Explanation

To calculate the 2-year implied spot rate from forward rates, we use the relationship between spot rates and forward rates:

For a 2-year spot rate (S₂), we can derive it from the 1-year forward rates:

(1 + S₂)² = (1 + f₀,₁) × (1 + f₁,₂)

Where:

• f₀,₁ = 0y1y forward rate = 2.31% = 0.0231
• f₁,₂ = 1y1y forward rate = 2.82% = 0.0282

Plugging in the values:

(1 + S₂)² = (1 + 0.0231) × (1 + 0.0282) (1 + S₂)² = (1.0231) × (1.0282) (1 + S₂)² = 1.0520

Now take the square root: 1 + S₂ = √1.0520 = 1.0256

S₂ = 1.0256 - 1 = 0.0256 = 2.56%

Verification:

• The 2-year spot rate (2.56%) is lower than the 1y1y forward rate (2.82%) because the first year's rate (2.31%) pulls down the average.
• The 2-year spot rate represents the geometric average of the two 1-year forward rates.

Why not the other options:

• B (2.82%): This is simply the 1y1y forward rate, not the 2-year spot rate.
• C (2.89%): This would be an arithmetic average or incorrect calculation of the geometric mean.

Therefore, the correct answer is A. 2.56%.