[tex]$4{,}587.50
- Option D: \$[/tex]1{,}215.00
- Option E: \[tex]$2{,}202.50
Therefore, the correct answer is:
A. \(10\% \times \$[/tex]9{,}875 + 12\% \times(\[tex]$30{,}000 - \$[/tex]9{,}875)\)
This option accurately represents the tax computation given Sue's taxable income of \$30,000 within the defined tax brackets.
