Explanation:

The effective duration of the liabilities is calculated using the formula:

$\text{Effective Duration} = \frac{(PV_{-} - PV_{+})}{(2 \times \Delta \text{Curve} \times PV_{0})}$

Where:

• $PV_{-}$ is the present value of liabilities when the interest rate decreases by 0.5% (198 million).
• $PV_{+}$ is the present value of liabilities when the interest rate increases by 0.5% (174 million).
• $PV_{0}$ is the present value of liabilities at the current interest rate (186 million).
• $\Delta \text{Curve}$ is the change in the benchmark yield curve (0.5%).

Plugging in the values:

$\text{Effective Duration} = \frac{(198 - 174)}{(2 \times 0.005 \times 186)} = \frac{24}{1.86} \approx 12.9$

Why Option B is Correct: The calculation correctly uses a 0.5% change in the benchmark yield curve and the appropriate formula for effective duration. The result is approximately 12.9.

Why Other Options Are Incorrect:

• Option A (6.5): Incorrectly uses a 1% change in the benchmark yield curve instead of 0.5%.
• Option C (25.8): Uses an incorrect formula for effective duration, omitting the factor of 2 in the denominator.