You purchase a 30-year bond today with a $10,000 face value that makes annual coupon payments at a 5% coupon rate. For this question, you will need to make use of the following equation: (a) If the yield to maturity on 30 year bonds at the time of purchase was 4%, how much did you pay for the 30 year bond? (b) After holding the bond for 1 year, you find that the yield to maturity on 29 year bonds is 5%. What is new price of your bond and what has been the rate of return from holding the bond over the first year? (c) After holding the bond for a second year, you find that the yield to maturity on 28 year bonds is 3.5%. What is new price of your bond and what has been the rate of return from holding the bond from the first year to the second?^1 The formula that you need: sigma^N_k = 1 1/(1 + i)^k = 1 - (1 + i)^-N/i