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Math Help - Dear Math Help Forum, How long will it take to double?

  1. #1
    Junior Member
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    May 2008
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    Dear Math Help Forum, How long will it take to double?

    Hi I'm stuck on this question:

    An investment grows at a continuous 12% rate per year. In how many years will the value of the investment double?

    I'm getting a weird decimal number .776

    Can anyone suggest a method I can use to calculate the time of a continuously growing investment?

    Thanks,
    Kataangel
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  2. #2
    Junior Member
    Joined
    Nov 2009
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    Try to make a formula for it, like

    For instance you have 100 dollar

    after one year you will have; 100*1.12 = 112
    after two years you will have; 112*1.12 = 100*1.12*1.12= 100* (1.12)^2=...

    after x years you will have; 100*(1.12)^x=....

    Now you have to end with 200 dollars in this case. Can you finish the formula?
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  3. #3
    MHF Contributor
    Joined
    Mar 2007
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    1,240

    Talking

    Use the continuously-compounded formula they gave you. Whatever the original amount P was, you are given that A = 2P, so just use P = 1 and A = 2. Plug in the value they've given you for r (or k). Then solve for t.
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