Reference no: EM13913213

Rosalind Setchfield's story shows how the process begins. The Yuma, Ariz., resident won $1.3 million in a 1987 Arizona lottery drawing, to be paid in 20 annual installments of $65,276.79. But in 1989, her husband, a construction worker, suffered serious injuries when a crane dropped a heavy beam on him. The couple's medical expenses -- and debt -- mounted. Six years later, in early 1995, a Singer salesman phoned Mrs. Setchfield with a promising offer. Singer would immediately give her $140,000 for one-half of each of her next nine prize checks, an amount equal to 48% of the $293,745.60 she had coming over that period. The windfall was made possible by Enhance Financial Services Group, a large municipal-bond reinsurer in New York that at the time was Singer's only customer. Enhance had instructed Singer to buy this and other prizes at a substantial discount and then arrange to have lotteries send Enhance the prize payments, or partial payments, that would otherwise be mailed to winners. Enhance had determined that it would pay $196,000 for the stake Singer acquired from Mrs. Setchfield for $140,000. To arrive at its price, the Enhance Group's treasurer calculated the return the company wanted to earn -- then about 9.5% interest, compounded annually -- and applied that rate in reverse to the $293,745.60 sum Enhance stood to collect over nine years. For bringing Mrs. Setchfield and Enhance together, Singer earned $56,000, keeping 29% of what Enhance offered. ------- Calculate the implied interest rate on the transaction between Rosalind Setchfield and Singer Asset Finance Co. as described in the article. Assume annual compounding and annual payments. Note that half of her annual lottery payment is $65,276.79/2 = $32, 638.40, and $32,638.40 times nine payments equals $293,745.60. For your answer, show the basic set up of the problem and the solution.