Assessment  version #2:

You have landed your dream job and expect to retire from this company after 30 years.  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 invest one cent into your retirement plan the first year of employment and double that amount each year there after.  That is, the first year you will receive one cent; the second year you will receive two cents; the third year you will receive four cents, continuing in this same pattern year after year.

v      Grand Plan:  Your retirement will be $1000 each year.  For example, the first year you will receive $1000; the second year you will receive $1000; the third year you will receive $1000, continuing in this same pattern year after year.

Part One:

On your first day of work your boss asks you which retirement plan you have chosen.  Since you expect to work with this company for thirty years, which plan do 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.  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 invest one cent into your retirement plan the first year of employment and double that amount each year there after.  That is, the first year you will receive one cent; the second year you will receive two cents; the third year you will receive four cents, continuing in this same pattern year after year.

v      Grand Plan:  Your retirement will be $1000 each year.  For example, the first year you will receive $1000; the second year you will receive $1000; the third year you will receive $1000, continuing in this same pattern year after year.

1.     Complete the table to represent the yearly pay of each plan for the first ten years.

2.     How much money will you earn in the twentieth year for each retirement plan?  Explain how you arrived at your answer.  Show all work.

3.     State a function (rule) that determines how much money will be contributed to the Penny Plan in any given year.

4.     State a function (rule) that determines how much money will be contributed to the Grand Plan in any given year.

Your boss comes in after lunch and tells you that he forgot to offer you the Grand Plus Plan, which pays an additional $1000 each year.  This means you receive $1000 in the first year, $2000 in the second year, and $3000 in the third year.

5.     Complete the table of values for the amount of money contributed yearly with the Grand Plus Plan for the first ten years.

6.     How much money will you earn in the twentieth year using the Grand Plus Plan?  Show how you arrived at your answer.

7.     State a function (rule) that determines how much money will be contributed to the Grand Plus Plan in any given year.

8.     Discuss the differences in each of the three types of functions (rules) derived for each retirement plan using algebraic and/or graphical techniques.

Part Three:

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.

1.     What is the total contribution employee A will have invested in the Penny Plan after 30 years?  State a function (rule) that determines the total contribution for a given number of years (n years).  Name the type of function that was obtained.  Show all work.

2.     What is the total contribution employee B will have invested in the Grand Plan after 30 years?  State a function (rule) that determines the total contribution for a given number of years (n years).  Name the type of function that was obtained.  Show all work.

3.     What is the total contribution employee C will have invested in the Grand Plus Plan after 30 years?  State a function (rule) that determines the total contribution for a given number of years (n years).  Name the type of function that was obtained.  Show all work.

4.     Based on your findings, which employee chose the best plan and why?

5.     How does this compare to your choice in part one?

Part Four:

1. 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.
2. 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.