Question

8. Suppose that you make $180,000 per year in taxable income and the tax brackets are as

follows: 10% from $0 to $50,000, 20% from $50,001 to $100,000, 30% from $100,001 to
$200,000, and 35% for all income higher than $200,000. What's your federal income tax for
the year?

Answer 1

$39,000

Explanation:

The tax t(x) on income x will be computed as ...

t(x) = 0.30(x -100,000) +0.20(100,000 -50,000) +0.10(50,000)

= 0.30x -100,000(0.30 -0.20) -50,000(0.20 -0.10)

= 0.30x -10,000 =5,000

= 0.30x -15,000

Then the tax on 180,000 is ...

t(180,000) = 0.30(180,000) -15,000 = 54,000 -15,000

t(180,000) = 39,000

The federal income tax for the year is $39,000.