Math Problem Statement

2024 Tax Rate Schedules

Individuals Schedule X-Single If taxable income is over: But not over: The tax is: $ 0 $ 11,600 10% of taxable income $ 11,600 $ 47,150 $1,160 plus 12% of the excess over $11,600 $ 47,150 $ 100,525 $5,426 plus 22% of the excess over $47,150 $ 100,525 $ 191,950 $17,168.50 plus 24% of the excess over $100,525 $ 191,950 $ 243,725 $39,110.50 plus 32% of the excess over $191,950 $ 243,725 $ 609,350 $55,678.50 plus 35% of the excess over $243,725 $ 609,350 — $183,647.25 plus 37% of the excess over $609,350

Schedule Y-1-Married Filing Jointly or Qualifying surviving spouse If taxable income is over: But not over: The tax is: $ 0 $ 23,200 10% of taxable income $ 23,200 $ 94,300 $2,320 plus 12% of the excess over $23,200 $ 94,300 $ 201,050 $10,852 plus 22% of the excess over $94,300 $ 201,050 $ 383,900 $34,337 plus 24% of the excess over $201,050 $ 383,900 $ 487,450 $78,221 plus 32% of the excess over $383,900 $ 487,450 $ 731,200 $111,357 plus 35% of the excess over $487,450 $ 731,200 — $196,669.50 plus 37% of the excess over $731,200

Schedule Z-Head of Household If taxable income is over: But not over: The tax is: $ 0 $ 16,550 10% of taxable income $ 16,550 $ 63,100 $1,655 plus 12% of the excess over $16,550 $ 63,100 $ 100,500 $7,241 plus 22% of the excess over $63,100 $ 100,500 $ 191,950 $15,469 plus 24% of the excess over $100,500 $ 191,950 $ 243,700 $37,417 plus 32% of the excess over $191,950 $ 243,700 $ 609,350 $53,977 plus 35% of the excess over $243,700 $ 609,350 — $181,954.50 plus 37% of the excess over $609,350

Schedule Y-2-Married Filing Separately If taxable income is over: But not over: The tax is: $ 0 $ 11,600 10% of taxable income $ 11,600 $ 47,150 $1,160 plus 12% of the excess over $11,600 $ 47,150 $ 100,525 $5,426 plus 22% of the excess over $47,150 $ 100,525 $ 191,950 $17,168.50 plus 24% of the excess over $100,525 $ 191,950 $ 243,725 $39,110.50 plus 32% of the excess over $191,950 $ 243,725 $ 365,600 $55,678.50 plus 35% of the excess over $243,725 $ 365,600 — $98,334.75 plus 37% of the excess over $365,600 Campbell, a single taxpayer, earns $404,000 in taxable income and $2,200 in interest from an investment in State of New York bonds. (Use the U.S. tax rate schedule.)

Required: How much federal tax will she owe? What is her average tax rate? What is her effective tax rate? What is her current marginal tax rate?

Solution

1. Federal Tax Calculation for Campbell (Single Taxpayer)

Campbell earns $404,000 in taxable income, and $2,200 from New York bonds, which are not subject to federal tax since municipal bond interest is typically tax-exempt.

Using Schedule X (Single) for the 2024 tax rates:

  • Taxable Income: $404,000
  • Federal Tax is calculated by applying the tax rates for each portion of the income bracket.

Breakdown by brackets:

  1. First $11,600 at 10%: 11,600×0.10=1,16011,600 \times 0.10 = 1,160

  2. From $11,600 to $47,150 ($47,150 - $11,600 = $35,550) at 12%: 35,550×0.12=4,26635,550 \times 0.12 = 4,266

  3. From $47,150 to $100,525 ($100,525 - $47,150 = $53,375) at 22%: 53,375×0.22=11,742.5053,375 \times 0.22 = 11,742.50

  4. From $100,525 to $191,950 ($191,950 - $100,525 = $91,425) at 24%: 91,425×0.24=21,94291,425 \times 0.24 = 21,942

  5. From $191,950 to $243,725 ($243,725 - $191,950 = $51,775) at 32%: 51,775×0.32=16,56851,775 \times 0.32 = 16,568

  6. From $243,725 to $404,000 ($404,000 - $243,725 = $160,275) at 35%: 160,275×0.35=56,096.25160,275 \times 0.35 = 56,096.25

Total Federal Tax Owed:

1,160+4,266+11,742.50+21,942+16,568+56,096.25=111,774.751,160 + 4,266 + 11,742.50 + 21,942 + 16,568 + 56,096.25 = 111,774.75 So, Campbell owes $111,774.75 in federal taxes.


2. Average Tax Rate

The average tax rate is calculated by dividing the total tax owed by the taxable income: Average Tax Rate=Total TaxTaxable Income=111,774.75404,0000.2767 or 27.67%\text{Average Tax Rate} = \frac{\text{Total Tax}}{\text{Taxable Income}} = \frac{111,774.75}{404,000} \approx 0.2767 \text{ or } 27.67\%


3. Effective Tax Rate

The effective tax rate is the total tax divided by the total economic income, which includes taxable income plus tax-exempt income from the bonds: Effective Tax Rate=Total TaxTaxable Income + Tax-exempt income=111,774.75404,000+2,2000.2758 or 27.58%\text{Effective Tax Rate} = \frac{\text{Total Tax}}{\text{Taxable Income + Tax-exempt income}} = \frac{111,774.75}{404,000 + 2,200} \approx 0.2758 \text{ or } 27.58\%


4. Marginal Tax Rate

Campbell's marginal tax rate is the tax rate applied to her last dollar of income. Since her taxable income falls within the $243,725 - $609,350 range, the marginal rate is 35%.


Summary:

  1. Federal Tax Owed: $111,774.75
  2. Average Tax Rate: 27.67%
  3. Effective Tax Rate: 27.58%
  4. Marginal Tax Rate: 35%

Would you like further clarifications or more details on any part of the calculations?

Here are five follow-up questions for deeper understanding:

  1. How would Campbell's tax change if she earned an additional $50,000?
  2. What is the significance of the average tax rate compared to the marginal tax rate?
  3. How do municipal bond investments affect taxable income?
  4. How does the progressive tax system impact high-income earners?
  5. How do deductions and credits influence Campbell's final tax liability?

Tip: Always double-check the difference between average and marginal tax rates—average applies to your total income, while marginal is the rate on your next dollar earned.

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Math Problem Analysis

Mathematical Concepts

Progressive Tax System
Income Brackets
Tax Rates
Average Tax Rate
Effective Tax Rate
Marginal Tax Rate

Formulas

Federal Tax Owed = Sum of taxes from each income bracket
Average Tax Rate = (Total Tax Owed / Taxable Income)
Effective Tax Rate = (Total Tax Owed / (Taxable Income + Tax-exempt Income))
Marginal Tax Rate = Tax rate applied to the last dollar of income

Theorems

Progressive Taxation

Suitable Grade Level

College or Professional