1. (a) Unit values in a mutual fund have experienced annual growth rats of 11%, 13%, -5%, 12% and 22% in the past five years. The fund manager suggests the fund can advertise an average annual growth of 10.6% over the past five years. What is the actual average an- nual compound growth rate over the past five years? (b) A mutual fund advertises that average annual compound rate of returns for various periods ending end of December 2005 are as follow: 10 years - 13% 5 years -17% 2 years - 15% 1 year - 22% Find the 5-year average annual compound rates of return for the period January 1, 1996 to December 31, 2000, and find the annual rate of return for calender year 2004. (e) Using the factor that the geometric mean of collection of positive numbers is less than or equal to the arithmetic mean, show that if annual compound interest rates over an n-year period are ii in the first year, iz in the second year, ... in in the the year, then the average annual compound rate of interest for n-year period is less than or equal to Site . k=1 [5]