Problem 2. Suppose we see the following yield curve for zero-coupon bonds: Maturity Yield to Maturity 1 year 2 years 3 years Y1 =6% y2 =7% y3 =8% (a) What price should a 3-year coupon bond with a coupon rate of 5% and a face value of $1,000 sell for today? What is the yield to maturity (y) on the 3-year coupon bond? (b) If a four-year annuity paying $100 per year (at the end of each year) has a price today of $334.57, what is the yield to maturity on a four year zero-coupon bond (94)? (c) A 10-year 4.5% coupon bond with $1,000 face value was issued 7 years ago. What is its price today? (Assume that the bond has just paid out any coupon due today, so the buyer does not get any coupon payments until 1 year from now). (d) You wish to lock in now (at time 0) a loan rate for a loan in the amount of $20 million in year 2 to be repaid in year 3 (cash received in year 2 and interest plus principal returned in year 3). What pattern of zero coupon bond holdings could you use to construct this loan now? You will be buying and selling different bonds. How many bonds (of $100 face value) of what maturity will you buy? How many bonds (of $100 face value) of what maturity will you sell