Answer: USD 755.65

## Explanation The correct futures price is calculated using the formula for pricing futures on assets with continuous dividend yields: \[ F_{0,T} = S_0 \times e^{(r - q)T} \] Where: - \( S_0 = 750 \) (current spot price) - \( r = 0.035 \) (continuously compounded risk-free rate) - \( q = 0.02 \) (continuously compounded dividend yield) - \( T = 0.5 \) (6 months = 0.5 years) \[ F_0 = 750 \times e^{(0.035 - 0.02) \times 0.5} = 750 \times e^{0.015 \times 0.5} = 750 \times e^{0.0075} = 750 \times 1.007528 = 755.65 \] **Why other options are incorrect:** - **A (USD 744.40)**: Uses \( F_{0,T} = S_0 \times e^{(q - r)T} = 750 \times e^{(0.02 - 0.035) \times 0.5} = 744.396 \) - incorrectly reverses the (r - q) term - **C (USD 761.33)**: Uses \( F_{0,T} = S_0 \times e^{(r - q)} = 750 \times e^{(0.035 - 0.02)} = 761.3348 \) - omits the time component T - **D (USD 763.24)**: Uses \( F_{0,T} = S_0 \times e^{(r)T} = 750 \times e^{0.035 \times 0.5} = 763.2405 \) - ignores the dividend yield entirely This calculation demonstrates the cost-of-carry model for futures pricing, where the futures price equals the spot price adjusted for the net cost of carry (risk-free rate minus dividend yield).

Author: LeetQuiz .