Answer: USD755.65

The correct answer for pricing a 6-month futures contract on a stock index, given the current index value of USD 750, a continuously compounded risk-free rate of 3.5% per year, and a continuously compounded dividend yield of 2.0% per year, is USD 755.65. This is calculated using the formula for the forward price on a financial asset: \[ F_{0,T} = S_0 \cdot e^{(r-q)T} \] where: - \( S_0 \) is the spot price of the asset (USD 750 in this case), - \( r \) is the continuously compounded risk-free interest rate (0.035 or 3.5%), - \( q \) is the continuous dividend yield on the asset (0.02 or 2.0%), - \( T \) is the time until delivery date in years (0.5 for 6 months). Plugging in the values, we get: \[ F_0 = 750 \cdot e^{(0.035 - 0.02) \cdot 0.5} = 755.65 \] This formula accounts for the cost of carry (the risk-free rate) and the income from the asset (the dividend yield) over the period until the contract's delivery date. The other options provided in the question are incorrect due to misapplications of the formula, such as using the wrong order of subtraction for \( r \) and \( q \), or not applying the formula correctly.

Author: LeetQuiz Editorial Team