The yield of a 1-year zero-coupon bond is 5% per annum {continuously compounded). A 2-year coupon bond with a coupon rate of T% per year (paid annually) has a price of 98 and a yield of ?.81% per annum (continuously compounded). The bonds have principal value of100. i} What is the forward rate over the 2"d year? Provide the answer as a semi- annually compounded forward rate, as well as a continuously compounded forward rate. Explain your answer and derive any formulas you use. (14 marks} ii) Explain in words whether the swap rate for a 2-year vanilla interest rate swap with notional value of 100M would be higher or lower than 7% per annum [paid at annual frequency). (5 marks) iii) What is the duration of a portfolio of 100 1-year zero coupon bonds, and 200 of the 2-year coupon bonds described above in (c). If interest rates fall by 20 basis points what is change in value of this bond portfolio. What percentage of that change in value is caused by the changes in value of the 1-year bond? (12 marks}