This question is designed to illustrate the mechanics of how investors may protect themselves against inflation risk by investing in TIPS (Treasury Inflation-Protected Securities) rather than regular Treasuries. For simplicity, in this question, we will only consider bonds with one-year maturity and pays a single coupon at maturity with a coupon rate of 2%. Further, assume that you can invest any fractional number of dollars (e.g. \$3,847.294910237593) into bonds. Before proceeding further, let me explain how TIPS payments adjust with inflation. Suppose you invest $100,000 into one-year-maturity TIPS with a 2% interest rate. Suppose inflation in the subsequent year turns out to be x=5%. Then, the bond principal will be adjusted to $100,000×(1+5%)=$105,000, and your coupon payment will become $105,000×2%=$2,100. Your total payment one year later is going to be $105,000+$2,100=$107,100. In contrast, payments from regular Treasuries do not adjust with inflation. For all questions below, your goal as an investor is to ensure that you receive no less than $10,000 one year from now in real terms. That is, if subsequent national inflation were x%, you want to receive no less than $10,000×(1+x%) payment next year under all scenarios. 3Suppose that the inflation rate next year will be x=10% with 50% probability or x=0% with 50% probability. You don't have a crystal ball so you don't know which scenario will happen. (a) Let's work out how much you have to invest to achieve your goal. - Suppose you can only invest in regular Treasuries (one-year-maturity, 2\% coupon rate). How much money do you have to invest today to ensure that you achieve your goal? - Suppose you can invest in TIPS. How much do you have to invest to ensure you achieve your goal?