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Calculating Reverse Compund interest

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  • #1

    Calculating Reverse Compund interest

    Hi, can somebody help me with this very simple problem,

    I have shares costing £3, in 6 years time they are worth £4.41. They have therefore increased by 1.41 over 6 years.

    At a glance it might appear as if it's increased by 7.8% per year but that would be incorrect, as the compound effect means that in reality it's increased by 6.6% per year.

    I can tell this by trial and error working it out.

    But could somebody provide me with the formula to get their quicker

    Cheers
    Matt
    Up The Millers
    Tags: None
  • #2
    If you assume it's compounded continuously, you get a simple differential equation, with a simple solution for the price of the share: S = S0exp(r*t). That means r = ln(S/S0)/t.
    "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
    -Bokonon

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    • #3
      It would also be nice if you said what all of the symbols mean...
      You just wasted six ... no, seven ... seconds of your life reading this sentence.

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      • #4
        The natural meanings given the problem.

        r is the interest rate, t is the time, S0 is the initial value, S is the final value.
        "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
        -Bokonon

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        • #5
          Originally posted by Ramo
          If you assume it's compounded continuously, you get a simple differential equation, with a simple solution for the price of the share: S = S0exp(r*t). That means r = ln(S/S0)/t.
          In this case, you should assume an interval of one year. IOW, interest is added at the end of each year.
          (\__/) 07/07/1937 - Never forget
          (='.'=) "Claims demand evidence; extraordinary claims demand extraordinary evidence." -- Carl Sagan
          (")_(") "Starting the fire from within."

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          • #6
            Does this equation allow for leap years?

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            • #7
              In this case, you should assume an interval of one year. IOW, interest is added at the end of each year.


              I wasn't sure how many times he wanted interest compounded annually. Continuous compounding is so much cleaner.

              If you're having annual compounding, S = So*(1 + r)^t. So r = (S/So)^(1/t) - 1.
              "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
              -Bokonon

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              • #8
                Originally posted by Ramo
                In this case, you should assume an interval of one year. IOW, interest is added at the end of each year.


                I wasn't sure how many times he wanted interest compounded annually. Continuous compounding is so much cleaner.
                While that looks good mathematically, nobody does that in real life.
                (\__/) 07/07/1937 - Never forget
                (='.'=) "Claims demand evidence; extraordinary claims demand extraordinary evidence." -- Carl Sagan
                (")_(") "Starting the fire from within."

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                • #9
                  We learned the equations for compound interest in 7th grade, but I don't remember them anymore).
                  Christianity: The belief that a cosmic Jewish Zombie who was his own father can make you live forever if you symbolically eat his flesh and telepathically tell him you accept him as your master, so he can remove an evil force from your soul that is present in humanity because a rib-woman was convinced by a talking snake to eat from a magical tree...

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                  • #10
                    FV = P(1 + r)n

                    FV = future value
                    P = starting principle
                    r = rate of return
                    n = time

                    edit: formula fixed
                    Last edited by chequita guevara; May 25, 2005, 19:23.
                    Christianity: The belief that a cosmic Jewish Zombie who was his own father can make you live forever if you symbolically eat his flesh and telepathically tell him you accept him as your master, so he can remove an evil force from your soul that is present in humanity because a rib-woman was convinced by a talking snake to eat from a magical tree...

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                    • #11
                      Originally posted by chegitz guevara
                      FV = P(1 + r)n

                      FV = future value
                      P = starting principle
                      r = rate of return
                      n = time
                      The "n" should be an exponent, not a simple multiplier.
                      "The French caused the war [Persian Gulf war, 1991]" - Ned
                      "you people who bash Bush have no appreciation for one of the great presidents in our history." - Ned
                      "I wish I had gay sex in the boy scouts" - Dissident

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                      • #12
                        Hi,
                        Thank you for your kind replies.

                        It was the annual I was after, i didnt see it in time before I left although i used the Continual compounding Ramo posted, which allowed me to get close enough to the Annual compounding by trail & error.
                        Cheers
                        Up The Millers

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                        • #13
                          Hey Boddingtons, I mean Worthingtons.
                          One day Canada will rule the world, and then we'll all be sorry.

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                          • #14
                            I don't think he's Bodds... no record in the name change log.

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                            • #15
                              Can you say DL.
                              One day Canada will rule the world, and then we'll all be sorry.

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