EXAMPLE 4.4 (Bond amortization) A 10% bond with face amount 10,000 matures 4 years after issue. Con- struct the amortization schedule for the bond over its term for nominal annual yield rates of (a) 8%, (b) 10%, and (c) 12%. SOLUTION (a) The entries in the amortization schedule are calculated as they were in Table 4.2, where k counts coupon periods. With a nominal yield rate of 8% the purchase price of the bond is 10,673.27. Then 11 = (10,673.27).04) = 426.93, and so on. The complete schedule is shown in Table 4.3a. TABLE 4.3a k Payment Interest Due Principal Repaid 0 1 2 3 4 5 6 7 8 Outstanding Balance 10,673.27 10,600.21 10,524.22 10,445.19 10,363.00 10,277.52 10,188.62 10,096.16 0 500 500 500 500 500 500 500 10,500 426.93 424.01 420.97 417.81 414.52 411.10 407.54 403.85 73.07 75.99 79.03 82.19 85.48 88.90 92.46 10,096.15 (b) With a nominal yield rate of 10% the purchase price is 10,000. The schedule is shown in Table 4.3b. TABLE 4.3b k Payment Interest Due Principal Repaid 0 1 2 3 4 5 6 7 8 Outstanding Balance 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 0 500 500 500 500 500 500 500 10,500 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 0 0 0 0 0 0 0 10,000 (c) With a nominal yield rate of 12% the purchase price is 9379.02; the schedule is shown in Table 4.3c. TABLE 4.3c k Payment Interest Due Principal Repaid 0 1 2 3 4 5 6 7 8 Outstanding Balance 9379.02 9441.76 9508.27 9578.77 9653.50 9732.71 9816.67 9905.67 0 500 500 500 500 500 500 500 10,500 562.74 566.51 570.50 574.73 579.21 583.96 589.00 594.34 - 62.74 - 66.51 - 70.50 - 74.73 - 79.21 - 83.96 - 89.00 9905.66 4.2.2 Graph OBA for each of the three cases in Example 4.4. (a) Show that for a bond bought at a premium, the graph of OB is concave downward. (b) Show that for a bond bought at a discount, the graph of OB is convex upward