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Math Help - Differential Equation for Continuously Compounded Interest

  1. #1
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    Differential Equation for Continuously Compounded Interest

    How do I use differential equations to get

    dM/dt = r(t)M(t)

    to equal to

    M = E.e^[-(integral from T to t) of r(s)ds]

    Where r is the continuous compounded interest which is a function of t and E= M(t) and theT represents some future time.

    Where did the ds come from or the r(s) for that fact
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  2. #2
    A Plied Mathematician
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    The r(s) and the ds both come from being "dummy" variables. What you're doing here to solve the problem is separating the variables: divide both sides by M(t), and then integrate w.r.t. t. The integral on the RHS is equivalent to an indefinite integral w.r.t. t.

    Does that make sense?
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  3. #3
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    Ahhhhh Yeah I see how it's done THANKS a lot!
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  4. #4
    A Plied Mathematician
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    You're welcome!
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