Answer: 2.96.

## 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).

Author: LeetQuiz Editorial Team