## Answers

a) Macaulay duration @ 20% or 0.20 interest rate(i) annually

Years | Cash flow | Present value (P. V) factor (1/(1+i)^n) | Present value (P. V) of cash flow (Cash flow * P. V. Factor) | Weight of P. V. Of cash flow | Duration (Year * Weight of P. V of cash flow) |

1 | $3,000 | (1/(1+0.20)^1) = 0.8333 | $2,500 | 0.56 | 0.56 (0.56*1) |

2 | $2,000 | (1/(1+0.20)^2) = 0.6944 | $1,389 | 0.31 | 0.62 (0.31*2) |

3 | $1,000 | (1/(1+0.20)^3) = 0.5787 | $578 | 0.13 | 0.39 (0.13*3) |

Total | $4,467 | 1 | 1.57 |

Duration = **1.57 years**

b) Macaulay duration @ 5% or 0.05 interest rate(i) annually

Years | Cash flow | P. V. Factor (1/(1+i)^n) | P. V. Of cash flow (Cash flow * P. V. Factor) | Weight of P. V. Of cash flow | Duration (years * P. V. Of cash flow) |

1 | $3,000 | (1/(1+0.05)^1) = 0.9524 | $2,857 | 0.51 | 0.51 |

2 | $2,000 | (1/(1+0.05)^2) = 0.9070 | $1,814 | 0.33 | 0.66 |

3 | $1,000 | (1/(1+0.05)^3) = 0.8638 | $864 | 0.16 | 0.48 |

Total | $5,535 | 1 | 1.65 |

Duration = **1.65 years**

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