1. Pompeii has been planning to develop a new warning system. The installation of the system costs more than what their budget allows so the mayor decides to issue 25-year bonds to finance the project. The bonds have a face value of $1,000 and they promise a coupon rate of 9.6% which will be paid monthly to the bond holders. a. Calculate the price you have to pay to purchase the bond if i. The Yield to Maturity (YTM) is 5.8% (annually) ii. The Yield to Maturity (YTM) is 10.9% (annually) b. Let's assume you would like to buy 50 bonds issued by Pompeii with a 25 -year tenure. If the YTM is 6.0% and the coupon rate is 9.6%, calculate how much more you have to pay when you purchase a bond which makes monthly coupon payments rather than annual payments. 2. Consider the following three zero-coupon (discount) bonds: 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