The applet for chapter 21 explores funding a retirement plan for just a few years early in one's career and then ceasing payments verses delaying funding initially and then funding for many years until retirement. The applet can be found on your text website: www.whfreeman.com/fapp7e. Open the previous link in a new window and then click on Applet Exercises. You will see an array of several applets. Click on the applet for chapter 21 (second column, third row).
Suppose Bob and Tom both find investments which yield an annual rate of 8.4% compounded monthly and that each eventually plan to deposit $150 per month. Consider the following two scenarios.
Scenario A: Bob invests for 10 years before
his accident and Tom waits 10 years before starting his investment.
Scenario B: Bob invests for 5 years before
his accident and Tom waits 5 years before starting his investment.
a) For scenario A, input the data into the applet spreadsheet, update the spreadsheet,
and then use the graphing tab to answer #1 below. For scenario B, input the data into the applet spreadsheet
(deleting the old data), update the spreadsheet, and then use the graphing tab to answer #2 below. Be
sure to print out your graphs (or create an accurate hand sketch) to turn in with your explanations.
1) In scenario A, will Tom ever catch up to Bob?
2) In scenario B, will Tom ever catch up to Bob?
b) For each of the above scenarios, calculate the amount of money each man invested over the 40 year period.
c) Use part a) and b) to determine the interest earned by each of the four above investments: two scenarios for Tom and two scenarios for Bob. You may use the applet spreadsheets calculated amounts for Tom's and Bob's final retirement fund amount at age 65.
d) Notice the "corner" in the graphs for scenario A. What aspects of the real world problem are causing this corner for Bob's graph? What about Tom's graph? Should these corners appear regardless of how long Bob invests? If so why? If not, for what time period would they disappear and why? Do these corner appear if Bob invests for 25 years? Explain. Be sure to print out your graphs (or create an accurate hand sketch) to turn in with your explanations.
e) Use your discoveries in part d to help create a formula for the amount of money that would be in Bob's account for scenario A and a formula for the amount of money that would be in Tom's account for scenario A. Then use these formulas to verify that the amounts the applet spreadsheet gave you for Bob and Tom for scenario A are correct.
f) Repeat part e for scenario B.
g) Would changing the interest rate for the scenarios change any of your answers in part a? Explain. Be sure to print out your graphs (or create an accurate hand sketch) to turn in with your explanations.
h) Write a few sentences explaining what this applet has taught you about retirement plans.