1. Gotham City has been planning to develop a new warning system to make Batman aware of danger. The installation of the system costs more than what their budget allows so the mayor decide to issue a 15-year bond to finance the project. The bonds have a face value of $1,000 and it promises a coupon rate of 6.8% which will be paid quarterly to the bond holders. a. Calculate the price you have to pay to purchase the bond if i The Yield to Maturity (YTM) is 6% (annually) ii. The Yield to Maturity (YTM) is 8.4% (annually) b. Let's assume you would like to buy 200 bonds issued by the Gotham City. If the YTM is 7.6% and the coupon rate is 6.8%, calculate how much more you have to pay when you purchase a bond which makes annual coupon payments rather than quarterly. 2. Consider the following three zero-coupon (discount) bonds: Bond Face Value Time to Maturity Market Price $1,000 One year $924.64 2 $1,000 Two years 5841.53 1 3 $1,000 Three years $744.59 a) Calculate the one-, two-, and three-year spot rates. b) Calculate the forward rate over the second year and the forward rate over the third year