Suppose you purchase a five-year, 15 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000. a. Show that the duration of this bond is equal to four years. b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is four years from today, you will still earn a 9 percent yield on your investment. c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent