Suppose you are a nonprofit organization with modest financial needs, and have just set up an endowment of $5000. You'd like to know how well your organization will fare over time, and so you set up a model of your account. You model the balance, plus the rate at which interest is collected, and the rate of withdrawal:

Interest Rate = .05

Withdrawal Rate = 0

Interest Earned = Interest Rate * Balance

Withdrawals = Withdrawal Rate

Balance = Balance + Interest - Withdrawal

Here's an animated diagram showing the same model with with interest rate fixed at 5% annual, and no withdrawals. As we expect, we see the balance grow exponentially.

When we add a $100 yearly withdrawal, the result is qualitatively similar, although the final balance after 50 years reaches only about 70% of its value with no withdrawals:

If we withdraw $250 per year, we are essentially taking all the interest, and the balance stays fixed at $5k:

If we draw even more - say $275 - the balance falls and eventually goes negative, to the point where we're borrowing money (at 5%) to make the withdrawals.

Now, the point of this post wasn't to give a lecture on exceeding your income, but to set up a very simple model that we could use in the next post to explore the ideas of Monte Carlo simulation.