Answer-first summary for fast verification
Answer: $126.78
The correct answer is **A** ($126.78). The futures price for a commodity with known storage costs is calculated as: \[ f_0(T) = [S_0 + PV_0(C)] \times (1 + r)^T \] Where: - \( PV_0(C) \) is the present value of the storage cost, discounted from the settlement date to today. - \( S_0 \) is the spot price of the commodity. - \( r \) is the risk-free rate. - \( T \) is the time to settlement. For this question: 1. Calculate the present value of the storage cost: \[ PV_0(C) = \$5 \times (1 + 3\%)^{-182/365} \] 2. Plug into the futures price formula: \[ f_0(T) = [\$120 + PV_0(C)] \times (1 + 3\%)^{182/365} \] \[ f_0(T) = \$126.78 \] **Option B** ($126.86) is incorrect because it does not discount the storage cost to its present value. **Option C** ($126.93) is incorrect because it compounds the storage cost instead of discounting it.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
No comments yet.
An analyst gathers the following information:
$120 per barrel.$5 per barrel, payable at the end of the futures contract.Based on 365 days per year, the futures price per barrel of crude oil is closest to:
A
$126.78
B
$126.86
C
$126.93