Help with calculations

Question

Now consider another hypothetical tax code. Assume the tax rate on the first $15,000 of taxable income is 10% and the tax rate on any additional income is 18%. The standard deduction ($6,350) and personal exemption ($4,050) still apply.

In other words:

• For taxable income from $0 to $15,000, you pay 10% of your taxable income in taxes, plus

• For taxable income above $15,000, you pay 18% of your taxable income.

1. If your total income before exemptions were $10,000 how much would you pay in taxes?

2. If your total income were $20,000 how much would you pay in taxes?

3. If your total income were $50,000 how much would you pay in taxes?

4. Write a function to model the total tax paid, T(x), with a total income of x dollars.

NOTE: For a Total Income of $80,000, an individual would pay $11,328 in taxes.

Answer 1

Exemptions are 6350 + 4050 = 10400

1. So in (1) as 10000 < 10400 you pay 0 tax
2. 20000 income. Taxable is 20000 - 10400 = 9600. This is 0-15000 so you pay 10% tax so 0.10 x 9600 = $ 960 tax
3. 50000. 50000 - 10400 = 39600. 39600 = 15000 + 24600 so tax = 0.10 x 15000 + 0.18 x 24600 = $ 5920.

T(x).

0 < x < 10400, T(x) = 0

10400 < x < 10400 + 15000 T(x) = 0.10 (x - 10400).

x > 10400 + 15000 T(x) = 0.10 x 15000 + 0.18 (x - 10400 - 15000).

You can check that T (80000) = 11328 as required.