Question

A certain state uses the following progressive tax rate for calculating individual income tax: Progressive Income Range ($) Tax Rate 0 - 10,000 10,001 - 50,000 50,001 - 100,000 3% 5% 5.5% Calculate the state income tax owed on a $90,000 per year salary. tax = $[ ? ] Round your answer to the nearest whole dollar amount.

Answer 1

$4500

Explanation:

You want the tax payable on $90,000 if 3% is charged on the first $10,000, 5% is charged on amounts between $10,000 and $50,000, and 5.5% is charged for amounts over $50,000.

Tax

The tax is computed as ...

tax = $10,000·0.03 +(50,000 -10,000)·0.05 +(90,000 -50,000)·0.055

= 0.055·90,000 -(0.055 -0.05)(50,000) -(0.05 -0.03)(10,000)

= $4950 -250 -200

= $4500

The state income tax owed on a $90,000 salary is $4500.

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Additional comment

We find it convenient to rewrite the computation to the form ...

tax = rate·(taxable amount) - (bracket adjustment)

For this tax table, we can write it as ...

tax = 0.03(amount) . . . . amount < 10,000

tax = 0.05(amount) -200 . . . . 10,000 ≤ amount < 50,000

tax = 0.055(amount) -450 . . . . 50,000 ≤ amount < 100,000

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