匿名
匿名 發問於 科學及數學數學 · 5 年前

MATHS: interest

Mary has found her dream house. It is selling for $500000. When she retires 2 years from now, she plans to sell her present house for $450000 an move. She decides to set aside $900 every two weeks until she retires in a fund earning 10.5%/a, compounded every second week. What is the difference between the future value of Mary's investment extra $50000 she needs for her dream home?

更新:

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2 個解答

評分
  • 5 年前
    最愛解答

    先澄清兩點:

    (1) 是否 10.5% p.a.

    (2) 你是否假設一年有 52 個星期?

    〔這個不同的假設會影響計算,因為若是的話,那 two-month compounded rate is 10.5%/26〕

    2015-06-18 11:27:38 補充:

    For each year, assume that there are 52 weeks.

    Then for two years, there are 104 weeks, that is, 52 two-weeks period.

    Consider a time line (vertical illustrated below) with each time unit being 2 weeks.

      0+

       |

      1+ <-- $900

       |

      2+ <-- $900

       |

      3+ <-- $900

       |

      ...

       |

     51+ <-- $900

       |

     52+ <-- $900

       |

       v

    For every two weeks, the interest rate is i = 10.5%/26.

    The amount of money Mary can accumulated is

    $900(1 + i)⁵¹ + $900(1 + i)⁵⁰ + ... + $900(1 + i)² + $900(1 + i) + $900

    = $900 + $900(1 + i) + $900(1 + i)² + ... + $900(1 + i)⁵⁰ + $900(1 + i)⁵¹

    = $900[(1 + i)⁵² - 1] / [(1 + i) - 1]

    = $900[(1 + i)⁵² - 1] / i

    = $51960.57972

    The difference is

    $51960.57972 - ($500000 - $450000)

    = $51960.57972 - $50000

    = $1960.57972

  • 匿名
    5 年前

    我也是這樣想,假設一年有 52 個星期..

    The answer is $51960.58 and $1960.58

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