## Description

**Question:**

A 6-year annuity of twelve $6,185 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. If the discount rate is 9 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the annuity $ If the discount rate is 9 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the annuity $ If the discount rate is 9 percent compounded monthly, what is the current value of the annuity?

**Answer:**

Discount rate=9% (0.09) compounded monthly

Semi annual interest rate=((1+(0.09/12))^6)-1=1.045852-1=0.045852

Present Value (PV) of payment=(Payment)/((1+i)^N)

i=0.045852, N=Period of payment

Payments and PV of payments are given below:

N | A | B=A/(1.045852^N) | |

Years from now | Semi annual period | Payment | PV of payment |

11.5 | 1 | $6,185 | 5913.838669 |

12 | 2 | $6,185 | 5654.565531 |

12.5 | 3 | $6,185 | 5406.659385 |

13 | 4 | $6,185 | 5169.621882 |

13.5 | 5 | $6,185 | 4942.976522 |

14 | 6 | $6,185 | 4726.267696 |

14.5 | 7 | $6,185 | 4519.059768 |

15 | 8 | $6,185 | 4320.936201 |

15.5 | 9 | $6,185 | 4131.498722 |

16 | 10 | $6,185 | 3950.366516 |

16.5 | 11 | $6,185 | 3777.175467 |

17 | 12 | $6,185 | 3611.577419 |

TOTAL | 56124.54378 |

Value of this annuity11 years from now=$56,124.54

Number of semi annual period from year 5 to year11=6*2=12

Value of annuity five years from now=$56,124.54378/(1.045852^12)= $ 32,772.54

Number of semi annual periods from 3 years to 5 years from now=4

Value of annuity three years from now= $ 32,772.54 /(1.045852^4)= $ 27,392.34

Number of semi annual period from now to 3 years=6

Current value of the annuity= $ 27,392.34/(1.045852^6)= $ 20,931.86

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