### Jane and Joan

NAME_________________________________________
Note: The effort you expend in clearly explaining your work solidifies your learning. In particular, research has shown that writing and speaking trigger different areas of your brain. By writing something down - even when you think you already understand it - your learning is reinforced by involving other areas of your brain. In addition, it will be a much more useful study guide when you review for a quiz or exam.
SHOW WORK means that you should show the computation (ie 1+1=2) that resulted in the answer to the problem.
Jane and Joan were twins. They both went to work at age 22 with identical jobs, and at the end of each year they received identical bonuses of \$2,000.00. But there was one difference:

• Jane: Jane believed that as a young woman she should take the opportunities to enjoy life and not be too concerned about saving for the future -- she had many years to put money into savings. For the first 10 years she spent her \$2000 bonuses on vacations in the Bahamas. At age 32, she decided she should start saving for her future and from that time on (for the next 34 years) she invested her \$2000 bonuses each year in a savings program paying 8% compounded annually. This continued through the end of her 65th year.
Question 1 How much total money did Jane put in to her retirement plan? Show work to justify that the answer is \$68000.

Question 2 Set up a formula with numbers substituted in for the variables to determine how much money Jane will have at the end of age 65?

Question 3 Solve for an answer. Write down the CALC KEYS you used to show that the answer is \$317253.34.

• Joan: As a young woman, beginning at age 22, Joan was conservative and was concerned about her future. Each year she invested her \$2000 bonuses in a savings program earning 8% interest compounded annually. After 10 years, at age 32, Joan decided to have some fun in life and she began spending her \$2000 bonuses on vacations in the Bahammas instead of saving them. This continued for the next 34 years until the end of her 65th year.
Question 4 How much total money did Joan put in to her retirement plan? Show work to justify that the answer is \$20000.

Question 5 Set up a formula with numbers substituted in for the variables to determine how much money she will have at the end of age 31? Explain why the formula that you chose was appropriate to use in this case.

Question 6 Solve for an answer. Write down the CALC KEYS you used to show that the answer is \$28973.12.

Question 7 Use the answer in Question 6 in order to set up a formula with numbers substituted in for the variables to determine how much money she will have at the end of age 65? Explain why the formula that you chose was appropriate to use in this case.

Question 8 Solve for an answer. Write down the CALC KEYS you used to show that the answer is \$396645.88.

Question 9 The first time I did this problem, I got \$396645.95 as an answer. What did I do wrong? (I'm looking for a general answer instead of a specific one, but if you can figure out the specific calculation that yields this answer, write that down too)

So Jane puts in \$68,000 total and ends up with \$317,253.34 while Joan puts in \$20,000 total and ends up with \$396,645.88. Notice that at a rate of 8%, Joan ends up ahead by saving earlier, even though she puts in a lot less money. Yet, if the interest rate had been different, it is not clear who would earn more money.
Extra Credit What interest rate yields equal amounts of money for Joan and Jane at the end of their 65th year? Explain how you got your answer.