Answer: Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,496.

## Explanation To lock in the forward rate for the period from year 3 to year 4, we need to calculate the forward rate using the given spot rates with continuous compounding. ### Forward Rate Calculation Using the formula for forward rates with continuous compounding: \[ F = \frac{R_2T_2 - R_1T_1}{T_2 - T_1} \] Where: - R₁ = 3-year spot rate = 1.5% = 0.015 - T₁ = 3 years - R₂ = 4-year spot rate = 2% = 0.02 - T₂ = 4 years \[ F = \frac{0.02 \cdot 4 - 0.015 \cdot 3}{4 - 3} = \frac{0.08 - 0.045}{1} = 0.035 \text{ or } 3.5\% \] ### Interest Income Calculation Interest income = GBP 800,000 × 3.5% = GBP 28,000 However, with continuous compounding, we need to use: \[ \text{Interest} = 800,000 \times (e^{0.035} - 1) \] \[ \text{Interest} = 800,000 \times (1.03562 - 1) = 800,000 \times 0.03562 = \text{GBP 28,496} \] ### Required Transactions To lock in this forward rate, the treasurer should: - **Borrow at the 3-year spot rate** (1.5%) for 3 years - **Lend at the 4-year spot rate** (2%) for 4 years This creates a synthetic forward position that locks in the 3.5% forward rate for the period from year 3 to year 4. ### Why Other Options are Incorrect - **A and B**: GBP 28,119 would be the interest if using simple annual compounding (800,000 × 0.035 = 28,000), but the question specifies continuous compounding - **D**: Uses the wrong transaction strategy - lending at 3-year rate and borrowing at 4-year rate would not lock in the forward rate

Author: LeetQuiz .