# Personal Wealth Model

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)

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.

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

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?

Yes that is so.

ok thank you