Answer: The implicit lease rate is 5.40%. Holding this rate constant, the forward market would be in backwardation if the annually compounded annual risk-free rate immediately fell to 5.0%.

The no-arbitrage relationship for an annually compounded commodity forward with lease rate \( l \) (also called the implicit lease rate or net convenience yield) is indeed: \[ F = S \times \frac{1 + r}{1 + l} \] Rearranged to solve for \( l \): \[ l = \frac{S \times (1 + r)}{F} - 1 \] **Precise calculation** (verified via direct computation): \( S \times (1 + r) = 42.47 \times 1.07 = 45.4429 \) \( \frac{45.4429}{43.11} \approx 1.054115 \) \( l \approx 0.054115 \) or **5.4115%**, which rounds to **5.41%**. FRM-style questions (and the official answer key) list this as **5.40%**, so we use the option value exactly as presented. This correctly eliminates options A and C. **Second part (rate falls to 5.0%, \( l \) held constant at 5.40%)** New theoretical forward price: \[ F_{\text{new}} = 42.47 \times \frac{1.05}{1.054} \approx 42.47 \times 0.9962 \approx 42.32 \] Since \( F_{\text{new}} < S \) (forward price below spot), the market is in **backwardation**. This occurs because the lease rate (benefit of holding the physical) now exceeds the risk-free rate (financing cost), producing a negative net cost of carry (\( r - l < 0 \)). **Contango vs. backwardation rule (FRM terminology)**: - \( r > l \) → positive net carry → \( F > S \) → **contango** - \( r < l \) → negative net carry → \( F < S \) → **backwardation** Your step-by-step logic, formulas (in KaTeX), and conclusion are spot-on. **Correct Answer: B**

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