Let's look at a 7% per week, 3,300% per year scheme, i.e. one with an extremely high advertised yield.
Its debt grows at an exponential rate, but the debt plays only an indirect role here. What really matters to the Ponzi scheme operator is the heap of money he is amassing.
Initially this heap grows, as new "investors" pay in. The 7% per week interest rate aims at people who calculate (just barely, because they are math-challenged) that they can get rich quick by paying in a moderate amount, if they compound their interest. This is exactly what the Ponzi operator wants.
As the Ponzi scheme becomes more popular, more people "invest", so the money heap keeps growing at first.
Then, however, as "investors" see their imagined wealth grow exponentially, a few of them are bound to withdraw some money for one reason or another. One reason could be that somebody wants to buy a car or a house, but they also believe that they will get even richer if they delay their purchase and keep riding the exponential curve.
Another group of "investors" who withdraw money do it for one of two possible reasons:
- They become weary, because they begin to see the risk and try to withdraw, as long as that is still possible.
- They calculate that they could reduce their risk to zero if they withdraw at least their original investment. Some may also regularly withdraw some of their interest and let another part of it compound, reckoning that this is a slower, but safer way to get rich.
The unpleasant fact for the Ponzi operator is that this group of withdrawers, even though it is small, still creates an exponentially growing flow of withdrawals. Exponential growth means that, sooner or later, these withdrawals will grow beyond the inflow of newly "invested" money, so his heap of money will begin to shrink.
This is when an intelligent Ponzi operator will shut down operations and disappear with the money. Of course the point in time is difficult to determine with any precision, as both new "investments" and withdrawals have a random component. There is always the hope for another big "investor", there are ups and downs on both sides, there is hope, self-overestimation, pride, and, most of all, greed. A Ponzi scheme operator has to deal with his own personality defects as well as the day-to-day problems of running the scheme, convincing "investors", keeping associates happy, covering his tracks, prepare for his escape, etc. He may make mistakes.
But even if he delays the end, it is still inevitable. You cannot fight an exponential curve forever. He could lower the interest, delay payments, invent excuses for changing the rules, try to reassure investors and associates, spread confusing information, which would all be signs of the coming termination of the scheme, but this can only go on for a short time. At last, when he sees his heap of money shrink week after week, he has to shut down and disappear.
Carlos Ponzi did not have this choice. He believed in his own scheme. His mathematical abilities were very limited. He ran it to the bitter end. I do think the modern Ponzi scheme operators are somewhat stupid, because if they were as intelligent as they probably believe to be, why then would they have to resort to criminal means? They could instead earn good amounts of money legally, which is not that difficult. But they are not as stupid as Carlos Ponzi. Unlike that guy, they will not give up all the money they have amassed at the height of their schemes.
So when will our current, most popular one end? I cannot be sure, but exponential growth sets tight limits. Nobody can tell whether some biggish "investor" suddenly turns up and extends the scheme by another month. But it seems unlikely, because big investors are usually not that stupid either. There are also not that many potential "investors" out there, because the active bitcoin users are all here in the forum, have already heard of the scheme, and have made their decision to "invest" or stand back. Where should new "investors" come from?
So here is my prediction. Short of the big miracle "investor", the scheme may well end within very few weeks from now. Anyway, it is extremely unlikely to continue for the rest of this year at current interest rates, as you can easily calculate.