Math / Algebra

QuestionA certain state uses the progressive tax rate below for calculating individual income tax. Calculate the state income tax owed on an $\$ 80,000$ per year salary. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Income \\ Range (\) \end{tabular} & \begin{tabular}{c} Progressive \\ Tax Rate \end{tabular} \\ \hline 0-4,000 & 2 \% \\ \hline 4,001-22,000 & 4 \% \\ \hline 22,001+ & 5 \%$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The income tax brackets are applied progressively, meaning each portion of the income is taxed at its respective rate.
2. The salary given is annual, and all calculations will be based on this annual figure.
3. The tax rates are applied only to the portion of income within each bracket.

STEP 2

1. Calculate the tax for the income range \$0-\$4,000 at 2%.
2. Calculate the tax for the income range \$4,001-\$22,000 at 4%.
3. Calculate the tax for the income range \$22,001-\$80,000 at 5%.
4. Sum the taxes from all ranges to get the total tax owed.

STEP 3

Calculate the tax for the income range \$0-\$4,000 at 2%.
$\text{Tax}_{0-4000} = 4000 \times 0.02 = 80$

STEP 4

Calculate the tax for the income range \$4,001-\$22,000 at 4%.
$\text{Tax}_{4001-22000} = (22000 - 4000) \times 0.04 = 18000 \times 0.04 = 720$

STEP 5

Calculate the tax for the income range \$22,001-\$80,000 at 5%.
$\text{Tax}_{22001+} = (80000 - 22000) \times 0.05 = 58000 \times 0.05 = 2900$

STEP 6

Sum the taxes from all ranges.
$\text{Total Tax} = \text{Tax}_{0-4000} + \text{Tax}_{4001-22000} + \text{Tax}_{22001+} = 80 + 720 + 2900 = 3700$
The state income tax owed on an \$80,000 per year salary is \$3,700.

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Studdy Solution

STEP 1

1. The income tax brackets are applied progressively, meaning each portion of the income is taxed at its respective rate.
2. The salary given is annual, and all calculations will be based on this annual figure.
3. The tax rates are applied only to the portion of income within each bracket.

STEP 2

1. Calculate the tax for the income range \$0-\$4,000 at 2%.
2. Calculate the tax for the income range \$4,001-\$22,000 at 4%.
3. Calculate the tax for the income range \$22,001-\$80,000 at 5%.
4. Sum the taxes from all ranges to get the total tax owed.

STEP 3

Calculate the tax for the income range \$0-\$4,000 at 2%.
$\text{Tax}_{0-4000} = 4000 \times 0.02 = 80$

STEP 4

Calculate the tax for the income range \$4,001-\$22,000 at 4%.
$\text{Tax}_{4001-22000} = (22000 - 4000) \times 0.04 = 18000 \times 0.04 = 720$

STEP 5

Calculate the tax for the income range \$22,001-\$80,000 at 5%.
$\text{Tax}_{22001+} = (80000 - 22000) \times 0.05 = 58000 \times 0.05 = 2900$

STEP 6

Sum the taxes from all ranges.
$\text{Total Tax} = \text{Tax}_{0-4000} + \text{Tax}_{4001-22000} + \text{Tax}_{22001+} = 80 + 720 + 2900 = 3700$
The state income tax owed on an \$80,000 per year salary is \$3,700.

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Studdy Solution

STEP 1

1. The income tax brackets are applied progressively, meaning each portion of the income is taxed at its respective rate.2. The salary given is annual, and all calculations will be based on this annual figure.3. The tax rates are applied only to the portion of income within each bracket.

STEP 2

1. Calculate the tax for the income range \$0-\$4,000 at 2%.2. Calculate the tax for the income range \$4,001-\$22,000 at 4%.3. Calculate the tax for the income range \$22,001-\$80,000 at 5%.4. Sum the taxes from all ranges to get the total tax owed.

STEP 3

Calculate the tax for the income range \$0-\$4,000 at 2%.Tax0−4000=4000×0.02=80 \text{Tax}_{0-4000} = 4000 \times 0.02 = 80 Tax0−4000​=4000×0.02=80

STEP 4

Calculate the tax for the income range \$4,001-\$22,000 at 4%.Tax4001−22000=(22000−4000)×0.04=18000×0.04=720 \text{Tax}_{4001-22000} = (22000 - 4000) \times 0.04 = 18000 \times 0.04 = 720 Tax4001−22000​=(22000−4000)×0.04=18000×0.04=720

STEP 5

Calculate the tax for the income range \$22,001-\$80,000 at 5%.Tax22001+=(80000−22000)×0.05=58000×0.05=2900 \text{Tax}_{22001+} = (80000 - 22000) \times 0.05 = 58000 \times 0.05 = 2900 Tax22001+​=(80000−22000)×0.05=58000×0.05=2900

STEP 6

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1. The income tax brackets are applied progressively, meaning each portion of the income is taxed at its respective rate.
2. The salary given is annual, and all calculations will be based on this annual figure.
3. The tax rates are applied only to the portion of income within each bracket.

1. Calculate the tax for the income range \$0-\$4,000 at 2%.
2. Calculate the tax for the income range \$4,001-\$22,000 at 4%.
3. Calculate the tax for the income range \$22,001-\$80,000 at 5%.
4. Sum the taxes from all ranges to get the total tax owed.

Calculate the tax for the income range \$0-\$4,000 at 2%.
$\text{Tax}_{0-4000} = 4000 \times 0.02 = 80$

Calculate the tax for the income range \$4,001-\$22,000 at 4%.
$\text{Tax}_{4001-22000} = (22000 - 4000) \times 0.04 = 18000 \times 0.04 = 720$

Calculate the tax for the income range \$22,001-\$80,000 at 5%.
$\text{Tax}_{22001+} = (80000 - 22000) \times 0.05 = 58000 \times 0.05 = 2900$