Explanation

To find the forward value of an existing futures contract:

Formula: $V_t = \frac{F_t - F_0}{(1 + r)^{T-t}}$

Where:

• $V_t$ = Value of forward contract at time t
• $F_t$ = Current forward price
• $F_0$ = Original forward price = 104
• $r$ = Risk-free rate = 3% = 0.03
• $T-t$ = Remaining time = 6 months = 0.5 years

First, calculate the current forward price $F_t$: $F_t = S_t \times (1 + r)^{T-t}$ $F_t = 107 \times (1 + 0.03)^{0.5}$ $F_t = 107 \times 1.014889$ $F_t = 108.59$

Now calculate the forward value: $V_t = \frac{108.59 - 104}{(1 + 0.03)^{0.5}}$ $V_t = \frac{4.59}{1.014889}$ $V_t = 4.52$

Wait, let me recalculate more precisely: $(1.03)^{0.5} = 1.0148891565$ $F_t = 107 \times 1.0148891565 = 108.592$ $V_t = \frac{108.592 - 104}{1.0148891565} = \frac{4.592}{1.0148891565} = 4.523$

The calculated value of 4.523 is closest to 2.96? Let me double-check:

Actually, the correct calculation should be: $V_t = (F_t - F_0) \times (1 + r)^{-(T-t)}$ $V_t = (108.592 - 104) \times (1.03)^{-0.5}$ $V_t = 4.592 \times 0.9853$ $V_t = 4.524$

I apologize - there seems to be a discrepancy. Let me recalculate with proper precision:

$(1.03)^{0.5} = 1.0148891565$ $(1.03)^{-0.5} = 0.985329$ $F_t = 107 \times 1.0148891565 = 108.593$ $V_t = (108.593 - 104) \times 0.985329 = 4.593 \times 0.985329 = 4.525$

This gives 4.525, which is closest to 4.53 (Option C).