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Help with simplification

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data

    solve for i

    4100=100{[(1+i)^22 - 1]/i(1+i)^22} + 5000[1/(1+i)^22]



    2. Relevant equations



    3. The attempt at a solution

    4100=100{/ i} + 5000[1/(1+i)^22]
    4100= 100+5000[1/i + 1/(1+i)^22]
    4100=5100[1/(1+ i)^23]
    0.803=[1/(1+ i)^23]
    (1+ i)^23= 1/0.803=1.24

    i= 23 sqrt(1.24) -1
     
  2. jcsd
  3. Jun 27, 2011 #2

    tiny-tim

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    hi cs23! :smile:

    (have a square-root: √ and try using the X2 icon just above the Reply box :wink:)

    sorry, not following that :confused:

    write 1+i in polar form (re), then you can immediately find (1+i)22 and 1/(1+i) :smile:
     
  4. Jun 27, 2011 #3

    gb7nash

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    Another trick is to substitute a = (1+i)^22. Solve for a. After that, finding i will become much easier.
     
  5. Jun 27, 2011 #4

    SammyS

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    In LaTeX that's: [tex]4100=100\frac{(1+i)^{22} - 1}{i(1+i)^{22}}+5000\frac{1}{(1+i)^{22}}[/tex]

    Following gb7nash's suggestion this becomes: [tex]4100=100\frac{a - 1}{i\cdot a}+5000\frac{1}{a}[/tex]
     
  6. Jun 27, 2011 #5

    gb7nash

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    Ah, I didn't notice that one i. My method won't work. :frown:
     
  7. Jun 27, 2011 #6

    SammyS

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    Well, it will make simplifying a little easier.


    ... maybe not much.
     
  8. Jun 27, 2011 #7

    SammyS

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    It probably needs to be done graphically or numerically.
     
  9. Jun 27, 2011 #8

    SteamKing

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    For clarification, you should state whether i = sqrt (-1) or if i represents an interest rate in some type of compounding interest problem.
     
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