3.2 Taxes

Introduction

What you’ll learn to do: Calculate income and sales tax

Governments collect taxes to pay for the services they provide. In the United States, federal income taxes help fund the military, the environmental protection agency, and thousands of other programs. Property taxes help fund schools. Gasoline taxes help pay for road improvements. While very few people enjoy paying taxes, they are necessary to pay for the services we all depend upon. In this section, we study how to calculate different types of taxes.

Learning Outcomes

  • Calculate sales and income taxes

 

Taxes

Governments collect taxes to pay for the services they provide. In the United States, federal income taxes help fund the military, the environmental protection agency, and thousands of other programs. Property taxes help fund schools. Gasoline taxes help pay for road improvements. While very few people enjoy paying taxes, they are necessary to pay for the services we all depend upon.

Taxes can be computed in a variety of ways, but are typically computed as a percentage of a sale, of one’s income, or of one’s assets.

recall calculations with percents

The word “percent” can be thought of as “per cent” or “per one hundred.”  To make calculations using percents, first convert the percent to a decimal by dividing by 100.  To do this, simply drop the % symbol and move the decimal two places to the left (adding more zeros to the left as needed).

Ex. Write 2.7% as a decimal.

We need to calculate 2.7/100.  To do this, write 02.7 then move the decimal two places left:  0.027 is the decimal representation of 2.7%.

Example: Sales Tax

The sales tax rate in a city is 9.3%. How much sales tax will you pay on a $140 purchase?

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When taxes are not given as a fixed percentage rate, sometimes it is necessary to calculate the effective tax rate: the equivalent percent rate of the tax paid out of the dollar amount the tax is based on.

Example: Property Tax

Jaquim paid $3,200 in property taxes on his house valued at $215,000 last year. What is the effective tax rate?

 

Taxes are often referred to as progressive, regressive, or flat.

  • A flat tax, or proportional tax, charges a constant percentage rate.
  • A progressive tax increases the percent rate as the base amount increases.
  • A regressive tax decreases the percent rate as the base amount increases.

ExampleS: Federal Income Tax

The United States federal income tax on earned wages is an example of a progressive tax. People with a higher wage income pay a higher percent tax on their income.

For a single person in 2011, the standard deduction was $5,800.   Taxable income (income after deductions) under $8,500 was taxed at 10%. Taxable income over $8,500 but under $34,500 was taxed at 15%.  See below for the full distribution of U.S. federal tax rates for 2011.

 

2011 Federal Income Tax Brackets and Rates

Tax Brackets (Pockets) for Single Individuals  Tax Rate
Up to $8,500 10%
$8,501 to $34,500 15%
$34,501 to $83,600 25%
$83,601 to $174,400 28%
$174,401 to $379,150 33%
$379,151 or more 35%

Example 1: Stephen’s gross salary in 2011 was $15,800.

a) Calculate Stephen’s federal income tax, assuming that his only deduction is the standard deduction of $5,800.

b) What was Stephen’s effective tax rate?

 

Example 2: D’Andrea earned $56,000 in 2011.

a) Calculate D’Andrea’s federal income tax, assuming that her only deduction is the standard deduction of $5,800.

b) What was D’Andrea’s effective tax rate?

 

 

 

Example: Gasoline Tax

A gasoline tax is a flat tax when considered in terms of consumption. A tax of, say, $0.30 per gallon is proportional to the amount of gasoline purchased.

Someone buying 10 gallons of gas at $4 a gallon would pay $3 in tax, which is $3/$40 = 7.5%.
Someone buying 30 gallons of gas at $4 a gallon would pay $9 in tax, which is $9/$120 = 7.5%, the same effective rate.

 

However, in terms of income, a gasoline tax is often considered a regressive tax. It is likely that someone earning $30,000 a year and someone earning $60,000 a year will drive about the same amount.

If both pay $60 in gasoline taxes over a year, the person earning $30,000 has paid $60/$30000 = 0.2% of their income, while the person earning $60,000 has paid $60/$60000 = 0.1% of their income in gas taxes.

 

Try It

A sales tax is a fixed percentage tax on a person’s purchases. Is this a flat, progressive, or regressive tax?

 

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