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Re: Discount Rate of Multiple Cash Flows

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  • slim_the_dude
    ... and n , ... To find the equation you seek requires us to find the root of a high order polynomial. In the example you gave, there is at least one term
    Message 1 of 5 , Mar 31, 2008
      --- In mathforfun@yahoogroups.com, "settle2117" <acravenho@...> wrote:
      >
      > Wow you are amazing.
      >
      > Is it possible to create an equation that solves for "i" every time?
      >
      > This is what I have so far:
      >
      > PV= Present Value
      > MP= Monthly Payment
      > i= nominal interest rate
      > n= number of payments
      >
      > PV= MP*(1-(1/(1+i)^n))/i
      >
      > I need it to be:
      >
      > i=
      >
      > I will always have the following variables given "PV", "MP",
      and "n",
      > but "i" will never be given.
      >
      > I appreciate your time.

      To find the equation you seek requires us to find the root of a high
      order polynomial. In the example you gave, there is at least one
      term containing i^120, so we're talking a 120-degree polynomial. I'm
      not aware of any technique that will yield an algebraic solution.
      As far as I know, numerical analyis techniques must be used.

      In fact, the problem you pose is exactly what the IRR function in
      Microsoft Excel does. (IRR stand for "internal rate of return".)
      I'm pretty sure that Microsoft also uses numerical analysis
      techniques to do this.

      I should say that I'm not the most knowledgable person here in
      MathForFun, so maybe somebody else can speak to this, but I'll be
      surprised if there is any algebraic solution to your problem.
    • cino hilliard
      Solutions to linear,quadratic and cubic http://www.math.rutgers.edu/~erowland/polynomialequations.html The solution of a quartic
      Message 2 of 5 , Apr 1, 2008
        Solutions to linear,quadratic and cubic
        http://www.math.rutgers.edu/~erowland/polynomialequations.html

        The solution of a quartic
        http://mathworld.wolfram.com/QuarticEquation.html
        Notice the exponential increase in complexity of the analytic solutions of degree 2,3,4.
        Even if there was a general solution for degree n, the steps involved would be forboding asn becomes large. If a formula did exist, in my estimation the chances of making a mistake
        for degree 120 is 100%.

        Numerical solutions are crisp, clean and quick. The bisection method is no slouch and almost always guarantees convergence. Newton's method is much faster and convergeswell with polynomials. The accuracy doubles with each iteration. However, Newton'smethod can fail in many other functions and is problematic with functions that are difficultto differentiate.
        Discussion on quintic.
        http://mathworld.wolfram.com/QuarticEquation.htm
        References here lay to rest the notion of generality beyond degree 4.

        Here is a little gcc root finding routine using the bisection method
        http://docs.google.com/Doc?id=dgpq9w4b_1672ph7k6k


        Enjoy,
        Cino












        To: mathforfun@yahoogroups.comFrom: TimKelleyGroups@...: Tue, 1 Apr 2008 01:36:36 +0000Subject: [MATH for FUN] Re: Discount Rate of Multiple Cash Flows





        --- In mathforfun@yahoogroups.com, "settle2117" <acravenho@...> wrote:>> Wow you are amazing. > > Is it possible to create an equation that solves for "i" every time?> > This is what I have so far:> > PV= Present Value> MP= Monthly Payment> i= nominal interest rate> n= number of payments> > PV= MP*(1-(1/(1+i)^n))/i> > I need it to be:> > i= > > I will always have the following variables given "PV", "MP", and "n",> but "i" will never be given.> > I appreciate your time.To find the equation you seek requires us to find the root of a high order polynomial. In the example you gave, there is at least one term containing i^120, so we're talking a 120-degree polynomial. I'm not aware of any technique that will yield an algebraic solution. As far as I know, numerical analyis techniques must be used.In fact, the problem you pose is exactly what the IRR function in Microsoft Excel does. (IRR stand for "internal rate of return".) I'm pretty sure that Microsoft also uses numerical analysis techniques to do this.I should say that I'm not the most knowledgable person here in MathForFun, so maybe somebody else can speak to this, but I'll be surprised if there is any algebraic solution to your problem.







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