Question

Asked Oct 29, 2019

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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 of Bernie Madoff is a more recent example.† Suppose the operator of a Ponzi scheme pays an initial return to investors of $21,000. 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.

R(t) =

(b)

How much must the operator pay to investors at the end of 3 years? (Round your answer to two decimal places.)

$

(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? (Enter a whole number of new investors.)

new investors

Step 1

Observe that in the initial return to investors of $21,000, 5 percent increment is already included, so if say x was the initial amount invested in the scheme, we will have

Step 2

So the initial investment was $20000,

Part a:

Since returns increase at a rate of 5% every month, we will use the formula for compound interest, with initial principal of $20000; rate of interest at 5% and duration of investment as t months, thus total returns after t months is calculated as shown:

Step 3

Part b:

3 years is same as 36 months so we plug the value of t=36 in the above formula...

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