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.

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.

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.

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

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

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.