A 30-year 10% coupon bond that pays the coupon twice a year is at par. Note that the coupon payment is not started yet. Find the Macaulay duration. Suppose that the Korean economy encounters the boom (good) or bust (bad) due to the development of the vaccine and medication for COVID-19. The Bank of Korea, the central bank, creates the tentative interest rate policy to boost investments based on the transition matrix with conditional interest rate as follows: Next State Boom Bust Interest rate Current State Boom Bust 0.4 0.6 0.6 0.4 10% 5% Interest rate 10% 5% (a) The Bank of Korea initiates two zero coupon bonds A & B (face value 100). The maturities of bonds A & B are one and two years, respectively. Find the prices of bond A & B if the current state is bust. (Hint: Use the transition matrix as the probability for the economic condition in the next state) (b) Find the yields of bonds A & B. (c) The Bank of Korea initiates two 4% coupon bonds C & D (face value 100). The maturities of bonds C & D are one and two years, respectively. Find the prices of bond C & D if the current state is bust. (d) Find the yields of bonds C & D. (e) Discuss the difference in yield curve based on the results of (b) and (d)