The price per bond can be calculated by discounting the future cash flows using the required yield to maturity. The price per bond today is $964.34 when the yield to maturity is 7.3%. If the yield to maturity increases to 8%, the new price per bond is $921.13, representing a percentage point change of -4.48%.
To determine the price per bond, we need to calculate the present value of the future cash flows generated by the bond. Each semiannual interest payment is $1,000 * 0.0625 / 2 = $31.25. The bond will make 40 semiannual interest payments over the 20-year period. To calculate the present value of these cash flows, we discount each payment using the required yield to maturity. The present value factor can be calculated using the formula (1 - 1 / (1 + r)^n) / r, where r is the yield to maturity divided by 2 (because the bond pays interest semiannually) and n is the number of periods. Once we calculate the present value of all the interest payments, we add the present value of the principal payment, which is equal to the face value of $1,000. Adding these two values gives us the price per bond today.
For part a), substituting the given yield to maturity of 7.3% into the formula, we find that the price per bond is $964.34.
For part b), we repeat the calculations using the new yield to maturity of 8%. We find that the price per bond is $921.13. The percentage point change in the price per bond is ((921.13 - 964.34) / 964.34) * 100 = -4.48%.