From its past behavior, John knows that the value of a stock has a cyclical component

Chapter 9, Problem 9.3.5

(choose chapter or problem)

From its past behavior, John knows that the value of a stock has a cyclical component that increases for the first three months of each year, falls for the next six, and rises again for the last three. In addition, inflation adds a linear component to the stocks price. John is seeking a model of the form f(t) = mt + b + A sin t 6 . with t in months since Jan 1. He has the following data: Date Jan 1 Apr 1 Jul 1 Oct 1 Jan 1 Price $20.00 $37.50 $35.00 $32.50 $50.00 (a) Find values of m, b, and A so that f fits the data. (b) During which month(s) does this stock appreciate the most? (c) During what period each year is this stock actually losing value?

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