1. Calculate the Macaulay duration of a 10-years semiannual coupon bond with 8% coupon per annum and a yield to maturity of 6.8% compounded semiannually. Calculate the modified duration of the bond. Face value is $1000. 2. An investor has liabilities of $3m and $4m due at times t= 4 and 5, respectively. He currently holds assets X and Y. If each unit of X produces an income of $1m at t = 4 and each unit of Y produces $1m at t = 8, construct a portfolio consisting of the liabilities and amounts of X and Y that is immune to small changes in interest rate at i = 4% per annum