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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:
    A=Pert
    A=1000e(.05)(5)


    Case 2:
    P=P0ekt
    P=1000ekt

    Evaluate the amount at one year to solve for k.

    1000(1.05)=1050
    1050=1000ek(1)

    Solve for k.

    1050/1000=ek(1)
    k=ln(1.05)
    P=1000eln(1.05)t


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

    Redbelly98

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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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