James P Houghton

# Endowments 0 - Model

07 Sep 2013

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.