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Math Help - profit question

  1. #1
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    profit question

    A company made $100,000 profit this year. If they anticipate that profits will increase by 6% a year going forward, how long will it take for the profits to double?
    A. Between 9 and 10 years
    B. Between 10 and 11 years
    C. Between 11 and 12 years
    D. Between 12 and 13 years
    E. None of the above

    I was able to solve the question using excel
    just wondering if there was some kind of equation in the case excel couldnt be used
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  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
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    Mauritius
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    This is a geometric progression, where the first term is 100 000, the second is 100 000(106/100) = 106 000, the thirs term 106 000(106/100) etc.

    It can be resumed as:

    P_n = 100 000 (\frac{106}{100})^n

    For the profit to double, you should have at least 200 000.

    200 000 = 100 000(\frac{106}{100})^n

    Solving for n,

    2 = (1.06)^n

    ln(2) = n ln(1.06)

    n = 11.9
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