Problem 1. (Institute of Actuaries Examination April 2003) $1000 is invested for 10 years. In any year, the yield on the investment will be 4% with probability 0.4, 6% with probability 0.2, 8% with probability 0.4, and is independent of the yield in any other year. (a) Calculate the mean accumulation at the end of 10 years. (b) Calculate the standard deviation of the accumulation at the end of 10 years. (c) Without carrying out any further calculations, explain how your answers to (a) and (b) would change (if at all) if: (i) the yields had been 5%, 6% and 7% instead of 4%, 6%, and 8% p.a. respectively. (ii) the investment had been made for 12 years instead of 10 years