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Personal Wealth Model

  1. May 19, 2008 #1
    Most people have an income that comes from 2 sources: salary and personal investements. From thies income, 'necessary' expenses (housing, food) are paid; some money is spent on 'luxuries' and the rest is saved (increasing investments).

    Given that income must equal outflow, show the steps in developing the following mathematics model for a person's wealth at any time t:

    dW/dt = (1-p)(s-n+rW)

    Where s = your salary
    W(t) = your wealth (savings), which is a function of time
    r = rate of interest on your wealth (savings)
    n = amount spent on necesseties
    p = proportion of your income after necesseties that you spend on luxuries

    My question is how do I get this model... I have no idea and it is starting to irritate me as this is due in a couple of days.
  2. jcsd
  3. May 19, 2008 #2


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    Homework Helper

    You have to group the expenditures together, and the money inflow together. Note that p is something you factor in only when everything else has been included, judging by the description of p.

    Expenditures: n(this is a fixed value, not proportion of income or anything else), (1-p)*X(proportion of income after deducting amount spent on necessities and X refers to everything else after you've included all factors)

    Inflow: s(salary), rW(this is interest rate on your savings).

    dW/dt = Inflow - expenditures
  4. May 19, 2008 #3
    ok i understand that to some extent.

    so dW/dt= inflow - expenditures
    = s + rW - n

    Then I am guessing as it is a model to show someones wealth at any time t, we must multiply this by (1-p) as this represents the money we save.

    Does this make sense or am I on the wrong track?
  5. May 19, 2008 #4


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    Homework Helper

    Yes that is so.
  6. May 19, 2008 #5
    ok thank you
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