Question

Suppose that you will receive annual payments of $12,500 for a period of 10 years. The first payment will be made 9 years from now. If the interest rate is 6%, what is the present value of this stream of payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer #1

Annual Payments = P = $12,500

n = 18 years

x = payment = 8 years

r = interest rate = 6%

Present Value of this stream of payments = [P * [1 - (1+r)^-(n-x)] / r] / (1+r)^x

= [$12,500 * [1 - (1+6%)^-(18-8)] / 6%] / (1+6%)^8

= [$12,500 * 0.441605223 / 0.06] / 1.59384807

= [$92,001.0882] / 1.59384807

= $57,722.6211

Therefore, present Value of this stream of payments is $57,722.62

Calculation of Present Value of Cash Flow
Stream |
|||

Year |
Cash Flow |
Discount Factor@6% |
Discounted Cash Flows |

A |
B |
C =(1+6%)^-A |
D = B*C |

9 | 12,500 | 0.591898464 | 7398.730794 |

10 | 12,500 | 0.558394777 | 6979.934711 |

11 | 12,500 | 0.526787525 | 6584.844067 |

12 | 12,500 | 0.496969364 | 6212.117045 |

13 | 12,500 | 0.468839022 | 5860.487778 |

14 | 12,500 | 0.442300964 | 5528.762055 |

15 | 12,500 | 0.417265061 | 5215.813259 |

16 | 12,500 | 0.393646284 | 4920.578546 |

17 | 12,500 | 0.371364419 | 4642.055232 |

18 | 12,500 | 0.350343791 | 4379.297389 |

Present value of Cash Flow stream | 57722.62088 |

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