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).