1. (Coupon bond price) Consider a 20 year bond that sells at face value (its price is equal to the final payment you get for it in 20 years). The nominal interest rate is expected to be fixed at 4% and is equal to the implicit rate on the bond. i) How much is the coupon rate of the bond? What is the coupon rate if instead the bond matures in 35 years? ii) Now consider the general case in which the price and face value of the bond may be different and the nominal interest rate is given by i. Write down the formula to compute the price of a bond that matures in 5 years. Consider now a bond with the following characteristics: maturity equal to 5 years, annual coupon payments equal to 100 dollars and face value of 1000 dollars. iii) If the nominal interest rate is equal to 4%, what is the price of the bond when issued? After the first year, the interest rate decreases from 4% to 3.5%. iv) What is the price of the bond at the beginning of the second year? If you sell this bond at that moment what is the rate of return on holding the bond for that year? Finally, consider two 10-year bonds. One of them is a zero-coupon with a face value 10,000. The other one pays annual coupons and has a face value of 2000. The interest rate is 5% v) What is the value of coupon payments if both bonds have the same price when they are isuued