*We construct the model of a simple Ponzi scheme, deduce how long the scheme will last and when a rational promoter will skip town. *

Basically, most of the dead P2P platforms or asset management products we see in our daily lives are Ponzi schemes.

### Construct the Model of a Simple Ponzi Scheme

Generally speaking, there are only two kinds of participants in a Ponzi scheme: **promoters** who attract capital by promising incredibly high profits; and **investors** who pay money for above-average profits. Eventually, the promoters will run away when the funds are not enough to pay back every investor.

To simplify explanations, we assume that in a micro-society, a promoter has initiated a Ponzi scheme. The scheme **will not be forced to stop** due to the lack of regulators. It will **only collapse** when the promoter can no longer pay back the existing investors.

*Assuming that the rules of the project and the initial conditions of each party are as follows:*

## Promoter’s Intention

*They attract more funds in order to extend the life cycle of the Ponzi scheme and gain enough time to skip town.*

- Only use the funds from the new investors to pay back the existing investors;
- There is no monthly operating cost (such as labor and site costs) at all, while the comprehensive sales cost accounts for 3% of the scale of products in each term.

### Investment Target

*The funding game designed by the promoter to attract investors.*

- The term for the product is one month, with a monthly RoR of 5%; investors can only reinvest or withdraw their money at maturity;
- When the product matures every month, the withdrawal rate is 40%; those who choose not to withdraw will reinvest;
- There is only one product during each term.

### Investors

*Participate in the scheme for higher profits.*

- The per capita investment is 1,000 RMB;
- There are 100 investors initially;
- The monthly growth rate of participants is 5%.

*Accordingly, we can identify the key equations for calculating the income and cost in this experiment**：*

### Current Income

= Funds from new participants in the current period + Reinvested funds from the prior period

= The number of new participants * Per capital investment + Total funds from the prior period * (1 — Withdrawal Rate)

### Current Cost

= money paid to the existing investors in the current period + operating cost + sales cost

= Prior-period income * (1+ Monthly RoR) + Operating Cost + Current income * Sales cost rate

### Net Capital Inflow

= Current Income — Current cost

### Balance

= the sum of each period’s net capital inflow

Simulation: Cash Flow Table of the Ponzi Scheme

We can see that in the 22nd month, the balance of the promoter will be reduced to 0. In other words, the promoter is no longer able to pay back the investors. Therefore, the** Ponzi scheme will last for up to 22 months.**

However, given that the balance of funds **reaches its peak in the fifth month**, a rational promoter tends to **skip town** at this moment to** maximize **his or her own revenue, which is 213,759 RMB in this case.

We can see that in the 22nd month, the balance of the promoter will be reduced to 0. In other words, the promoter is no longer able to pay back the investors. Therefore, the** Ponzi scheme will last for up to 22 months.**

However, given that the balance of funds **reaches its peak in the fifth month**, a rational promoter tends to **skip town** at this moment to** maximize **his or her own revenue, which is 213,759 RMB in this case.

**Read “The Ponzi Scheme 101: A Ponzi’s Life Cycle and Ways to Survive, Part 2” here.**

this is great work. what i do not know is this, it seems to be a good platform to make money even though it is a scam. how do i withdraw everything early before the net capital inflow reaches zero