Selected topics in finite mathematics/Taxes

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Objectives[edit]

  1. Understand how a tiered tax rate structure works.
  2. Understand how capital gains taxes work and how they relate to the tiered rates.
  3. Understand how Social Security and Medicare taxes work.

Note that (1) above is quite general, while (2) and (3) are more specific to the tax structure in the United States

Details[edit]

Income Taxes: Taxes are taxes that come directly from the income you make.Usually an individual's gross income is different from their taxable income. The taxable income is generally the income that is taxable after determining exemptions, deductions, and adjustments.

Income Filing as an Independent Marginal Tax Rate Long-term Capital Gains Rate
All income below $10,000 10% 0%
All income above $10,000 25% 15%

Exemptions: These are characteristics of one's income that are not considered taxable. In 2013, every person has an exemption of $3900 per person.

Deductions: When an individual files as an independent, they can either deduct $6,100 from their income that is not taxable, or deduct itemized deductions as income that is not considered taxable. Itemization must exceed the $6100 figure.

Adjustments:These are also types of expenses that won't be considered taxable.

Tax Credits: a credit that is counted directly toward the income taxes and individual pays. Purchases like environmentally friendly appliances often carry such a perk.

Capital Gains: A capital gain is a profit rom the sale of a capital asset such as stock. Capital gains are added to a person's taxable income directly but are taxed at different rates than the rest of the taxable income.

Payroll Taxes: These taxes are on your earned income, normally on a salary from a job but not unearned income. Social Security is a government-mandated program that came around during the Great Depression that provides retirement benefits. Medicare, a government program that provides healthcare for the elderly, is another example of a payroll tax.

Social Security: a government-mandated program providing retirement benefits.

Medicare: a government mandated program providing healthcare for the elderly.

Gross Income Filing as an Independent Social Security: Employee Social Security: Employer Medicare: Employee Medicare: Employer
All Income Below $100,000 7% 7% 1% 1%
All Income Above $100,000 0% 0% 1% 1%

Examples[edit]

Lucy works full time as a cashier in Starbucks and has a taxable income of 14,000. How much does she pay in income tax?

Income filing as an independent Marginal Tax Rate Long-term Capital Gains rate
All income below $10,000 10% 0%
All income above $10,000 25% 15%


(10,000 × 0.1) + (4,000 × .25)= $2,000 in income tax


Danny works as a teacher and has a gross income of $41,255. He has a wife and two kids(exemptions).

Gross Income:41255

Taxable Income:41255-3900(4)-6100= 19555

Tax:(10000×.01) + (9555×.25)=2488.75 in income tax


[Give an example of income taxes with a deduction?]

[Give an example of income taxes with an adjustment?]

[Give an example of income taxes with a credit?]

[Give an example of income taxes with capital gains?]

[Give an example of payroll taxes?]

Nonexamples[edit]

FAQ[edit]

Homework[edit]

If a family of 3 (one child) has a gross income of $40,000, how much do they pay in taxes?


If a family of 3 (two children) has a gross income of $40,000, how much do they pay in taxes?


If a family of 3 (one child) has a gross income of $40,000 but also donated $10,000 to a charity, how much do they pay in taxes?


If a family of 3 (one child) has a gross income of $40,000 but also saved $10,000 in a tax-deferred fund, how much do they pay in taxes?

Homework Solutions[edit]