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Use the U. S. 2011 federal income tax function for a single person as defined in Example 2 of Section 1.1. What is the taxable income of a single person who paid $$\$ 20,000$$ in federal taxes for \(2011 ?\)

Short Answer

Expert verified
The taxable income of a single person who paid $$\$ 20,000$$ in federal taxes for 2011 is $$\$ 87,000$$.

Step by step solution

01

Determine the tax paid for each bracket

For the first tax bracket (10%): Tax paid = 10% x $$\$ 8,500$$ = $$\$ 850$$ For the second tax bracket (15%): Tax paid = 15% x ($$\$ 34,500$$ - $$\$ 8,500$$) = 15% x $26,000 = $$\$ 3,900$$ For the third tax bracket (25%): We don't know the taxable income yet, so we cannot calculate the tax for this bracket at this moment.
02

Calculate the tax remaining to be paid

Subtract the taxes paid in the first two brackets from $$\$ 20,000$$: Tax remaining to be paid = $$\$ 20,000$$ - ($$\$ 850$$ + $$\$ 3,900$$) = $$\$ 15,250$$
03

Calculate the income for the third tax bracket

Since the tax remaining to be paid ($$\$ 15,250$$) falls in the third tax bracket (25%), we can calculate the income for this bracket by dividing the remaining tax by the tax rate (25%): Income for the third tax bracket = $$\$ 15,250$$ ÷ 25% = $$\$ 61,000$$
04

Calculate the total taxable income

Add the income in each tax bracket to find the total taxable income: Total taxable income = $$\$ 8,500$$ (first bracket) + ( $$\$ 34,500$$ - $$\$ 8,500$$) (second bracket) + $$\$ 61,000$$ (third bracket) = $$\$ 87,000$$ So, the taxable income of a single person who paid $$\$ 20,000$$ in federal taxes for 2011 is $$\$ 87,000$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Tax Brackets
Tax brackets are categories that define the amount of tax you will pay based on your income level. In the United States, the federal income tax system is progressive, which means that income is taxed at different rates depending on the amount of taxable income. This system ensures that individuals with higher incomes pay a proportionally higher tax rate.

Each tax bracket is associated with a percentage, which represents the rate at which your income is taxed within that bracket. For example, if the first tax bracket is taxed at 10%, only the income that falls within this bracket is taxed at 10%. The next bracket might tax income at 15%, and so on. Understanding which bracket your income falls into is important to figure out how much tax you owe in each bracket.
  • The process starts with the smallest tax bracket and applies to successive portions of your income as it increases.
  • Once your income exceeds the upper limit of one bracket, the remaining income is taxed at the next bracket's rate.
Tax brackets help to ensure fairness in the tax system. They help ensure that people with higher incomes contribute more in taxes than those with lower incomes, reflecting their greater ability to pay.
Calculating Taxable Income
Taxable income is the portion of your total income that is subject to taxes. It's important to differentiate between your gross income and taxable income. Gross income includes all the money you earn, while taxable income is what remains after allowable deductions, exemptions, and credits are taken into account.

Calculating taxable income involves several steps:
  • First, sum up all your income sources for the year, including wages, salaries, bonuses, and any other income.
  • Next, subtract all deductible expenses and adjustments to income, such as retirement contributions and student loan interest.
  • Finally, apply any personal exemptions or standard deductions to further reduce the total.
The result is your taxable income, which is then used to determine the amount of taxes owed according to the relevant tax brackets. Understanding and accurately calculating your taxable income is crucial for ensuring that you pay the correct amount of tax. This ensures compliance with tax laws and helps you avoid potential penalties.
Percentage Calculations in Taxation
Percentage calculations are fundamental when determining how much tax you owe within each bracket. It's all about applying the percentage rate of each tax bracket to the income that falls within that bracket. This step-by-step process determines the total tax liability.

Here's how percentage calculations work in the context of taxation:
  • Identify the portion of your income that fits within each bracket. Apply the bracket's percentage rate to that portion.
  • For income in the first bracket taxed at 10%, the calculation is simply 10% of that income segment.
  • For the next bracket, say at 15%, compute 15% of that income exceeding the first bracket threshold.
Using these calculations, you sum up the tax amounts from each bracket to find your total tax owed.

These calculations rely on straightforward multiplication and division of your income by the applicable percentage rates. Comprehending these percentage calculations allows for a precise understanding of how much tax you are required to pay. This translates into better financial planning and budgeting for future expenses.

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Most popular questions from this chapter

Show that the composition of two one-to-one functions is a one-to-one function.

Suppose you are exchanging cur. rency in the London airport. The currency exchange service there only makes transactions in which one of the two currencies is British pounds, but you want to exchange dollars for Euros. Thus you first need to exchange dollars for British pounds, then exchange British pounds for Euros. At the time you want to make the exchange, the function \(f\) for exchanging dollars for British pounds is given by the formula \(f(d)=0.66 d-1\) and the function \(g\) for exchanging British pounds for Euros is given by the formula \(g(p)=1.23 p-2\) The subtraction of 1 or 2 in the number of British pounds or Euros that you receive is the fee charged by the currency exchange service for each transaction. How many Euros would you receive for exchanging 200 after going through this two-step exchange process?

Show that if \(f\) is the function defined by \(f(x)=m x+b,\) where \(m \neq 0,\) then the inverse function \(f^{-1}\) is defined by the formula \(f^{-1}(y)=\frac{1}{m} y-\frac{b}{m}\).

For each of the functions \(f\) given. (a) Find the domain of \(f\). (b) Find the range of \(f\). (c) Find a formula for \(f^{-1}\). (d) Find the domain of \(f^{-1}\). (e) Find the range of \(f^{-1}\). You can check your solutions to part (c) by verifying that \(f^{-1} \circ f=I\) and \(f \circ f^{-1}=I\) (recall that \(I\) is the function defined by \(I(x)=x\) ). \(f(x)=2 x-7\)

Suppose \(f\) and \(g\) are functions, each with domain of four numbers, with \(f\) and \(g\) defined by the tables below: $$\begin{array}{c|c}x & f(x) \\\\\hline 1 & 4 \\\2 & 5 \\\3 & 2 \\\4 & 3\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 2 & 3 \\\3 & 2 \\\4 & 4 \\\5 & 1\end{array}$$ Give the table of values for \(g \circ f\).

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