Explanation

To calculate the no-arbitrage forward rate for a 6 × 12 FRA (which covers the period from 180 days to 360 days), we use the formula:

$$(1 + r_{360} \times \frac{360}{360}) = (1 + r_{180} \times \frac{180}{360}) \times (1 + f_{6×12} \times \frac{180}{360})$$

Where:

• r_{180} = 2.00% (180-day spot rate)
• r_{360} = 2.50% (360-day spot rate)
• f_{6×12} = forward rate we're solving for

Substituting the values:

$$(1 + 0.025 \times 1) = (1 + 0.02 \times 0.5) \times (1 + f_{6×12} \times 0.5)$$ $$1.025 = (1 + 0.01) \times (1 + 0.5f_{6×12})$$ $$1.025 = 1.01 \times (1 + 0.5f_{6×12})$$ $$1 + 0.5f_{6×12} = \frac{1.025}{1.01} = 1.014851$$ $$0.5f_{6×12} = 0.014851$$ $$f_{6×12} = 0.029702 = 2.9702\%$$

The calculated forward rate is approximately 2.97%, which is less than 3.00%. Therefore, the correct answer should be A (less than 3.00%).

Note: The original answer provided in the text appears to be incorrect based on the calculation.