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Social Security & medicare. Gross Pay vs Net Pay. Gross Pay → What your total pay is before deductions Net Pay → The amount your paycheck is for → Also known as your “take home pay” Net Pay = Gross Pay - Deductions. Deductions. For each paycheck, you can have several deductions:

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Gross pay vs net pay
Gross Pay vs Net Pay

  • Gross Pay

    → What your total pay is before deductions

  • Net Pay

    → The amount your paycheck is for

    → Also known as your “take home pay”

  • Net Pay = Gross Pay - Deductions


Deductions
Deductions

  • For each paycheck, you can have several deductions:

  • Social Security

  • Medicare

  • Tax Withholdings

  • Retirement Plans

  • Union Dues

  • Many More


Social security
Social Security

  • Retirement benefits for people who are at least 62

  • Disability benefits for workers who are disabled or unable to work

  • Survivors’ benefits, paid to spouses and dependent children when a social security recipient dies

  • Originated in 1935 at 1%

  • Current rate is 6.2%


Medicare
Medicare

  • Medical insurance for some disabled people and people over 65

  • Originated in 1966 at 0.35%

  • Current rate is 1.45%

  • Both Social Security and Medicare were established in the Federal Insurance Contribution Act

    • FICA


Social security medicare1
Social Security & Medicare

  • Social Security

    • Currently pay 6.2% of taxable income to S.S.

    • Maximum taxable income of $106,800

    • Increasing to $110,100 next year

    • What is the most you could pay in Social Security Tax in one year?


Social security medicare2
Social Security & Medicare

  • Medicare

    • Currently pay 1.45% of taxable income to Medicare

    • No maximum

    • What is the most you could pay in Medicare in one year?


Example
Example

  • Ramiro got his first job in 2006. In that year, Social Security tax was 6.2% of income up to $94,200. Medicare tax was 1.45%. If Ramiro earned $73,210 in 2006, how much did he pay in Social Security and Medicare?

Social Security

Medicare

= 73,210 • 0.062

= 73,210 • 0.0145

= 4,539.02

= 1,061.545

Total Withholdings

= 4,539.02 + 1,061.55

= 5,600.57


Example1
Example

  • What are the social security and Medicare withholdings for an executive whose annual gross earnings are $98,430 in 2007, when the maximum taxable income was $97,500?

Medicare

Social Security

= 98,430 • 0.0145

= 98,430

= 97,500

• 0.062

= 1,427.24

= 6,045

= 6,045 + 1,427.24

Total Withholdings

= $7,472.24


Social security medicare3
Social Security & Medicare

  • Social Security

    • Currently pay 6.2% of taxable income to S.S.

    • Maximum taxable income of $106,800

    • Increasing to $110,100 next year

    • What is the most you could pay in Social Security Tax in one year?


Social security medicare4
Social Security & Medicare

  • Medicare

    • Currently pay 1.45% of taxable income to Medicare

    • No maximum

    • What is the most you could pay in Medicare in one year?


Example2
Example

  • You currently earn an annual salary of $247,500. You must pay a social security tax rate of 6.2% of taxable income up to $106,800.

  • What is your monthly salary?

  • What month will you reach the maximum taxable income?

  • How much will you pay in social security in February?


Example3
Example

  • You currently earn an annual salary of $247,500. You must pay a social security tax rate of 6.2% of taxable income up to $106,800.

  • What is your monthly salary?

  • What month will you reach the maximum taxable income?

  • How much will you pay in social security in Nov.?


Example4
Example

  • You currently earn an annual salary of $247,500. You must pay a social security tax rate of 6.2% of taxable income up to $106,800.

  • What is your monthly salary?

  • What month will you reach the maximum taxable income?

  • How much will you pay in social security in June?



Social security medicare6
Social Security & Medicare

  • Maximum you could pay into S. S. each year:

$1,070.85

$1,587.67

$2,170.80

$2,532.60

$3,003.00

$3,379.50

$3,924.45


Social security medicare7
Social Security & Medicare

  • In 1990, Jerry’s gross pay was $78,000.

  • What was his monthly gross pay?

  • In what month did he his the maximum?

  • How much did he pay in S.S. tax in Jan?

  • How much S.S. tax did he pay in Dec?

$6,500

August

$497.25

$0


Social security medicare8
Social Security & Medicare

  • In 1978, Dawn earned $48,000.

  • What was her monthly gross pay?

  • In what month did she reach the maximum Social Security income?

  • How much S.S. tax did she pay in Feb?

  • How much S.S. tax did she pay in May?

  • How much S.S. did she pay in Nov.?

$4,000

May

$242

$102.85

$0



Social security medicare10
Social Security & Medicare

  • Yesterday, we covered Social Security & Medicare

  • Social Security

    • Currently at 6.2%

    • Maximum taxable income of $106,800

    • Pay a maximum of $6,621.60

  • Medicare

    • Currently at 1.45%

    • No maximum taxable income


Social security medicare11
Social Security & Medicare

  • How much would you have to currently earn to pay as much in Medicare as you do in Social Security?


