3. Saving for retirement (30 points) Having recently graduated, Jack and Jill just started working for the same company. The company has offered each of them a retirement savings plan (e.g., an Individual Retirement Annuity, sometimes called an IRA) in which for each year that they save $5000 in the retirement plan, the company will also contribute $5000 to their plan. Contributions to the plan, if any, are made at the end of each year, and the money in the plan is invested in a broad index of stocks. Jill has decided to start the plan in year 1 - contributing $5000 at the end of each year for the next 30 years. Jack has decided postpone his starting the plan for 6 years because of his loan payments for a Tesla. Thus, Jack will make his first contribution to the plan in year 7. Note that interest is paid based on the beginning of the year balance and does not include the yearly contribution since this is paid at the end of the year and does not have time to accrue interest. Use Excel to answer the following: (a) If the return each year is exactly 10%, how much will Jill have in the account at the beginning of year 31? (Submit answer via Blackboard: 5 pts) (b) If the return each year is exactly 10%, how much will Jack have in the account at the beginning of year 31? (Recall Jack started saving in year 7.) (Submit answer via Blackboard: 5 pts) (c) Suppose that instead the returns alternate between 30% and -10% (i.e., 30% for year 1, -10% for year 2, 30% for year 3, -10% for year 4, 30% for year 5, etc. Observe that the average return is 10%. How much will Jill have in the account at the beginning of year 31? (Submit answer via Blackboard: 5 pts) (d) If, similar to (c), the returns alternate between 30% and -10%, how much will Jack have in the account at the beginning of year 31? (Submit answer via Blackboard: 5 pts) (e) What is the difference between your answers to (a) and (b)? Also what is the difference between your answers (c) and (d)? What insight does this give? (Handwrite answer: 5 pts) () What is the difference between your answers to (a) and (c)? Also what is the difference between your answers (b) and (d)? What insight does this give? (Handwrite answer: 5 pts)