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

If your total income before exemptions were $10,000, you would pay $0 taxes.

If your total income before exemptions were $20,000, you would pay $960 taxes.

If your total income before exemptions were $50,000, you would pay $5928 taxes.

A function that models total tax paid is T(x) = (0.10 x $15,000) + 0.18(x - 10,400 - 15,000).

What are the total tax paid?

No tax would be paid if income is $10,000. This is because $10,000 is less than the total deduction of $10,400($6350 + $4050).

Tax paid if total income is $20,000 = 0.10($20,000 - $10,400) = $960. The 18% tax would not be paid because income after the deductions is less than $15,000.

Tax paid if total income is $50,000 = 0.10 x $15,000 + 0.18($50,000  - $10,400 - $15,000) = $1500 + $4,428 = $5928

T(x) = (0.10 x $15,000) + 0.18(x - 10,400 - 15,000).

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