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 500 qualified dividend distribution from her mutual​ fund, and Investor B received ​$1 comma 500 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 500. 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 investor will receive the greatest after-tax amount, we need to examine the tax treatment of the income sources in question. The relevant tax rates are based on 2023 U.S. federal tax law for individuals with a taxable income of $100,000:

  1. Investor A: Received a $1,500 qualified dividend. Qualified dividends are taxed at the capital gains rate. For an income level of $100,000, the long-term capital gains rate is typically 15%.

  2. Investor B: Received $1,500 in interest income from a certificate of deposit. Interest income is taxed as ordinary income, which at a taxable income of $100,000 falls in the 24% tax bracket.

  3. Investor C: Realized a long-term capital gain of $1,500 from selling stock. Long-term capital gains are taxed at the same rate as qualified dividends—15%.

After-Tax Calculation:

  • Investor A (Qualified Dividend):
    Tax on $1,500 at 15% = $1,500 × 0.15 = $225.
    After-tax amount = $1,500 - $225 = $1,275.

  • Investor B (Interest Income):
    Tax on $1,500 at 24% = $1,500 × 0.24 = $360.
    After-tax amount = $1,500 - $360 = $1,140.

  • Investor C (Capital Gain):
    Tax on $1,500 at 15% = $1,500 × 0.15 = $225.
    After-tax amount = $1,500 - $225 = $1,275.

Conclusion:

Investors A and C, who face the 15% capital gains tax rate, will receive a greater after-tax amount ($1,275) compared to Investor B, who faces the higher ordinary income tax rate (24%) and will receive only $1,140.

The correct answer is C. Investors A and C.

Would you like further clarification or details on this? Here are five related questions for deeper exploration:

  1. How would the outcome change if their taxable income was $40,000 instead of $100,000?
  2. What happens to the tax treatment if the capital gain is short-term instead of long-term?
  3. How would state income tax impact the final after-tax amounts?
  4. Why are dividends and capital gains taxed at lower rates than interest income?
  5. How do tax brackets change for married investors filing jointly versus individually?

Tip: Always consider both the type of income and the taxpayer’s marginal tax bracket to determine the true after-tax amount.

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Math Problem Analysis

Mathematical Concepts

Taxation
Capital Gains
Dividends
Interest Income

Formulas

Tax = Income × Tax Rate
After-tax amount = Income - Tax

Theorems

Capital Gains Tax Rate
Ordinary Income Tax Rate

Suitable Grade Level

University Level (Finance, Taxation, Economics)

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