From Midterm 1, Form C Question 15.

Consider the asset below

YEAR | BENEFIT |

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 4 |

6 | 4 |

7 | 4 |

8 | 4 |

9 | 3 |

10 | 2 |

11 | 1 |

When the interest rate is 10%, what is the present worth of the benefits in periods five through eight?

A) $13.66

B) $12.68

C) $8.66

D) $20.00

E) None of the Above

The correct answer is C, $8.66.

P= 4(P/A i=10% n=4)

Use the constant series formula for P given A, A being the constant which in this case= 4

P= 4((1.104) -1)/( (1.104).1 (1.104))= 8.66

Note: One must further divide by (1 + i) raised to n number of periods that would discount the value back to time period zero. If one fails to do this, one ends up with the incorrect answer of $12.68. If one simply sums the benefits in periods four through eight, one finds the incorrect answer of $20.00. It is unclear how to arrive at the incorrect answer of $13.66.