Answer: 2.56%

## 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.

Author: LeetQuiz .