Chapter 9 If Hw

5. Duration for YTM at 10%

| | YTM | 0.1 | |

| | Coupon | 50 | |

| | | | |

Time, t | Cash Flow,CF | DF | CF * DF | CF * DF * t |

0.5 | 50 | 0.952380952 | 47.61904762 | 23.80952381 |

1 | 50 | 0.907029478 | 45.35147392 | 45.35147392 |

1.5 | 50 | 0.863837599 | 43.19187993 | 64.78781989 |

2 | 50 | 0.822702475 | 41.13512374 | 82.27024748 |

2.5 | 50 | 0.783526166 | 39.17630832 | 97.94077081 |

3 | 50 | 0.746215397 | 37.31076983 | 111.9323095 |

3.5 | 50 | 0.71068133 | 35.53406651 | 124.3692328 |

4 | 50 | 0.676839362 | 33.8419681 | 135.3678724 |

4.5 | 50 | 0.644608916 | 32.23044581 | 145.0370061 |

5 | 1050 | 0.613913254 | 644.6089162 | 3223.044581 |

| | | 1000 | 4053.910838 |

Duration = 4053.91 / 1000 = 4.05 years

Duration for YTM at 12%

| | YTM | 0.12 | |

| | Coupon | 50 | |

| | | | |

Time, t | Cash Flow,CF | DF | CF * DF | CF * DF * t |

0.5 | 50 | 0.943396226 | 47.16981132 | 23.58490566 |

1 | 50 | 0.88999644 | 44.499822 | 44.499822 |

1.5 | 50 | 0.839619283 | 41.98096415 | 62.97144623 |

2 | 50 | 0.792093663 | 39.60468316 | 79.20936632 |

2.5 | 50 | 0.747258173 | 37.36290864 | 93.40727161 |

3 | 50 | 0.70496054 | 35.24802702 | 105.7440811 |

3.5 | 50 | 0.665057114 | 33.25285568 | 116.3849949 |

4 | 50 | 0.627412371 | 31.37061857 | 125.4824743 |

4.5 | 50 | 0.591898464 | 29.59492318 | 133.1771543 |

5 | 1050 | 0.558394777 | 586.3145158 | 2931.572579 |

| | | 926.3991295 | 3716.034095 |

Duration = 3716.03 / 926.40 = 4.01 years

Duration for YTM at 14%

| | YTM | 0.14 | |

| | Coupon | 50 | |

| | | | |

Time, t | Cash Flow,CF | DF | CF * DF | CF * DF * t |

0.5 | 50 | 0.934579439 | 46.72897196 | 23.36448598 |

1 | 50 | 0.873438728 | 43.67193641 | 43.67193641 |

1.5 | 50 | 0.816297877 | 40.81489384 | 61.22234077 |

2 | 50 | 0.762895212 | 38.1447606 | 76.2895212 |

2.5 | 50 | 0.712986179 | 35.64930897 | 89.12327244 |

3 | 50 | 0.666342224 | 33.31711119 | 99.95133357 |...