Math Problem Statement

Consider three unmarried investors who need to partially liquidate investments to raise cash. In this​ case, all investments have been held for 3 or more years. Investor A waited for a

​$1 comma 0001,000

qualified dividend distribution from her mutual​ fund, and Investor B received

​$1 comma 0001,000

in interest income from a certificate of deposit.​ However, because Investor C could not wait for a​ distribution, he decided to sell appreciated stock shares with a​ long-term capital gain of

​$1 comma 0001,000.

Assuming no​ commissions, no sales​ charges, no state income​ tax, and other taxable income of​ $100,000, which investment will provide the greatest​ after-tax amount?

Question content area bottom

Part 1

Assuming no​ commissions, no sales​ charges, no state income​ tax, and other taxable income of​ $100,000, the investments that will have the greatest​ after-tax amount belong​ to:  ​(Select best answer​ below.)

A.

Investors A and B.

B.

Investors B and C.

C.

Investors A and C.

D.

Investors​ A, B, and C.

Solution

To determine which investment provides the greatest after-tax amount, we need to analyze the tax treatment of the income received by each investor:

  1. Investor A (Qualified Dividend Income of $1,000):

    • Qualified dividends are taxed at the long-term capital gains rate. Since the other taxable income is $100,000, the investor likely falls in the 15% capital gains tax bracket.
    • So, tax on the dividend = 1,000×0.15=1501,000 \times 0.15 = 150.
    • After-tax amount = 1,000150=8501,000 - 150 = 850.
  2. Investor B (Interest Income of $1,000):

    • Interest income is taxed as ordinary income. With other taxable income of $100,000, Investor B is likely in the 24% tax bracket for ordinary income.
    • Tax on interest = 1,000×0.24=2401,000 \times 0.24 = 240.
    • After-tax amount = 1,000240=7601,000 - 240 = 760.
  3. Investor C (Capital Gains of $1,000):

    • Long-term capital gains are taxed at the same rate as qualified dividends, which in this case would also be 15%.
    • Tax on capital gains = 1,000×0.15=1501,000 \times 0.15 = 150.
    • After-tax amount = 1,000150=8501,000 - 150 = 850.

Conclusion:

  • Investors A and C receive the highest after-tax amount of $850 each, while Investor B receives $760.
  • Thus, Investors A and C will have the greatest after-tax amount.

Correct answer: C. Investors A and C.


Do you want further details or have any questions?

Here are 5 related questions for further exploration:

  1. How does the capital gains tax rate vary by income level?
  2. What is the tax difference between qualified dividends and non-qualified dividends?
  3. How are ordinary dividends taxed compared to qualified dividends?
  4. What are the different tax brackets for ordinary income?
  5. How can holding periods affect long-term versus short-term capital gains?

Tip: Holding investments for longer than a year can qualify gains for lower long-term capital gains tax rates, making it a more tax-efficient strategy for many investors.

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Math Problem Analysis

Mathematical Concepts

Taxation
Income Tax Calculation
Investment Returns

Formulas

Tax on qualified dividends = Dividend amount × Capital gains tax rate
Tax on interest income = Interest amount × Ordinary income tax rate
Tax on long-term capital gains = Gain amount × Capital gains tax rate

Theorems

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Suitable Grade Level

Grades 11-12, College Level