Suppose that a forward contract on an asset is written at time zero and there are \(M\) periods until delivery. Suppose that the proportional carrying charge in period \(k\) is \(q S(k)\), where \(S(k)\) is the spot price of the asset in period \(k\). Show that the forward price is

[Consider a portfolio that pays all carrying costs by selling a fraction of the asset as required. Let the number of units of the asset held at time \(k\) be \(x(k)\) and find \(x(M)\) in terms of \(x(0)\).]

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F= (1-9)-MS d(0,M)