Math Problem Statement

Over But Not Over Tax Due $0 $15,000 2.5% of taxable income $15,000 $30,000 $375 plus 6.3% of excess over $15,000 $30,000 $1,320 plus 6.4% of excess over $30,000 Use the Tax table above the answer the following question. Find the tax due on a taxable income of $23,111.

Solution

To find the tax due on a taxable income of $23,111 using the tax table provided, we'll follow these steps:

  1. Identify the correct tax bracket for $23,111:

    • Since $23,111 falls between $15,000 and $30,000, the applicable tax rule is:
      Tax due=$375+6.3% of the excess over $15,000\text{Tax due} = \$375 + 6.3\% \text{ of the excess over } \$15,000
  2. Calculate the excess income over $15,000: Excess=23,11115,000=8,111\text{Excess} = 23,111 - 15,000 = 8,111

  3. Calculate 6.3% of the excess: 6.3% of 8,111=0.063×8,111=511.003\text{6.3\% of } 8,111 = 0.063 \times 8,111 = 511.003

  4. Add this to the base amount of $375: Tax due=375+511.003=886.003\text{Tax due} = 375 + 511.003 = 886.003

  5. Rounding to the nearest cent (if necessary): Tax due=886.00\text{Tax due} = 886.00

Thus, the tax due on a taxable income of $23,111 is $886.00.

Would you like a detailed explanation of any step or have any questions? Here are some related questions you might find useful:

  1. How would the tax due change if the taxable income was $35,000?
  2. What would be the tax due for an income just below the $15,000 threshold, like $14,999?
  3. How do you calculate the tax for an income of exactly $30,000?
  4. Can you demonstrate the tax calculation for a higher income, like $50,000?
  5. What if the tax rates or thresholds change? How would we adapt the calculation?

Tip: Always double-check the tax brackets and rates when calculating taxes, as they may change annually or based on jurisdiction.

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Math Problem Analysis

Mathematical Concepts

Tax Calculation
Piecewise Functions
Percentage Calculation

Formulas

For taxable income ≤ $15,000: Tax = 2.5% of taxable income
For taxable income between $15,000 and $30,000: Tax = $375 + 6.3% of (taxable income - $15,000)
For taxable income > $30,000: Tax = $1,320 + 6.4% of (taxable income - $30,000)

Theorems

Piecewise Function Application

Suitable Grade Level

Grades 9-12