3. Suppose that the term structure of interest rates is flat and that market rates are 10% per year. You are examining a 30-year 5% annual coupon bond with a face value of $1,000. You have also purchased a 10-year zero-coupon bond issued just moments ago at a price of $385.54 a. Show that the price of the 30-year bond is approximately $528.68 b. Show that the duration of the 30 year bond is approximately 11.43 c. Explain why you do not need to do any calculations to determine the duration of the 10-year bond. d. If you held 1 unit of each bond (i.e. $1000 face value of each bond) show that the duration of your portfolio is approximately 10.83 e. Using your result from part d, show that the expected \% change in portfolio value for a 120bps increase in rates and a 30bps decrease in rates are 11.81% and 2.95%, respectively. f. Is one of your estimates in part e likely to be more accurate than the other? Explain