7. A stock will pay a dividend of $1 in one month and $2 in four months. The risk-free rate of interest for all maturities is 12%. The current price of the stock is $90.
(a) Calculate the arbitrage-free price of (i) a three-month forward contract on the stock and (ii) a six-month forward contract on the stock.
(b) Suppose the six-month forward contract is quoted at 100. Identify the arbitrage opportunities, if any, that exist, and explain how to exploit them.
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