There are two popular public opinions about Bitconnect. One is that it is a traditional dollar ponzi scheme and thus will not last long term. Another, is that it can be sustained because it is different from a traditional ponzi scheme. The traditional ponzi scheme argument uses history to validate the argument. While the argument that Bitconnect will last uses cryptocurrency and not history to validate it's argument. I will start off with why i think that traditional ponzi schemes do not work, then i will state why i think Bitconnect can last a long time. I will follow these statements with mathematical models for why i think Bitconnect can potentially change the way we view ponzi schemes. 

Traditional ponzi schemes don't work

Dan has 100 dollars 

Joe says to Dan that if he gives him the 100 dollars he will give him 25 percent interest every month and pay him back fully in 4 months.

Joe has no other investors and is relying on getting other investors to pay Dan back. Thus, to continue the ponzi scheme, Joe would have to continue to grow his investor base at a rate faster then he accepts new money.

Joe has been succesful and has 800 dollars and has paid Dan in full. 

Assuming 8 investors all gave Joe 100 dollars at the same time, Joe owes his investors 1,953 dollars in 4 months assuming they all reinvest there interest every month ( This calculation can be found using a financial calculator and in putting Months 4, interst per month 25 percent, 800 dollars invested at beginning period.) In order to pay these investors the 1,953 dollars they are promised Joe would have to collect 1,153 dollars of new money in 4 months(1953-800). It now becomes easy to see that simply one bad 4 month period can make a ponzi scheme collapse, and that is not even accounting for if Joe took money for himself. It doesn't matter if its a billion dollar ponzi scheme or an 100 dollar traditional ponzi scheme, if either has just one un lucky short term period it can collapse. 

Bitconnect is different from a traditional ponzi scheme

    The important difference that seperates Bitconnect from a traditional ponzi scheme is that they issue their own currency. Traditional ponzi schemes are collected in dollars that do not add value over time. While, Bitconnect may be a ponzi scheme that  makes profit by it's native coin adding value over time through laws of supply and demand. I will now present important facts and make assumptions to help simplify things and explain my point.

Important facts 

1. We need Bitconnect coins to make a loan.

2. When the loan term is over Bitconnect pays us back in dollars not Bitconnect coins.

3.  Bitconnect's highest gauranteed interest rate is around 7.5 percent per month.

Now i will make the following assumptions to create a case.

4. The price of one Bitconnect coin was around 45 cents when originated.

5. The price on 7/16/2017 of one Bitconnect is around 47 dollars.

Assumptions

1. There is a fixed supply of 10 million Bitconnect coins and they all cam to existence when Bitconnect started operating.  (Not true, but necessary to simplify)

2. The 10 million coins were all bought at 45 cents and were all used to lend on the platform at the same time. Thus, there was no speculation. Every Bitconnect coin that is bought is used to lend not speculate. (Not true, but necessary to simplify)

3. Every 24 hours there are only 150,000 Bitconnect tokens allowed to trade(10 million *1.5 percent- 1 percent for interest, .5 percent for principle on average)

4. Bitconnect is lending at a rate of 1 percent per day.

5. All loan contracts end in 200 days. 

6. If the price of Bitconnect goes above the rate that investors are owed Bitconnect takes 40 percent as profit.

7. All investors are reinvesting for 200 days and not selling Bitconnet coins. 

8. There is no bot that trades bitcoin but there is a bot that tracks the price of bitcoin to figure out interest rates because higher volatility equals a better chance for gretter demand of lending coins.

9. There is a bot that automates the payments and only pays when it owes the money. 

10. The creators of bitconnect can access Bitcoins that the users have in their accounts. 

11. The value of their stake in Bitconnect coin will always be greater then the value of their customers Bitcoin accounts. 

In 200 days assuming the price was 45 cents per Bitconnect, there were 4.5 million dollars worth of loans(.45*10 mil).

In 200 days assuming everyone reinvests their interest payments, the Bitconnect bot will owe everyone 32,922,080 dollars.(Financial calculator- 200 days, 1 percent interest per day, 4500000 dollars present value). Assuming the price of Bitconnect stays fixed at 47 dollars per coin. The bot will have 470,000,000 dollars worth of coins to pay the customers out. After paying investors out the bitconnect bot will have 437,077,920 (470000000-32922080) dollars worth of coins at current market rates and no obligations to pay back any more investors. Bitconnect can easily afford to take 174,831,168(437,077,920*.4) to use to pay for marketing and salaries expense. And the remaining 262,246,752(437,077,920*.6) dollars will remain with the bot as insurance in case the price goes down so Bitconnect can remain solvent just in case demand stays contant or goes down.

How long can Bitconnect pay 30 percent interest if the price of bitconnect stays at 47 dolars?

investors would be able to lend 4,420,282 coins worth 207,753,254 to the bot. The bot would then have 470,000,006(207,753,254+262,246,752) dollars. The bot would continue to be able to pay the interest payment for 226 days not including the principle payment (470000000/20077532). It is however very likely that if the price did not change that by day 80 or so Bitconnects Volatility software would probably indicate that the price of Bitcoin is stable which is why people are not lending as much, and the interest rate will become much lower to sustain the constant demand for periods of years. 

Disclaimer: I am long Bitconnect. This is not investment advice.