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呂布 發問於 科學及數學數學 · 6 年前

AS GS

Mr Chan will deposit $25 000 in a bank account at the beginning of each year from 2007 to 2012.If the interest is compounded yearly and the interest rate is 4% pa,find the total amount that he can get at the beginning of 2013.

答案係$172,000.點計

1 個解答

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  • 6 年前
    最愛解答

    Deposit from 2007 to 2013 will be accumulated for 6 years.

    Deposit from 2008 to 2013 will be accumulated for 5 years.

    Deposit from 2009 to 2013 will be accumulated for 4 years.

    Deposit from 2010 to 2013 will be accumulated for 3 years.

    Deposit from 2011 to 2013 will be accumulated for 2 years.

    Deposit from 2012 to 2013 will be accumulated for 1 year.

    The total amount that he can get at the beginning of 2013 is

    $25000 × (1 + 4%)⁶ + $25000 × (1 + 4%)⁵ + $25000 × (1 + 4%)⁴

    + $25000 × (1 + 4%)³ + $25000 × (1 + 4%)² + $25000 × (1 + 4%)¹

    = $25000 × ( 1.04 + 1.04² + 1.04³ + 1.04⁴ + 1.04⁵ + 1.04⁶ )

    = $25000 × 1.04 × (1 + 1.04 + 1.04² + 1.04³ + 1.04⁴ + 1.04⁵ )

    = $25000 × 1.04 × (1 - 1.04⁶) / (1 - 1.04)

    = $172457.3620224

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