Math Problem Statement

Problem 3-25 Tax Rates (LO4)

Use Table 3.6. (Do not round intermediate calculations. Enter the average tax rate as a percent rounded to 1 decimal place.)

a. What would be the marginal tax rate for a married couple with income of $89,700?

b. What would be the average tax rate for a married couple with income of $89,700?

c. What would be the marginal tax rate for an unmarried taxpayer with income of $89,700?

d. What would be the average tax rate for an unmarried taxpayer with income of $89,700?

What would be the marginal and average tax rates for a married couple and a single taxpayer with an income of $89,700?

Solution

Let's solve this step by step using the information provided in the table.

a. Marginal Tax Rate for a Married Couple with Income of $89,700:

From the table, for married taxpayers filing jointly:

  • The income of $89,700 falls in the range $77,401–$165,000, which has a tax rate of 22%.

So, the marginal tax rate for a married couple with an income of $89,700 is 22%.


b. Average Tax Rate for a Married Couple with Income of $89,700:

To calculate the average tax rate, we need to calculate the total tax paid and divide it by the total income.

  1. For the first $19,050, the tax rate is 10%:

    • Tax = $19,050 * 0.10 = $1,905.
  2. For the next portion, from $19,051 to $77,400 (which is $77,400 − $19,050 = $58,350), the tax rate is 12%:

    • Tax = $58,350 * 0.12 = $7,002.
  3. For the remaining portion, from $77,401 to $89,700 (which is $89,700 − $77,400 = $12,300), the tax rate is 22%:

    • Tax = $12,300 * 0.22 = $2,706.

Total tax paid:

  • $1,905 + $7,002 + $2,706 = $11,613.

Average tax rate:

Average tax rate=(Total tax paidTotal income)100=(11,61389,700)100=12.95%\text{Average tax rate} = \left( \frac{\text{Total tax paid}}{\text{Total income}} \right) * 100 = \left( \frac{11,613}{89,700} \right) * 100 = 12.95\% Thus, the average tax rate is 13.0% (rounded to 1 decimal place).


c. Marginal Tax Rate for an Unmarried Taxpayer with Income of $89,700:

For single taxpayers, the income of $89,700 falls in the range $82,501–$157,500, which has a tax rate of 24%.

So, the marginal tax rate for an unmarried taxpayer with income of $89,700 is 24%.


d. Average Tax Rate for an Unmarried Taxpayer with Income of $89,700:

Again, let's calculate the total tax paid for the single taxpayer and divide it by their total income.

  1. For the first $9,525, the tax rate is 10%:

    • Tax = $9,525 * 0.10 = $952.50.
  2. For the next portion, from $9,526 to $38,700 (which is $38,700 − $9,525 = $29,175), the tax rate is 12%:

    • Tax = $29,175 * 0.12 = $3,501.
  3. For the next portion, from $38,701 to $82,500 (which is $82,500 − $38,700 = $43,800), the tax rate is 22%:

    • Tax = $43,800 * 0.22 = $9,636.
  4. For the remaining portion, from $82,501 to $89,700 (which is $89,700 − $82,500 = $7,200), the tax rate is 24%:

    • Tax = $7,200 * 0.24 = $1,728.

Total tax paid:

  • $952.50 + $3,501 + $9,636 + $1,728 = $15,817.50.

Average tax rate:

Average tax rate=(Total tax paidTotal income)100=(15,817.5089,700)100=17.64%\text{Average tax rate} = \left( \frac{\text{Total tax paid}}{\text{Total income}} \right) * 100 = \left( \frac{15,817.50}{89,700} \right) * 100 = 17.64\% Thus, the average tax rate is 17.6% (rounded to 1 decimal place).


Summary of Answers:

  • a. Marginal tax rate (married couple, $89,700): 22%
  • b. Average tax rate (married couple, $89,700): 13.0%
  • c. Marginal tax rate (single taxpayer, $89,700): 24%
  • d. Average tax rate (single taxpayer, $89,700): 17.6%

Do you need more details or have any questions?

Here are some related questions you might want to explore:

  1. How would the tax calculations change if the income was $100,000 for both cases?
  2. What is the difference in taxes paid between single and married taxpayers at the $89,700 income level?
  3. How does the marginal tax rate system affect overall tax fairness?
  4. If the tax rates were adjusted for inflation, how would that impact tax brackets today?
  5. What are the potential benefits of filing jointly versus separately for married couples?

Tip: Always check the latest tax rates and brackets, as they can change annually based on government policies.

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Math Problem Analysis

Mathematical Concepts

Tax Calculation
Marginal Tax Rate
Average Tax Rate
Piecewise Calculation

Formulas

Marginal Tax Rate = Tax rate for the highest income bracket reached
Average Tax Rate = (Total Tax Paid / Total Income) * 100

Theorems

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Suitable Grade Level

College-Level Finance / Economics