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Profit maximization equation

  1. Apr 24, 2009 #1
    Hey guys

    I just came across this website i think its awsome..!!

    Hope i can contribute tooo!

    I had a question:

    If a Share costs 3 dollars, and it doubles every 3 months
    And nother share costs 1 dollar and doubles in One month

    How many shares of each would you buy with 1000 dollars, to gain the most profits in 6 months>?
     
  2. jcsd
  3. Apr 24, 2009 #2

    HallsofIvy

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    If you invest x dollars in the first, it would be worth [itex](x/3)2^{n/4}[/itex] dollars in n years. If you invest x dollars in the second it would be worth [itex]x(2^{n/12}}[itex].
    The ratio of those is
    [tex]\frac{1}{3}2^{n/4-n/12}= \frac{1}{3}2^{n/6}[/tex]
    For N= 6, that ratio is 2/3< 1. What does that tell you?
     
  4. Apr 27, 2009 #3
    Latex Image generator doesn't appear to be working so:

    The first gives an annual ROI of:
    (3*212/3)/3

    The second gives an annual ROI of:
    (1*212/1)/1

    You want the maxmimum amount of shares of the one that gives the largest ROI for 6months.
     
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