Please show all work/explanations for the entire problem set.

1) An investor enters into a long position in 10 gold itures contracts at a futures price of $1000/oz and closes out the position at a price of $1020;r oz. If one gold futures contract is for 50 ounces: what are the investor's gains or losses? 2) Plutonium is trading at a oneyear futures price of $5,000 per gram. A futures contract comprises 100 grams. The initial margin is $100,000 and the maintenance margin is $80,000. You are short one futures contract. At which price per gram of plutonium will you incur a margin call? 3) An investor enters into a forward contract to purchase 100,000 shares of IBM stock in 2 4) 5) months at prices of $105 per share. After one month, the investor notes that the forward price for the same contract (which now has a onemonth maturity) is $103 per share. She also notes that the one-month interest rate is l % continuously compounded. What is the value of the forward contract held by the investor? An investor enters into a forward contract to buy 5,000 barrels of oil at $80 a barrel in three months. Two months later, suppose that the spot price for oil is $83 a barrel, and the one-month interest rate is l % continuously compounded. Assuming that there are no storage costs, what is the value of the contract the investor holds after two months? Stock B is trading at $1100. The risk-free rate is 1% continuously~compounded for all maturities and the dividend on the stock is $10 each quarter-end. What is the six-month forward price of the stock, assuming interest calculations are on a continuously compounded basis? 6) The spot price of gold is $1000 per 02. The one-year risk-free rate is 2% continuously compounded. There are no costs or benets of holding gold. If the one-year forward price of gold is $103, describe an arbitrage trading strategy that would allow you to prot. 7) If the stock market index is at a level of 1,120 and the one-year forward on the index is 1,210, calculate the implied repo rate in continuously-compounded terms (assuming zero dividends on the index). If you can invest money at a continuously compounded rate of 8%, describe an arbitrage trading strategy that would allow you to prot. 8) Consider 3 6X12 FRA where the underlying six-month period is 183 days and the notional is $100. The FRA xed rate is 5%. At maturity of the contract the underlying Libor for six months is 7%. What is the settlement amount on the FRA (recall that FRAs are settled in presentovalue)? Assume the Actual/360 convention. 9) You are given the following data concerning a 6>