Ponzi Scheme Math

I would like to see more depth in Sal's current lesson on Ponzi schemes, with numbers closer to what Ponzi and Madoff were actually using.

Specifically, I'd like to see realistic percentage returns in the examples given, and the inclusion of a "fee" for the fund operator. (They're not doing this for free, are they?)

Particularly interesting is the calculation of longevity, i.e. how long the scheme can operate and pay dividends to investors before the funds are depleted. Here is my simple calculation for this: 

Fund Longevity = (fund capital) / (number of investors) *( (dividends paid) + (fee charged) )

It is interesting to vary the size of the fund and number of investors and see the results. But most surprising is these schemes can last if they go undetected. You might mention and show a photo of Harry Markopolos as the guy who actually did the math and detected Madoff's Ponzi scheme.

Using the above formula, a small fund of just $1,500 with 100 investors, 12% annual return (what I read that Madoff was paying his investors), and 3% fee would last 100 years.

Now using Madoff's fund of $18B invested, with 4,800 investors and the same payouts and fees, the fund would last 25,000,000 years before depletion. Of course not all this was invested at one time, and many investors withdrew their investments at various times, so the amount of actual capital varied over the years.

The above formula could be made more interesting by including variables for periodic payouts, i.e. investors withdrawing their funds, new investors depositing funds, and for "growth" reinvested into the fund.