Assessment
Version #1:
You
have landed your dream job and expect to retire from this company after
30 years of employment. You will earn an excellent salary with a
choice of retirement plans. You must choose either the Penny Plan
or the Grand Plan. Your employer gives you the following
information about the plans.
v Penny Plan: Your employer will deposit one cent into your retirement plan at the end of your first year of employment and double that amount each year there after. That is, the first year your account will receive one cent; the second year your account will receive two cents; the third year your account will receive four cents, continuing in this same pattern year after year.
v Grand Plan: Your retirement account will have $1000 deposited at the end of each year of employment. For example, the first year your account will receive $1000; the second year you will receive $1000; the third year your account will receive $1000, continuing in this same pattern year after year.
Part One:
Which plan would you choose and why?
(Turn this page into your teacher and pick up part two.)
You have landed your dream job and expect to retire from this company after 30 years of employment. You will earn an excellent salary with a choice of retirement plans. You must choose either the Penny Plan, the Grand Plan, or the Grand Plus Plan. Your employer gives you the following information about the plans.
v Penny Plan: Your employer will deposit one cent into your retirement plan at the end of your first year of employment and double that amount each year there after. That is, the first year your account will receive one cent; the second year your account will receive two cents; the third year your account will receive four cents, continuing in this same pattern year after year.
v Grand Plan: Your retirement account will have $1000 deposited at the end of each year of employment. For example, the first year your account will receive $1000; the second year you will receive $1000; the third year your account will receive $1000, continuing in this same pattern year after year.
v Grand Plus Plan: Your retirement plan will have an additional $1000 deposited into your retirement account each year. This means your account will receive $1000 in the first year, $2000 in the second year, and $3000 in the third year, continuing in this same pattern year after year.
(Use this page to answer questions 1 through 3.)
Part Two:
1. How much will be deposited into your retirement account during the 20th year of employment for each plan? Provide evidence to support your answers using both function rules and tables or graphs.
2. Compare and contrast the properties of the graphs/function rules for each retirement plan. Include a description of each type of function.
3. Employee A, employee B, and employee C want to compare how much money they will have in their retirement plans after 30 years. Employee A chose the Penny Plan. Employee B chose the Grand Plan. Employee C chose the Grand Plus Plan.
A. What is the total amount of money that each employee will have in their retirement account at the end of thirty years employment? Support your answers with function rules and tables or graphs.
B. Based on your findings, which employee chose the best plan and why?
Constructed response:
4. Now that you have a steady job, you can indulge in your favorite hobby: skeet shooting. At your first tournament, skeet is shot into the air at 82 ft/s and an angle of 20 degrees. Its height is a function of time and is described by the equation h(t) = -16t2 + 28t. This results in the skeet reaching a maximum height of 12.25 feet after 0.875 seconds. In the next shot, the skeet is released at 88 ft/s and an angle of 20 degrees. Describe the effect the resulting equation of h(t) = -16t2 + 30t will have on the maximum height reached by the skeet. Support your answer with a graph, algebra, or a table.
5. A young couple just had their first baby. They want to help provide financial security for their child’s retirement. They have $1,000.00 to invest for their child’s future. The investment they have chosen has an expected return ranging from six to eight percent annually.
A. How much will the account be worth in 65 years (estimated retirement age) if the account has a 6% compounded annually rate of return? Show the work necessary to obtain your answer.
B. How much will the account be worth in 65 years if the account has an 8% compounded annually rate of return? Show the work necessary to obtain your answer.