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Compound interest using DE

  1. Nov 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Assume that Po dollars is deposited into an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous) find the amount in the account after T years.

    3. The attempt at a solution

    I have two differential equations, but I'm not sure which one will work:

    dp/dt= rP+200t

    Or,

    dp/dt = rP +200

    My first choice was the 1st one, but I searched the question on google, and people said that the DE is the second one. Can you tell me the correct equation, and explain why?
     
    Last edited by a moderator: Nov 9, 2012
  2. jcsd
  3. Nov 9, 2012 #2

    Ray Vickson

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    If B(t) is the balance at time t (that is, the amount in the account), look at what happens over the short time interval from t to t + Δt. How much money is withdrawn in time Δt? How much interest es earned in time Δt? What will be the new balance B(t+Δt) at time t + Δt?

    Working carefully through the details like that is the way to ensure getting the correct DE.

    RGV
     
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