Question

A bond pays annual interest. Its coupon rate is 9.6%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity is currently 6.6%. The modified duration of this bond is ______ years.

Answer #1

**Step 1:
Calculation of Duration**

time |
Cash flow |
[email protected]% |
Present Value
(Cashflow*PVAF/PVF) |
Weight based on PV |
Time * weight |

1 | 96 | 0.9381 | 90.06 | 0.0817 | 0.0817 |

2 | 96 | 0.8800 | 84.48 | 0.0766 | 0.1532 |

3 | 96 | 0.8255 | 79.25 | 0.0719 | 0.2156 |

4 | 1096 | 0.7744 | 848.75 | 0.7698 | 3.0793 |

**Duration** =
Time * weight

=.0817+.1532+.2156+3.0793

**= 3.5298 years**

**Step 2:
Calculation of Modified Duration**

**Modified Duration = Duration
/ (1+Yield to maturity)**

= 3.5298 / 1.066

= 3.3113

**= 3.31 years**

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