4. (Duration of a bond, 3 points) The duration of a bond is a measure of how long, on average, the holder of the bond has to wait before receiving cash payments. Suppose that a bond has coupon payments ci at time ti,i = 1, ,n, and a continuously compounded yield y. The price of the bond is given by The duration D of the bond is defined as ice- (a) Show that D satisfies =--BD (b) If the yield is increased by a small arnount y, show' that DA