3. The following table summarizes prices of various default-free zero- coupon bonds (expressed as a percentage of face value) Maturity (years) Price (per $100 face value) 96.1589.85 3 85.16 5 80.25 2 82.27 3.1 Compute the yield to maturity (YTM) for each of the five zero-coupon bonds and plot the zero-coupon yield curve (for the first five years). For a typical coupon bond, what are the two conditions that have to be met for the computed or promised YTM to be realized? If these two conditions or assumptions are not met, what kind of risk would you have? (15 %) 3.2 Based on your answer in 3.1, compute, under the pure expectations theory, the two-year forward rate three years from now. What can you conclude about forward rates when the yield curve is flat? (5 %) 3.3 Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. Under the pure expectations theory, what rate would you obtain if there are no arbitrage opportunities? Show your calculations (3 %) 3.4 There are three main theories for the term structure of interest rates: (1) Pure expectations (unbiased); (2) Liquidity preference (term premium); and (3) Market segmentation. According to the pure expectations theory, the term structure is determined solely by the market's expectations regarding future interest rates. Discuss how the other two theories differ from the pure expectations theory and provide empirical evidence for each of these three theories (10% %)