# 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?Answer: The sales tax will be 9.3% of $140. To compute this, we first rewrite 9.3% as a decimal: 0.093 is the decimal representation of 9.3%. Then, we multiply $140 by the percent written as a decimal: $140(0.093) = $13.02.

### Try It

[ohm_question]80109[/ohm_question]**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?Answer: Recall that to obtain a percent from a ratio, divide the part by the whole and multiply by 100. Therefore, we can compute the equivalent percentage from the ratio: 3200/215000 = 0.01488, or about 1.49% effective rate.

- 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.

**T**

**axable 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.

Answer: After subtracting the 2011 standard deduction of $5,800, his taxable income was $10,000. He would pay 10% on the portion of his income up to $8,500 and 15% on the income over $8,500 (but less than $34,500). 8500(0.10) = 850 10% of $8500 1500(0.15) = 225 15% of the remaining $1500 of income Total tax: = $1075

b) What was Stephen's effective tax rate?Answer: The effective tax rate paid is 1075/15,800 = 6.80%

**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.

Answer:
Again, we start by subtracting the standard deduction of $5,800 to get her taxable income of $50,200. Using the tax table above, we see this salary lands in the third tax bracket (or pocket), so at least some portion of her salary will be taxed at 25%--in particular, the amount in excess of the $34,500 that went into the first two brackets (pockets).
We calculate:
$50,200 - $34,500 = **$15,700** goes into the third pocket and gets taxed at 25%
$34,500 - $8,500 = **$26,000** goes into the second pocket and gets taxed at 15%
**$8,500** goes into the first pocket and gets taxed at 10%
Notice that $15,700 + $26,000 + $8,500 = $50,200 -- her taxable income! Now that we have filled the pockets, we are ready to calculate the actual taxes as follows:
8500(0.10) = 850 10% of $8500 in the first pocket
26000(0.15) = 3900 15% of the $26000 in the second pocket
15,700(0.25) = 3925 25% of the $15,700 in the third pocket
Total tax: = $8,675

Answer: The effective tax rate paid is 8675/56000 = 15.49%. Notice that the effective rate has increased with income, showing this is a progressive tax.

### 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? [practice-area rows="4"][/practice-area]Answer: While sales tax is a flat percentage rate when considering the purchase price, when considering sales tax relative to someone's income, it can be considered a regressive tax for the same reasons as the gasoline tax.

### Try It

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