Problem 1. Ernie has adopted a two-year investment plan in which $10,000 is to be deposited into his account at time 0. His investment is placed into a stock index fund that will either gain 25% each year or lose 15% each year. The one-year annual effective rate of interest is 7.5%. Ernie is concerned about losing money and his in- vestment advisor Bert has offered him the following insurance for protecting the value of his investment portfolio. The insurance provides for Ernie to receive a minimum payout at the end of two years which is equal to the value of his initial investment and in return for this protection, Ernie's annual investment gain is capped at g% where g