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Sagot :
To determine which sentence about Kim's taxes payable is true, we'll follow closely through the tax calculations per the given tax brackets:
1. Tax Bracket Division:
- Income from \[tex]$0 to \$[/tex]9,875 is taxed at 10\%.
- Income from \[tex]$9,876 to \$[/tex]40,125 is taxed at 12\%.
- Income from \[tex]$40,126 to \$[/tex]85,525 is taxed at 22\%.
2. Calculate Tax for Each Bracket:
- For the first bracket (\[tex]$0 to \$[/tex]9,875):
[tex]\[ 9,875 \times 0.10 = 987.50 \][/tex]
- For the second bracket (\[tex]$9,876 to \$[/tex]40,125):
[tex]\[ (40,125 - 9,875) \times 0.12 = 30,250 \times 0.12 = 3,630.00 \][/tex]
- For the portion of income in the third bracket (\[tex]$40,126 to \$[/tex]72,000):
[tex]\[ (72,000 - 40,125) \times 0.22 = 31,875 \times 0.22 = 7,012.50 \][/tex]
3. Calculate Total Tax Payable:
- Sum of taxes from each bracket:
[tex]\[ 987.50 + 3,630.00 + 7,012.50 = 11,630.00 \][/tex]
4. Calculate Average Tax Rate:
- Average tax rate is calculated by dividing the total tax payable by the total income:
[tex]\[ \frac{11,630.00}{72,000} \approx 0.1615277 \text{ or } 16.15\% \][/tex]
5. Compare Statements:
- A. The average tax rate on the taxable income is 10\%: This statement is false because the average tax rate is 16.15\%.
- B. The tax payable is 22\% of the taxable income: This statement is false because the tax amounting to 22% of \[tex]$72,000 would be \$[/tex]15,840, but the actual tax payable is \[tex]$11,630. - C. The actual tax is more than 22\% of the taxable income: This is false as 22% of \$[/tex]72,000 is greater than the actual tax.
- D. A part of the taxable income is taxed at 12\%: This statement is true since the portion of income from \[tex]$9,876 to \$[/tex]40,125 is explicitly taxed at 12%.
Thus, the correct sentence regarding Kim's taxes payable is:
D. A part of the taxable income is taxed at 12\%.
1. Tax Bracket Division:
- Income from \[tex]$0 to \$[/tex]9,875 is taxed at 10\%.
- Income from \[tex]$9,876 to \$[/tex]40,125 is taxed at 12\%.
- Income from \[tex]$40,126 to \$[/tex]85,525 is taxed at 22\%.
2. Calculate Tax for Each Bracket:
- For the first bracket (\[tex]$0 to \$[/tex]9,875):
[tex]\[ 9,875 \times 0.10 = 987.50 \][/tex]
- For the second bracket (\[tex]$9,876 to \$[/tex]40,125):
[tex]\[ (40,125 - 9,875) \times 0.12 = 30,250 \times 0.12 = 3,630.00 \][/tex]
- For the portion of income in the third bracket (\[tex]$40,126 to \$[/tex]72,000):
[tex]\[ (72,000 - 40,125) \times 0.22 = 31,875 \times 0.22 = 7,012.50 \][/tex]
3. Calculate Total Tax Payable:
- Sum of taxes from each bracket:
[tex]\[ 987.50 + 3,630.00 + 7,012.50 = 11,630.00 \][/tex]
4. Calculate Average Tax Rate:
- Average tax rate is calculated by dividing the total tax payable by the total income:
[tex]\[ \frac{11,630.00}{72,000} \approx 0.1615277 \text{ or } 16.15\% \][/tex]
5. Compare Statements:
- A. The average tax rate on the taxable income is 10\%: This statement is false because the average tax rate is 16.15\%.
- B. The tax payable is 22\% of the taxable income: This statement is false because the tax amounting to 22% of \[tex]$72,000 would be \$[/tex]15,840, but the actual tax payable is \[tex]$11,630. - C. The actual tax is more than 22\% of the taxable income: This is false as 22% of \$[/tex]72,000 is greater than the actual tax.
- D. A part of the taxable income is taxed at 12\%: This statement is true since the portion of income from \[tex]$9,876 to \$[/tex]40,125 is explicitly taxed at 12%.
Thus, the correct sentence regarding Kim's taxes payable is:
D. A part of the taxable income is taxed at 12\%.
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