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