Question

(Future value) Sarah Wiggum would like to make a single lump-sum investment and have $1.7 million at the time of her retirement in 28 years. She has found a mutual fund that expects to earn 5 percent annually. How much must Sarah invest today? If Sarah earned an annual return of 16 percent, how much must she invest today?

- If Sarah can earn 5 percent annually for the next 28 years, how much will she have to invest today?

$ (Round to the nearest cent.)

- If Sarah can earn 16 percent annually for the next 28 years, how much will she have to invest today?

$ (Round to the nearest cent.)

Answer #1

Part A:

**Present Value:**

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n

Where r is Int rate per period

n - No. of periods

Particulars |
Amount |

Future Value | $ 1,700,000.00 |

Int Rate | 5.0000% |

Periods | 28 |

Present Value = Future Value / ( 1 + r )^n

= $ 1700000 / ( 1 + 0.05 ) ^ 28

= $ 1700000 / ( 1.05 ) ^ 28

= $ 1700000 / 3.9201

= $ 433659.18

Part B:

**Present Value:**

Particulars |
Amount |

Future Value | $ 1,700,000.00 |

Int Rate | 16.0000% |

Periods | 28 |

Present Value = Future Value / ( 1 + r )^n

= $ 1700000 / ( 1 + 0.16 ) ^ 28

= $ 1700000 / ( 1.16 ) ^ 28

= $ 1700000 / 63.8004

= $ 26645.58

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