Rather than getting a summer job or internship to increase his $500 savings account balance, a member of the Poole College of Management student investment club decides to put his $500 to work by making an investment. He pools his $500 with the money contributed by the other members of the investment club and the club makes a 10-week investment in bitcoin. The investment returns are compounded on a weekly basis. The 10 weekly return rates, in decimal form, are in this Excel file Bitcoin Returns. Note that the average (mean) weekly return rate, to 4 decimal places, is r = .0814.
1. At the end of 10 weeks this member of the investment club is disappointed with the results of his $500 investment. He has used the simple interest formula I = Prt, where I = interest, P = his principal ($500), r = average weekly return rate, and t = time (10 weeks) to calculate what he thinks the terminal value of his investment should be. What is his calculated terminal value?
2. 1. Since the returns are compounded weekly, you will show the student the correct terminal value by using the geometric mean. What is the geometric mean return rate of this investment? Express your answer as a decimal, not a percentage, rounded to 4 decimal places.
2. What is the terminal value of this investment?