Math Problem Statement

Jana has the opportunity to buy the boat of her dreams but needs to determine the best way to fund the purchase. The cost of the boat is

​$15 comma 00015,000​,

and​ she's considering taking on a second job at which she can earn this amount or selling some investments to generate the cash.​ However, she realizes that she will also have to pay taxes on any amount she receives. If Jana is in the

3535

percent marginal tax bracket and earns

​$15 comma 00015,000

from a second​ job, by how much will her​ end-of-year tax liability​ increase? What if she elects to sell some investments that​ she's held for several years at a gain of

​$15 comma 00015,000​?

How would your answer change if she had held the investments for just 6​ months?

Question content area bottom

Part 1

If Jana is in the

3535​%

marginal tax bracket and earns

​$15 comma 00015,000

from a second​ job, her​ end-of-year tax liability will increase by

​$enter your response here.

​(Round to the nearest​ dollar.)

Part 2

If Jana elects to sell some investments that​ she's held for several years at a gain of

​$15 comma 00015,000​,

her​ end-of-year tax liability will increase by

​$enter your response here.

​(Round to the nearest​ dollar.)

Part 3

If Jana elects to sell some investments that​ she's held for jsuat 6 months at a gain of

​$15 comma 00015,000​,

her​ end-of-year tax liability will increase by

​$enter your response here.

​(Round to the nearest​ dollar.)

Solution

To solve this problem, we will calculate the tax implications for each scenario described:


Part 1: Tax Liability from a Second Job

Jana earns $15,000 from a second job and is in the 35% marginal tax bracket. The tax liability will be calculated as:

Tax Liability=Income×Marginal Tax Rate\text{Tax Liability} = \text{Income} \times \text{Marginal Tax Rate}

Tax Liability=15,000×0.35=5,250\text{Tax Liability} = 15,000 \times 0.35 = 5,250

Answer: $5,250


Part 2: Tax Liability from Selling Investments Held for Several Years

Investments held for more than one year qualify for long-term capital gains tax rates. Assuming Jana's tax rate is 20% for long-term capital gains (standard rate for high-income individuals), the calculation is:

Tax Liability=Gain×Long-Term Capital Gains Tax Rate\text{Tax Liability} = \text{Gain} \times \text{Long-Term Capital Gains Tax Rate}

Tax Liability=15,000×0.20=3,000\text{Tax Liability} = 15,000 \times 0.20 = 3,000

Answer: $3,000


Part 3: Tax Liability from Selling Investments Held for Just 6 Months

Investments held for less than one year are taxed as ordinary income at the marginal tax rate (35% in this case). The calculation mirrors the first part:

Tax Liability=Gain×Marginal Tax Rate\text{Tax Liability} = \text{Gain} \times \text{Marginal Tax Rate}

Tax Liability=15,000×0.35=5,250\text{Tax Liability} = 15,000 \times 0.35 = 5,250

Answer: $5,250


Summary of Results

  1. From the second job: $5,250
  2. From selling long-term investments: $3,000
  3. From selling short-term investments: $5,250

Questions to Consider:

  1. How does the marginal tax bracket impact Jana's decision between a second job and selling investments?
  2. Would Jana save money on taxes by timing the sale of investments differently?
  3. How do long-term capital gains tax rates compare to ordinary income tax rates for someone in a 35% bracket?
  4. What strategies can Jana use to minimize her tax liability?
  5. What are the potential risks of selling investments versus working extra hours?

Tip: Always consider the tax implications of different income sources to make an informed financial decision.

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Math Problem Analysis

Mathematical Concepts

Taxation
Income Tax Calculation
Capital Gains Tax

Formulas

Tax Liability = Income × Marginal Tax Rate
Tax Liability = Gain × Capital Gains Tax Rate

Theorems

Basic Taxation Rules

Suitable Grade Level

College or Advanced High School