The yield to maturity (YTM) on 1-year zero-coupon (discount) bonds is 4%, the YTM on 2-year zero-coupon bonds is 5% and the YTM on 3-year zero-coupon bonds is 6%. The YTM on 3-year maturity bonds with coupon rates of 10% (paid annually) is 5.5%. Assume that the face value for each unit of the bond is $1 and assume that there is no chance of default for any of these bonds in part a), part b) and part c). a) What is the price of each of the four bonds? b) Form a portfolio of zero-coupon bonds that replicates the payments of the 3-year coupon paying bond. How many (fractional) units of each zero coupon bond must be in the portfolio? c) What arbitrage opportunity is available for an investment banking firm? What is the profit on the activity per unit of the coupon-paying bond? d) Based on these bond yields, is there still an arbitrage opportunity if there is some chance only the 3-year bond with coupon payments will default? Briefly explain your answer.