Explanation

To calculate the price of a stock index futures contract, we use the formula:

$\text{Futures price} = S_0 \times \left[\frac{(1 + r)}{(1 + q)}\right]^T$

Where:

• $S_0$ = Current spot price = USD 3,200
• $r$ = Risk-free interest rate = 1.80% = 0.018
• $q$ = Dividend yield = 2.40% = 0.024
• $T$ = Time to maturity = 6 months = 0.5 years

Substituting the values:

$\text{Futures price} = 3,200 \times \left[\frac{(1 + 0.018)}{(1 + 0.024)}\right]^{0.5}$

$\text{Futures price} = 3,200 \times \left[\frac{1.018}{1.024}\right]^{0.5}$

$\text{Futures price} = 3,200 \times \left[0.99414\right]^{0.5}$

$\text{Futures price} = 3,200 \times 0.99707 = 3,190.61$

This rounds to approximately USD 3,191, which matches option B.

Why other options are incorrect:

• A (USD 3,181): This would be the 1-year futures price calculation
• C (USD 3,209): This occurs when the interest rate and dividend yield are reversed in the formula
• D (USD 3,229): This happens when the dividend yield component is omitted from the calculation