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6. Suppose the annual yield to maturity on a 1 year zero coupon bond is 2 %, a 2 year zero coupon bond is 3 %, and a 3 year zero coupon bond is 4 %. (a) Consider a bond of face value 10.000 that pays a 5 % coupon payment on years 1, 2, and 3. It also repays the face value on year 3 in addition. What is the fundamental value of this bond? Does it trade at a discount or premium? Is there a way you could have known whether it traded at a discount or premium without computing its fundamental value? (b) Suppose the bond is traded at a market price of 10,100. Is there an arbitrage opportunity? What trades could you make to exploit this arbitrage opportunity? If the bond traded at 10,500, would the same set of trades continue to make you money? If not, would there be a different set of trades you could make to exploit an arbitrage opportunity? (c) Suppose the bond is priced at its fundamental value. What is the bond's Macauley duration and modified duration? (d) Imagine the bond's yield to maturity decreased by a small amount. What would be the percentage change in the bond's price? Is this greater or less than the percentage change in a 3 year zero coupon bond's price if its yield to maturity decreased by the same amount (if it had the same initial yield to maturity)? Why