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Math Help - continous interest

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    continous interest

    The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously.
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    Quote Originally Posted by harry View Post
    The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously.
    You will not get much help with this as it is so obscurely worded that
    I suspect most of the helper don't understand what is being asked here.

    RonL
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by harry View Post
    The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously.
    CaptainBlack is right. I read this over and over to see if I was misreading the question. Anyway, I’ve decided to take a stab at it.

    So we start with $1000 and this money is decreasing exponentially. But then, it is gaining interest while it is decreasing. So the principle at any time is given by A(t) where:

    A(t) = 1000*e^-0.04t
    Now we will use this as the initial amount in the formula for continuous compounding at 6%, that is, use it as P0 in:

    P(t) = P0*e^0.06t

    =>P(t) = (1000*e^-0.04t)*e^0.06t
    ……...= 1000*e^0.02t

    => P(10) = 1000*e^0.02(10)
    ………...= 1000*e^0.2
    ……….~= 1221.40


    Does this make sense guys?
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