### Social Security & medicare

```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

1.
2.
3.
4.
5.
6.
For each paycheck, you can have several
deductions:
Social Security
Medicare
Tax Withholdings
Retirement Plans
Union Dues
Many More
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




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 & 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 & 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

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
= 73,210 • 0.062
= 4,539.02
Medicare
= 73,210 • 0.0145
= 1,061.545
Total Withholdings = 4,539.02 + 1,061.55 = 5,600.57
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?
Social Security
= 97,500
98,430 • 0.062
= 6,045
Medicare
= 98,430 • 0.0145
= 1,427.24
Total Withholdings = 6,045 + 1,427.24 = \$7,472.24
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 & 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

a)
b)
c)
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 month will you reach the maximum taxable
income?
How much will you pay in social security in
February?
Example

a)
b)
c)
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 month will you reach the maximum taxable
income?
How much will you pay in social security in Nov.?
Example

a)
b)
c)
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 month will you reach the maximum taxable
income?
How much will you pay in social security in June?
Social Security & Medicare

Page 319, 2-4
Social Security & Medicare

Maximum you could pay into S. S. each year:
Year
Social Security
Maximum
Taxable Income
1978
1980
1982
1984
1986
1988
1990
6.05%
6.13%
6.7%
6.7%
7.15%
7.51%
7.65%
17,700
25,900
32,400
37,800
42,000
45,000
51,300
Maximum You
Could Pay Into S.S.
\$1,070.85
\$1,587.67
\$2,170.80
\$2,532.60
\$3,003.00
\$3,379.50
\$3,924.45
Social Security & Medicare
3)
a)
b)
c)
d)
In 1990, Jerry’s gross pay was \$78,000.
What was his monthly gross pay? \$6,500
In what month did he his the maximum? August
How much did he pay in S.S. tax in Jan? \$497.25
How much S.S. tax did he pay in Dec? \$0
Social Security & Medicare

a)
b)
c)
d)
e)
In 1978, Dawn earned \$48,000.
What was her monthly gross pay? \$4,000
In what month did she reach the maximum Social
Security income? May
How much S.S. tax did she pay in Feb? \$242
How much S.S. tax did she pay in May? \$102.85
How much S.S. did she pay in Nov.? \$0
SOCIAL SECURITY &
MEDICARE
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 & Medicare

How much would you have to currently earn to pay
as much in Medicare as you do in Social Security?
Social Security & Medicare


Today, we are going to create piecewise functions
detailing Social Security & Medicare
Recall, a piecewise function looks like:
C(x) =
0.15 x when 0 ≤ x < 500
0.20 x when 500 ≤ x < 1500
0.22 x when 1500 ≤ x
Social Security & Medicare

1)
2)
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 & 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 & 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 & 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 &
MEDICARE
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 & 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 & 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 & Medicare

On Friday, we started working on the 6.5
worksheet. Finish this worksheet now.
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 & 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 & Medicare
3. In 1978, the Social Security and Medicare tax rate combined was
6.05% up to \$17,700 earned.
a)
Express the Social Security tax as a piecewise function.
b)
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.
c)
If a person earned \$50,000 in 1978 and \$50,000 in 1988, what
was the difference in taxes paid?
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 & 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%.
a.
b.
c.
d.
e.
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 & 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 & 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 & 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 & Medicare
9. In 2009, Dr. Kirmser’s gross pay was \$381,318.60.
S.S. = 6.2% max @ \$106,800
a.
b.
c.
d.
e.
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 &
MEDICARE
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 & Medicare

1)
2)
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 & Medicare
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 & Medicare
10. If x represents income, express the Social Security function s(x)
for 2005 as a piecewise function.
Social Security = 6.2%
Maximum taxable income of \$90,000
Social Security & Medicare
b. Graph the Social Security function for 2005.
Social Security & Medicare
c. Find the coordinates of the cusp.
Social Security & Medicare
d. If x represents income, what is the Medicare function m(x) for
2005?
Social Security & Medicare
d. Graph the Medicare function for 2005 on the same axes as the
Social Security function in part b.
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 & 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 & Medicare

page 319
Social Security & Medicare


What would it mean if the slope of the graph was
equal to 1?
Is this possible?
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 & 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 & 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 & Medicare
5) In 1991, Social Security and Medicare taxes were
itemized separately on paycheck stubs and tax forms.
a)
b)
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 & 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 & 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 & 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 & 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 & Medicare
10) Keesha earned x dollars per month in 2006,
where x < \$5,600.
a)
b)
c)
Did she earn more or less than the maximum
taxable income?
Express her Social Security tax algebraically.
Express her Medicare algebraically.
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 & 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 &
MEDICARE
Social Security & Medicare
What we have covered in this section:
a)
FICA Taxes in general
a)
b)
When you earn less than the maximum
When you earn more than the maximum
Piecewise Functions
b)
a)
b)
Creating a function
Using a function to answer a question
Social Security & Medicare
What we have covered in this section:
Earning more than the max
c)
c)
d)
e)
f)
g)
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 & Medicare
What we have covered in this section:
Graphing Social Security functions
d)
d)
e)
f)
g)
Labeling the axis
Finding two points
Calculating the cusp
What happens after the cusp
Social Security & Medicare
What we have covered in this section:
e)
f)
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 & Medicare
What we have covered in this section:
g)
h)
Social Security refund
Algebraic expressions
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