Why is this rate different from the yield to maturity

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Consider the following zero-coupon curve: Maturity (year) Zero-coupon rate (%) 1 4.00 2 4.50 3 4.75 4 4.90 5 5.00 (a) What is the price of a 5-year bond with a $100 face value, which delivers a 5% annual coupon rate? 5 Marks (b) What is the yield to maturity of this bond? 5 Marks (c) We suppose that the zero-coupon curve increases instantaneously and uniformly by 0.5%. What is the new price and the new yield to maturity of the bond? What is the impact of this rate increase for the bondholder? 10 Marks (d) Suppose now that the zero-coupon curve remains stable over time. You hold the bond un￾til maturity. What is the annual return rate of your investment? Why is this rate different from the yield to maturity? 2. Consider a coupon bond with n = 20 semesters (i.e., 10 years) to maturity, an annual coupon rate c = 6.5% (coupons are paid semiannually), and nominal value N = $1, 000. Suppose that the semiannually compounded yield to maturity (YTM) of this bond is y2 = 5.5%. (a) Compute the current price of the bond using the annuity formula. 5 Marks (b) Compute the annually compounded YTM and the current yield of the bond. Compare them with y2. 5 Marks (c) If the yield to maturity on the bond does not change over the next semester, what is the Holding Period Return (HPR) obtained from buying the bond now and selling it one semester from now, just after coupon payment? At what price will the bond sell one semester from now just after coupon payment?

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