Social security medicare12
Social Security & Medicare

  • Today, we are going to create piecewise functions detailing Social Security & Medicare

  • Recall, a piecewise function looks like:

0.15 x when 0 ≤ x < 500

0.20 x when 500 ≤ x < 1500

C(x) =

0.22 x when 1500 ≤ x


Social security medicare13
Social Security & Medicare

  • Creating a piecewise function:

  • Create an algebraic expression for S.S. (and Medicare if applicable) for income less than the maximum amount

  • Determine total amount possible to be paid into S.S. when maximum amount is hit


Social security medicare14
Social Security & Medicare

  • Express the 2006 as a piecewise function:

    2006: S.S. rate of 6.2% w/ max at $94,200

    Medicare rate of 1.45% w/ no max


Social security medicare15
Social Security & Medicare

  • Express the 1999 as a piecewise function:

    1999: S.S. rate of 6.2% w/ max at $72,600

    Med. rate of 1.45% w/ max no max


Social security medicare16
Social Security & Medicare

  • Express the 2009 as a piecewise function:

    2009: S.S. rate of 6.2% w/ max at $106,800

    Med. rate of 1.45% w/ no max



Social security medicare18
Social Security & Medicare

  • Stephanie was just hired at a new job making $135,000 a year. How much will she pay in FICA taxes in her first year?


Social security medicare19
Social Security & Medicare

  • Stephanie was just hired at a new job making $135,000 a year. How much will she pay in FICA taxes in her first year?

  • In what month will she surpass the taxable income amount of $106,800 and how much will she pay in that month?


Social security medicare20
Social Security & Medicare

  • In 2007, the Social Security tax rate was 6.2% with a maximum taxable income of $97,500 and the Medicare tax rate was 1.45%. Express this as a piecewise function.


Social security medicare21
Social Security & Medicare

  • On Friday, we started working on the 6.5 worksheet. Finish this worksheet now.


Social security medicare22
Social Security & Medicare

1. Dr. Gumman got his first job in 1990. In that year, the government took out 7.45% of each income for Social Security and Medicare, until a person made $51,300. If Dr. Gumman earned $31,340 in 1990, how much did he pay to Social Security and Medicare?


Social security medicare23
Social Security & Medicare

2. Lauren earned a total of “d” dollars last year. The government took out 6.2% for Social Security and 1.45% for Medicare. Write an algebraic expression that represents what she paid to Social Security and Medicare combined.


Social security medicare24
Social Security & Medicare

3. In 1978, the Social Security and Medicare tax rate combined was 6.05% up to $17,700 earned.

  • Express the Social Security tax as a piecewise function.

  • Ten years later, the percent had increased to 7.51% and the maximum taxable income had increased to $45,000. Express this as a piecewise function.

  • If a person earned $50,000 in 1978 and $50,000 in 1988, what was the difference in taxes paid?


Social security medicare25
Social Security & Medicare

4. In 2010, the government took out 6.2% of earnings for Social Security to a maximum taxable income of $106,800. For Medicare, 1.45% of earnings was paid. How much money would someone have to have earned in 2010 so that their payments to Medicare were equal to their payments into Social Security?


Social security medicare26
Social Security & Medicare

5. In 1998, Lisa earned $149,461.20. The Social Security maximum taxable income was $68,400, and the Social Security percent was 6.2%.

  • What was her monthly gross pay?

  • In what month did she hit the maximum?

  • How much S.S. tax did she pay in May?

  • How much S.S. tax did she pay in July?

  • How much S.S. tax did she pay in June?


Social security medicare27
Social Security & Medicare

6. In 2010, for the first time since 2004 the maximum taxable income was not raised. Find the maximum a person could pay into Social Security in 2010.

Rate of 6.2% w/ max income of $106,800.


Social security medicare28
Social Security & Medicare

7. Let t(x) represent the total combined Social Security and Medicare taxes for the year 2007. If x represents the income, express this total as a piecewise function.

2007: S.S. = 6.2% max @ $97,500


Social security medicare29
Social Security & Medicare

8. Mr. Jackson had 2 jobs in 2005. The first job, in which he earned $74,007, was from January to August, and the second job, in which he earned $35,311, was from August to the end of the year. At the first job, he earned $74,007. As a result, he paid too much Social Security tax. How much should be refunded?


Social security medicare30
Social Security & Medicare

9. In 2009, Dr. Kirmser’s gross pay was $381,318.60.

S.S. = 6.2% max @ $106,800

  • What was her monthly gross pay?

  • In what month did she hit the maximum?

  • How much S.S. tax did she pay in Feb.?

  • How much S.S. tax did she pay in Sept.?

  • How much S.S. tax did she pay in April?



Social security medicare32
Social Security & Medicare

  • So far, we have:

    • Calculated total FICA taxes

    • Determined when you over surpass the maximum taxable income

    • Created piecewise functions for FICA taxes

  • Today:

    • Graph these FICA taxes


Social security medicare33
Social Security & Medicare

  • In 2006, the social security tax rate was 6.2% of income up to $94,200. Graph this function:

  • What units would make sense to label the x-axis (income)?

