4. You are in charge of the bond trading and forward loan department of a large investment bank. You have the following YTMs for five default-free pure discount bonds as displayed on your computer terminal: where YTMi denotes the yield to maturity of a default-free pure discount bond maturing at time i. (1) A new summer intern from Harvard tells you that 3 year treasury notes with annual coupons of $100 and face value of $1,000 are trading for $1,000. Would you ask the intern to recheck the price of this coupon bond? If so, why? (2) What is the annualized forward interest rate between the end of year 3 and the end of year 5 ? In other words, what is the geometric average forward interest rate for years 4 and 5 ? (3) If the expected one year short rate for year 2 (i.e., from year 1 to year 2 ) is 5%, then what is the liquidity premium for year 2