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Continous Interest

  1. Jul 29, 2008 #1
    I was reviewing continous interest formulas when something stumped me.

    The accepted formula for continous interest is A=Pert, and the proof of it is simple enough to understand.

    However, my math book solves the formula in a different way. It starts with the standard model for growth rate, P=P0ekt, and than solves for k.

    Example: Determine how much money will exist in an account if Ed deposits 1000$ in an account with 5% interest for 5 years.

    Case 1:

    Case 2:

    Evaluate the amount at one year to solve for k.


    Solve for k.


    The growth constants are different in both cases. What is the cause of this?
  2. jcsd
  3. Jul 29, 2008 #2


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    In Case 1, you are letting 5%-per-year be the growth constant (the "r" in the exponent).
    This gives an annual yield (different than the growth rate) of
    e^0.05 - 1
    = 1.05127... -1
    = 0.05127... or 5.127...%

    In Case 2, you are saying the the annual yield (not the growth rate) is 5%.

    The 5% represents a different parameter in the two cases: it's the growth constant in Case 1, and it's the annual yield in Case 2.
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