2. Suppose that a forward contract on an asset is written at time zero and there are M years until delivery. Suppose that the proportional carrying charge in year k is qS(k), where S(k) is the spot price of the asset at the end of year k. Show that the forward price is where r is the risk-free interest rate and S is the current price of the asset. [Hint: 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 calculate how many units needed for each period.] 2. Suppose that a forward contract on an asset is written at time zero and there are M years until delivery. Suppose that the proportional carrying charge in year k is qS(k), where S(k) is the spot price of the asset at the end of year k. Show that the forward price is where r is the risk-free interest rate and S is the current price of the asset. [Hint: 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 calculate how many units needed for each period.]