1. A bond with 4 years of maturity with face value $15000 pays annual coupon with coupon rate 4%. The effective risk-free rate provided by the bank is 6%. (a) (3 points) If the bond price is $14000, prove that this bond actually has a yield even worse than the risk-free rate provided by the bank. (b) (2 points) Find the duration of the bond if YTM = 5.8%. (c) (2 points) Hence, using the duration of the bond, estimate the new price of the bond if the YTM increases by 0.2%