Chapter 4.2, Problem 3E

Reminder Round all answers to two decimal places unless otherwise indicated.

Ponzi Schemes A Ponzi scheme is a fraudulent investment operation in which returns to investors are paid from funds collected from new investors rather than from profit earned by the operator. The scheme takes its name from the notorious operation of Charles Ponzi in $1920$. The case Bernie Madoff is a more recent example. Suppose the operator of a Ponzi scheme pays an initial return to investors of $ $20,000$. Each month, he must recruit enough new investors to increase the return by $5\%$.

a. Find a formula that gives the return R, in dollars, that the operator must pay after $t$ months.

b. How much money must the operator pay to investors at the end of $3$ years?

c. Assume that new investors pay $ $2000$ to join the scheme. How many new investors must be recruited at the end of $3$ years in order to pay the existing investors? Round your answer to the nearest whole number.