Understanding Social Security and Medicare in Advanced Financial Algebra
Social Security and Medicare are essential components of financial planning, providing income for retirees and healthcare coverage for seniors. Learn how these programs work, calculate payroll withholdings, and explore piecewise functions related to Social Security taxes. Dive into real-world examples and assignments to deepen your understanding of these crucial aspects of financial algebra.
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Section 5-5 Social Security and Medicare Advanced Financial Algebra
What are Social Security and Medicare? Social Security provides income for people after they retire also provides income for disabled people costs are split evenly between you and your employer a percent of your paycheck is deducted, up to a set maximum per year today s workers pay for current retirees started in 1935 Medicare health care coverage for people 65 and older you may need to buy supplemental coverage, especially for prescriptions
Example 1 paycheck withholdings Ramiro got his first job in 2016. In that year, Social Security tax was 6.2% of income up to $118,500. Medicare tax was 1.45%. If Ramiro earned $73,210 in 2016, how much did he pay for Social Security and Medicare taxes? SOLUTION: Social Security is 6.2% of his income = (.062) * $73,210 = $4,539.02 withheld Medicare is 1.45% of his income = (.0145) * $73,210 = $1,061.55 withheld Total = $4,539.22 + $1,061.55 = $5,600.57
Example 2 Social Security tax as a piecewise function SOLUTION: Since social security is 6.2% of one s income = (.062) * income However, in 2016, one only had to pay on income up to $118,500 and not on any income above that amount. So anyone making over $118,500 only has to pay 6.2% of that number = (.062) * $118,500 = $7,347 f(x) = .???? ???? ? $???,??? ???? ? > $???,??? $????
Example 3 graph Social Security piecewise function from Example 2 SOLUTION: f(x) = .???? ???? ? $???,??? ???? ? > $???,??? $????
Example 4 In 1988, Social Security tax was 7.51%, to the maximum income of $45,000. If Grace earned $51,211 in 1988, how much Social Security tax did she pay? SOLUTION: Since she was over the maximum taxable income, she only has to pay taxes on that $45,000. 7.51% = .0751 as a decimal (.0751) * $45,000 = $3,379.50
Assignment: Pg 323 # 2, 3, 6 (talk about cusps), 8, pg 304 #17, pg 311 #5, 23 Pg 323 #2 3.
Assignment: Pg 323 # 2, 3, 6 (talk about cusps), 8, pg 304 #17, pg 311 #5, 23 Pg 323 #6 a. Express the 1993 Social Security tax function as a piecewise function t(x), where x is the annual (yearly) income. b. Graph the function. c. What are the coordinates of the cusps on the graph? #8 In 2011, the Social Security tax rate was lowered to 4.2% to help stimulate the economy. The government figured that if people paid less taxes they would have more money to buy goods and services. How much did a worker who earned $128,900 in 2011 save on FICA (Social Security and Medicare) taxes with this reduction?
Assignment: Pg 323 # 2, 3, 6 (talk about cusps), 8, pg 304 #17, pg 311 #5, 23 continued Pg 304 #17 Pg 311 #5
Assignment: Pg 323 # 2, 3, 6 (talk about cusps), 8, pg 304 #17, pg 311 #5, 23 continued Pg 311 #23 McCormack Chrysler pays their sales staff by commission. They are paid a percent of the profit the dealership makes on the car. If the profit is $500 or less, the commission rate is 17%. If the profit is greater than $500 and less thank or equal to $1,100, the commission rate is 20%. If the profit is above $1,100, the rate is 22%. a. If x represents the profit, express the commission c(x) as a piecewise function. b. If the dealer purchases the car for $21/696 and Kristin, a salesperson, sells it for $22,800, how much commission does she earn for the sale? c. Kristin is thinking of leaving McCormack Chrysler and working at Glassman Chevrolet from your 5-3 notes Example 5. How much more commission would she have made for the same sale at Glassman?
