Question

A certain state uses the following progressive

tax rate for calculating individual income tax:
Income
Range ($)
Progressive
Tax Rate
0-3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax owed on a $90,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter

Answer 1

$4918

Explanation:

You want the tax owed on $90,000 using the given tax rate table.

Tax computation

The tax is the sum of the amounts of tax due in each income range.

tax = 0.0575(90,000 -17,000) +0.05(17,000 -5000) +0.03(5000 -3000) +0.02(3000)

= 0.0575(90,000) -(17000(.0575 -.05) +5000(.05 -.03) +3000(.03 -.02))

= 0.0575(90,000) -(127.50 +100 +30)

= 5175 -257.50 = 4917.50

Rounded to the nearest dollar, the tax due is $4,918.

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Additional comment

The tax will be the maximum of ...

• 0.02x
• 0.03x -30 . . . . . . . . . . applicable over 3000
• 0.05x -130 . . . . . . . . . .applicable over 5000
• 0.0575x -257.50 . . . . applicable over 17000

You can compute them all and find the maximum, or you can choose the function applicable to the income amount. The result is the same.

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