3. A bond with a par value of $1000 is redeemable at par or face value in fifteen years. The bond carries a coupon rate of 4.6%. The interest payments are made at the end of every six months (semi-annually). The current annual yield to maturity on similar bonds is 5.4%. a) Draw a diagram showing the two important cash flows involved in determining the purchase price of the bond. Use numeric data from the problem to set up the proper numerical values on the diagram. (1 point) b) Set up the mathematical expressions using numbers from the problem to find the purchase price of the bond and compute the purchase price of the bond. (6 points) c) Find the current annual yield on the bond. (2 points) d) Suppose the bond can be called six years from today. If the bond is called, the bondholder will receive an extra year's interest at the time of redemption as a bonus. Set up the mathematical expression for finding the purchase price of this callable bond. You do not have to evaluate the expression. (3 points)