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Answer: USD 4,855
## Explanation The value of a long forward contract is calculated as: \[ V = (F_t - F_0) \times e^{-r(T-t)} \times \text{Quantity} \] Where: - \( F_t \) = current forward price = USD 1,050 - \( F_0 \) = original forward price = USD 1,000 - \( r \) = risk-free rate = 4% per year - \( T-t \) = time remaining = 9 months = 0.75 years - Quantity = 100 ounces \[ V = (1,050 - 1,000) \times e^{-0.04 \times 0.75} \times 100 \] \[ V = 50 \times e^{-0.03} \times 100 \] \[ V = 50 \times 0.9704 \times 100 \] \[ V = 4,852 \] The closest value is USD 4,855 (Option B).
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Three months ago a company entered in a one-year forward contract to buy 100 ounces of gold. At the time, the one-year forward price was USD 1,000 per ounce. The nine-month forward price of gold is now USD 1,050 per ounce. The annually-compounded risk-free rate is 4% per year for all maturities, and there are no storage costs. Which of the following is closest to the value of the contract?
A
USD 5,000
B
USD 4,855
C
USD 7,955
D
USD 1,897
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