Explanation

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

Formula: $(1 + S_2)^2 = (1 + f_{0,1}) \times (1 + f_{1,2})$

Where:

• $S_2$ = 2-year spot rate
• $f_{0,1}$ = 0y1y forward rate = 2.31%
• $f_{1,2}$ = 1y1y forward rate = 2.82%

Calculation:

1. Convert percentages to decimals:
   • $f_{0,1} = 0.0231$
   • $f_{1,2} = 0.0282`$2. Calculate the product: $$(1 + 0.0231) \times (1 + 0.0282) = 1.0231 \times 1.0282 = 1.05196$$3`. Solve for$S_2: $$(1 + S_2)^2 = 1.05196$$ $1 + S_2 = \sqrt{1.05196} = 1.02564$$S_2 = 0.02564 = 2.564%$$

Result: The 2-year implied spot rate is approximately 2.56%, which corresponds to option A.

Why not the other options?

• Option B (2.82%): This is simply the 1y1y forward rate, not the 2-year spot rate.
• Option C (2.89%): This would be the average of the forward rates, but spot rates are calculated geometrically, not arithmetically.