Math Problem Statement

Workers in the U.S. pay several types of taxes on income including state taxes, FICA taxes and federal income tax. Your federal income tax rate is based on the amount of money you make. Income is broken into levels called tax brackets (or pockets). The table below shows the tax brackets for 2021 for a single person.

Recall that taxable income is the gross income minus any allowable deductions. For the purposes of this problem, we assume that the only deduction taken is the standard deduction for a single person which in 2021 is $12,550.

Taxable Income Tax Rate for this Bracket $0 – $9,950 10% $9,951– $40,525 12% $40,526 – $86,375 22% $86,376 – $164,925 24% $164,926 – $209,425 32% $209,426 – $523,600 35% $523,601 or more 37% Calculate the income tax for a person whose gross salary is $27,500. Be sure to first subtract the standard deduction!

Solution

To calculate the federal income tax for a person with a gross salary of $27,500 in 2021, we need to follow these steps:

1. Subtract the Standard Deduction

The first step is to subtract the standard deduction from the gross salary to get the taxable income.

Taxable Income=Gross SalaryStandard Deduction\text{Taxable Income} = \text{Gross Salary} - \text{Standard Deduction}

For 2021, the standard deduction for a single person is $12,550.

Taxable Income=27,50012,550=14,950\text{Taxable Income} = 27,500 - 12,550 = 14,950

2. Apply Tax Brackets

Now, we use the taxable income to determine the federal income tax by applying the tax rates in each bracket.

Taxable Income=14,950\text{Taxable Income} = 14,950

From the tax bracket table, we can see that:

  • The first $9,950 is taxed at 10%.
  • The remaining amount up to $14,950 (which is 14,9509,950=5,00014,950 - 9,950 = 5,000) is taxed at 12%.

3. Calculate the Tax

Let's break it down by bracket:

  • For the first $9,950 at 10%: 9,950×0.10=9959,950 \times 0.10 = 995

  • For the next $5,000 at 12%: 5,000×0.12=6005,000 \times 0.12 = 600

4. Total Tax

Finally, sum the taxes from each bracket:

Total Tax=995+600=1,595\text{Total Tax} = 995 + 600 = 1,595

Thus, the federal income tax for a person with a gross salary of $27,500 is $1,595.


Would you like more details on the calculation or any other clarifications?

Here are 5 related questions that you might find interesting:

  1. How would the tax calculation change if the gross salary were $50,000?
  2. What if there were other deductions apart from the standard deduction?
  3. How do tax brackets work for married couples filing jointly?
  4. Can FICA taxes be calculated in a similar way?
  5. How does state income tax factor into total tax liability?

Tip: Always check for tax updates each year, as brackets and deductions can change annually.

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Math Problem Analysis

Mathematical Concepts

Tax Brackets
Income Deductions
Basic Arithmetic
Percentage Calculations

Formulas

Taxable Income = Gross Income - Standard Deduction
Tax for Each Bracket = Amount in Bracket × Tax Rate
Total Tax = Sum of Taxes from Each Bracket

Theorems

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Suitable Grade Level

Grades 10-12