Answer: USD 755.65

The price of a 6-month futures contract on a stock index can be calculated using the formula for the forward price of a financial asset, which is given by: \[ F_0,T = S_0 e^{(r-q)T} \] where: - \( S_0 \) is the spot price of the asset (in this case, the stock index value). - \( r \) is the continuously compounded risk-free interest rate. - \( q \) is the continuous dividend yield on the asset. - \( T \) is the time until the delivery date in years. Given the information from the question: - The spot price of the stock index (\( S_0 \)) is USD 750. - The continuously compounded risk-free rate (\( r \)) is 3.5% per year. - The continuously compounded dividend yield (\( q \)) is 2.0% per year. - The time until delivery (\( T \)) is 0.5 years (since it's a 6-month contract). Plugging these values into the formula, we get: \[ F_0 = 750 e^{(0.035 - 0.02) \times 0.5} \] \[ F_0 = 750 e^{0.015 \times 0.5} \] \[ F_0 = 750 e^{0.0075} \] \[ F_0 = 750 \times 1.00756 \] (using a calculator for \( e^{0.0075} \)) \[ F_0 \approx 755.65 \] Therefore, the correct price of the 6-month futures contract is approximately USD 755.65, which corresponds to option B in the multiple-choice answers provided. This calculation ensures there is no arbitrage opportunity between the spot and futures markets, as the futures price reflects the cost of carrying the asset (in this case, the stock index) until the delivery date, adjusted for the risk-free rate and dividends.

Author: LeetQuiz Editorial Team