Answer-first summary for fast verification
Answer: $7.47
Here the storage cost is a **cash amount** paid quarterly in advance, so we add the present value of the storage costs to the spot price and then grow the total at the risk-free rate. Quarterly storage payment: \[ 0.64/4 = 0.16 \] For a six-month horizon, there are two payments: - at \(t=0\): \$0.16 - at \(t=0.25\): \$0.16\) discounted by \(e^{-0.04\times 0.25}\) Present value of storage costs: \[ PV = 0.16 + 0.16e^{-0.01} \approx 0.16 + 0.1584 = 0.3184 \] Then: \[ F_0 = (7.00 + 0.3184)e^{0.04\times 0.5} = 7.3184 \times e^{0.02} \approx 7.3184 \times 1.0202 \approx 7.47 \] **Correct answer: C. $7.47**
Author: Manit Arora
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Question-165.2. Assume the spot price of wheat is $7.00 per bushel. The storage cost is $0.64 per bushel per year payable quarterly in advance. The riskless interest rate curve is flat at 4.0% for all maturities (continuously compounded). What is the implied six-month futures price, F(0.5)?
A
$6.69
B
$7.28
C
$7.47
D
$7.58
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