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Get familiar with the reaction system: Introducing the Reaction System

Algebra gurus

KornbreadKornbread
in Announcements
   There is a short ish' way of working this but I can't remember what it was or even what this is called.   

Comments

  • WolfWolf
    What are you trying to solve for?

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  • KornbreadKornbread
    Return of a 30yr bond held for 1 year. 
  • WolfWolf
    ...in the equation.

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  • a4eaudioa4eaudio
    Other than the last term in your eqution, that has an F rather than a cF, it is a finite geometric sequence. Ignoring the last term, you can factor the cF out and get P1 = x + x^2 + ... + x^n; which equals P1 = x (1 - x^n) / (1 - x). (I'm using P1 rather than P since this is a solution to only part of your equation.) See, mathworld.wolfram.com/GeometricSeries.html where the formula is the second from the bottom, where I have used x rather than r.

     

    Using my notation, x = 1 / (1+r) and some tedious algebra shows P1 = (1 - 1/(1+r^n))/r which is similar to the first term in this equation:

    where they have used C instead of cF, i instead of r and M instead of F. See, www.investopedia.com/university/advancedbond/bond-pricing.asp 

    Note, in your equation if you are given any 3 of your variables you can theoretically solve for the 4th. While you can solve algebraically for c, F or P you cannot solve for r algebraically if n>3 (or at least I think that is the case) because it is a non-linear and non-quadratic equation. 

    Solving algebraically means writing down an equation such that r = .... 

    That doesn't mean you can't solve for r, it just means you can't write down a simple equation. If you plugged in values for P, C and F in Excel you can use the "goal seek" tool in the "what if analysis" option under Data to solve for r, since it is a non-linear numerical algorithm.

    Hope that helps a little.
  • KornbreadKornbread
    That made my head hurt. 

    Found an online summation calculator that made life much easier.

    Thank you for the help.

    Working 7 days a week now.  Routine is work@4am, home@4pm, take dogs out (do not sit down or will fall asleep), shower, start on homework, wife gets home around 5pm and feeds me, bed around 9'ish -10'ish.

    Damn it Jr., wish I could quit work.              
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