10.3 Smith enters into a 1-year forward contract to sell an ounce of platinum two years from now. Today's price of platinum is 2000 per ounce and the delivery price is 2100. (a) Find the continuously compounded annual risk-free rate of interest for a one year maturity, assuming the contract is set up with no arbitrage opportunities. (b) Suppose that Smith does not own an ounce of platinum right now, but plans to purchase it in one year, and then in order to to complete the forward contract, Smith will immediately sell it at that time for 2100. Smith decides to buy a call option today with an expiry date of 1 year and a strike price of 2050. The price of the call option today is 80. Smith borrows 80 at the risk-free rate (found in part (a)) to buy the option. Suppose that the price of platinum at the end of the year is P. At the end of the year, after the forward contract and options contract expire, find Smith's gain for the year as a function of P