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6. We now move to compute, for each pair of securities with adjacent maturities, the forward interest rates implied by this yield curve. a. Starting from the semiannual yields, compute all the forward rates. b. Convert the semiannual forward rates into their corresponding BEY. 7. Graph the term structure of interest rates, i.e. plot the yield curve and the forward interest rates in the same graph. 8. Focus now on the Treasury note with maturity at the end of June 2022. 
a. Compute its yield to maturity. Since coupons are paid semiannually, keep the yield to maturity at semiannual frequency. 
b. Compute the duration, expressed as a semiannual value. c. Annualize the duration. d. Compute the modified duration, expressed as a semiannual value. e. Compute the convexity of the bond, expressed as a semiannual value. f. Compute the new bond price with a second-order approximation if the semiannual yield to maturity increases by 3%. 9. According to the expectation hypothesis, what is the expected realized yield on the Treasury note that matures at the end of December 2022? 10. Let us investigate more the implications of the expectation hypothesis and the liquidity preference theory, given this yield curve that you plotted. a. If the expectation hypothesis holds, what is the six-month interest rate that investors expect from the beginning of July 2022? 
b. If the liquidity preference theory holds, what would you think about the same interest rate described in point a) above? Give a clear mathematical condition as your answer.