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 $27,000. Be sure to first subtract the standard deduction!

Solution

To calculate the federal income tax for a person with a gross salary of $27,000 in 2021, let's follow these steps:

Step 1: Subtract the standard deduction.

The standard deduction for a single person in 2021 is $12,550. So, we subtract this from the gross salary to find the taxable income:

Taxable Income=27,00012,550=14,450\text{Taxable Income} = 27,000 - 12,550 = 14,450

Step 2: Identify the applicable tax brackets.

From the table, we can see that the taxable income of $14,450 falls into two brackets:

  • The first $9,950 is taxed at 10%.
  • The amount from $9,951 to $14,450 (i.e., $4,500) is taxed at 12%.

Step 3: Calculate the tax for each bracket.

  1. Tax on the first $9,950: 9,950×10%=9959,950 \times 10\% = 995

  2. Tax on the remaining $4,500: 4,500×12%=5404,500 \times 12\% = 540

Step 4: Add the taxes from both brackets.

Total tax=995+540=1,535\text{Total tax} = 995 + 540 = 1,535

So, the total federal income tax for a person with a gross salary of $27,000 is $1,535.


Would you like more details on any step?

Here are 5 related questions to expand on this:

  1. How does the tax calculation change for different gross salaries?
  2. What is the purpose of the standard deduction?
  3. How would deductions other than the standard deduction affect taxable income?
  4. What happens if income exceeds $40,525, crossing into the 22% tax bracket?
  5. How are tax credits different from deductions in reducing tax liability?

Tip: Understanding how tax brackets work can help you plan your finances more efficiently.

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Math Problem Analysis

Mathematical Concepts

Tax calculation
Piecewise functions
Percentages
Subtraction

Formulas

Taxable Income = Gross Salary - Standard Deduction
Tax on each bracket = Income in that bracket × Tax Rate

Theorems

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Suitable Grade Level

Grades 10-12