Question

An Apple annual coupon bond has a coupon rate of 6.9%, face
value of $1,000, and 4 years to maturity. If its yield to maturity
is 6.9%, what is its **Modified Duration**? Answer in
years, rounded to three decimal places.

Answer #1

Period |
Cash Flow |
Discounting factor |
PV Cash Flow |
Duration Calc |

0 | ($1,000.00) | =(1+YTM/number of coupon payments in the year)^period | =cashflow/discounting factor | =PV cashflow*period |

1 | 69.00 | 1.07 | 64.55 | 64.55 |

2 | 69.00 | 1.14 | 60.38 | 120.76 |

3 | 69.00 | 1.22 | 56.48 | 169.45 |

4 | 1,069.00 | 1.31 | 818.59 | 3,274.36 |

Total | 3,629.12 |

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year) |

=3629.12/(1000*1) |

=3.629118 |

Modified duration = Macaulay duration/(1+YTM) |

=3.63/(1+0.069) |

=3.395 |

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