Two undergraduate students were discussing how they were going to go about saving for retirement. Both were going to establish IRA accounts and both thought a contribution of $5,000 per year was an appropriate amount to save. Both students were savvy investors and believed they could get 8% annual return on whatever they had in their accounts.

The engineering student said that she was going to wait until she was 31 before she began contributing. She believed she could put the money to better use in her 20s and that there would be plenty of time to catch up. She said she would start at 31 and continue contributing $5,000 each year until she reached 60. (Contributions are made at the beginning of the year.)

The finance major thought about it and said he would start contributing $5,000 per year right away at age 21 but stop contributing after age 30. He believed that at that age he would have put enough away that, with time, would grow to a nice amount.

As such the finance major would contribute a total of $50,000 into his IRA in the ten years from age 21 to 30, and the engineering student would contribute $150,000 in the years from age 31 to 60.The engineering student admitted that she would have contributed three times as much, but felt it would be the prudent thing to do since it would unquestionably result in a much bigger total amount at the end of year 60. The finance major wasn't so sure of that result and said he was sticking with his strategy.

1. Assuming each gets exactly 8% annual return each year on whatever they have in their accounts, which student will have the most money in their account at the end of year 60? Build a spreadsheet that represents each year for each student and calculate what they would have at the end of year 60. (Just calculate these with the spreadsheet.)
2. For what rate of return would they have the same amount at the end of year 60? (Use Solver.)
3. Assume that each year's return for each student varies independently from year to year and from each other but each according to a normal distribution with mean 8% and standard deviation of 4%. What is the average amount each will have at the end of year 60? Simulate this 1000 times using Monte Carlo and 123 as the initial random number seed. From the 1000 trial simulation, what is the probability that the engineering student ends up with a greater amount than the finance student? Are you confident that the true probability is not 50%?