  • What units would make sense to label the y-axis (Social Security tax)?



Social security medicare35
Social Security & Medicare

  • In 1991, the Social Security tax rate was 6.2% on income up to $53,400. Create a piecewise function for this and graph the function.


Social security medicare36
Social Security & Medicare

10. If x represents income, express the Social Security function s(x) for 2005 as a piecewise function.

Maximum taxable income of $90,000

Social Security = 6.2%


Social security medicare37
Social Security & Medicare

b. Graph the Social Security function for 2005.


Social security medicare38
Social Security & Medicare

c. Find the coordinates of the cusp.


Social security medicare39
Social Security & Medicare

d. If x represents income, what is the Medicare function m(x) for 2005?


Social security medicare40
Social Security & Medicare

d. Graph the Medicare function for 2005 on the same axes as the Social Security function in part b.


Social security medicare41
Social Security & Medicare

e. Elena worked three jobs in 2005. The total of her three incomes was less than $90,000. At Hamburger Coach, she made h dollars. At the Binghamton Book Exchange, she made b dollars. At Ruby’s Restaurant, she made r dollars. Express the combined total of her social security and Medicare taxes as an algebraic expression.


Social security medicare42
Social Security & Medicare

f. In 2005, how much money would someone have to have earned so that their payments into Medicare were equal to their payments into Social Security? Round to the nearest dollar.


Social security medicare43
Social Security & Medicare

  • In your notebook, please complete numbers 5-10 on page 319


Social security medicare44
Social Security & Medicare

  • What would it mean if the slope of the graph was equal to 1?

  • Is this possible?


Social security medicare45
Social Security & Medicare

  • Some politicians have suggested removing the maximum taxable income and apply Social Security to all income. Why would this be unfair to very wealthy people?

  • Should this idea be implemented?


Social security medicare46
Social Security & Medicare

  • Some politicians have suggested removing the maximum taxable income and apply Social Security to all income. Why would this be unfair to very wealthy people?

  • Should this idea be implemented?


Social security medicare47
Social Security & Medicare

  • A politician is listening to a new Social Security tax plan. The graph is shown below. The two parts of the graph are disconnected where x = 100,000. Why would this be an unfair Social Security tax function?

$8,000

$6,000


Social security medicare48
Social Security & Medicare

5) In 1991, Social Security and Medicare taxes were itemized separately on paycheck stubs and tax forms.

  • Find the maximum a person could contribute to Social Security and Medicare:

  • If f(x) represents the Social Security tax, express this as a piecewise function.


Social security medicare49
Social Security & Medicare

6) Express the 1993 Social Security tax function as a piecewise function t(x), where x is the annual income. Graph the function. What are the coordinates of the cusp?


Social security medicare50
Social Security & Medicare

7) Graph the Social Security tax function for 1992. What are the coordinates of the cusp? On the same axis, graph he Medicare function.


Social security medicare51
Social Security & Medicare

8) In 2007, Jessica earned p dollars, where

p >100,000. Express the amount her employer contributed to her Social Security tax in February algebraically.


Social security medicare52
Social Security & Medicare

9) In 1995, Eve earned d dollars, where d < 50,000. Express the amount she paid to Social Security and Medicare as a function of d.


Social security medicare53
Social Security & Medicare

10) Keesha earned x dollars per month in 2006, where x < $5,600.

  • Did she earn more or less than the maximum taxable income?

  • Express her Social Security tax algebraically.

  • Express her Medicare algebraically.


Social security medicare54
Social Security & Medicare

15) In a year when the maximum income for Social Security was $106,800, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222. Both of his employers took out Social Security tax. As a result, Bard had paid excess Social Security tax, and the government must return some of it to him. How much does the government owe him?


Social security medicare55
Social Security & Medicare

16) An All-Star baseball player earning $25,000,000 per year plays 162 games per year. If you divide the salary by the number of games, does that baseball player reach this year’s maximum taxable income in the first game of the year?



Social security medicare57
Social Security & Medicare

What we have covered in this section:

  • FICA Taxes in general

    • When you earn less than the maximum

    • When you earn more than the maximum

  • Piecewise Functions

    • Creating a function

    • Using a function to answer a question


Social security medicare58
Social Security & Medicare

What we have covered in this section:

  • Earning more than the max

    • Finding monthly pay

    • Finding the month you will surpass the maximum

    • Calculating S.S. prior to that month

    • Calculating S.S. after that month

    • Calculating S.S. for that month


Social security medicare59
Social Security & Medicare

What we have covered in this section:

  • Graphing Social Security functions

    • Labeling the axis

    • Finding two points

    • Calculating the cusp

    • What happens after the cusp


Social security medicare60
Social Security & Medicare

What we have covered in this section:

  • How much would you have to earn so that you pay the same amount into Medicare that you pay into Social Security

  • Questions that we reviewed together about graphs


Social security medicare61
Social Security & Medicare

What we have covered in this section:

  • Social Security refund

  • Algebraic expressions


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