In a Ponzi scheme, where Ponzi promised investors a 50% profit within 45 days or a 100% profit within 90 days, how many investors would be required by the end of two and a quarter years with
The same promised return?

Question

Quizplus · Accepted Answer

A Ponzi scheme pays returns to its investors from the new capital paid to the operators by new investors, rather than from profit earned. In this scenario, to maintain the promised return of 100% profit within 90 days (or a quarter of a year), the scheme would need to double the amount of money invested every quarter. Over two and a quarter years (which equals 9 quarters), the money would need to double 9 times. Starting with a base of 1 (representing the initial investment), doubling 9 times is 2^9, which equals 512. However, since the question asks for the number of investors, not the total amount of investment, and assuming each investor contributes an equal share, the number of investors required would also follow this pattern. Thus, starting with 1 investor, to sustain the scheme for 9 quarters, you would need 2^9 investors, which equals 512. However, the correct calculation for the number of additional investors needed over the initial one to reach this total is 2^9 - 1, which equals 511 additional investors to the initial one, making the total count incorrect as per the provided options. The correct approach to answering the question directly from the options provided seems to have been misunderstood in the explanation. The focus should be on the total count as per the doubling pattern, which was initially calculated as 512, directly matching an option, but the explanation veered off. The correct interpretation should be straightforward: to sustain the scheme for 9 quarters, doubling the investment each quarter, you'd nominally need a total that doubles each quarter, leading to a misunderstanding in the explanation provided. The correct answer based on the options given and the initial doubling explanation should indeed be 512, but due to a misinterpretation in the explanation phase. The essence is that each quarter, the scheme requires double the previous total to pay out the promised returns, not specifically doubling the number of investors unless starting from one. The explanation mistakenly conflated the total amount needed with the number of investors directly, which in the context of the question's options, should align with the pattern of doubling per quarter, leading to a direct match with one of the provided choices without subtracting one.

In a Ponzi Scheme, Where Ponzi Promised Investors a 50