Answer: 2.50%

## Explanation The 2-year implied forward rate in one year's time (denoted as $f_{1,2}$) can be calculated using the relationship between spot rates and forward rates. ### Formula: The relationship between spot rates and forward rates is given by: $(1 + z_3)^3 = (1 + z_1)^1 \times (1 + f_{1,2})^2$ Where: - $z_1$ = 1-year spot rate = 1.50% = 0.015 - $z_3$ = 3-year spot rate = 2.25% = 0.0225 - $f_{1,2}$ = 2-year forward rate starting in 1 year ### Calculation: $(1 + 0.0225)^3 = (1 + 0.015)^1 \times (1 + f_{1,2})^2$ $(1.0225)^3 = (1.015) \times (1 + f_{1,2})^2$ $1.0690 = 1.015 \times (1 + f_{1,2})^2$ $(1 + f_{1,2})^2 = \frac{1.0690}{1.015} = 1.0532$ $1 + f_{1,2} = \sqrt{1.0532} = 1.0263$ $f_{1,2} = 0.0263 = 2.63%$ Wait, let me recalculate more precisely: $(1.0225)^3 = 1.0225 \times 1.0225 \times 1.0225 = 1.0689$ $1.0689 / 1.015 = 1.0531$ $\sqrt{1.0531} = 1.0262$ $f_{1,2} = 2.62%$ However, let me check if the question is asking for the 2-year forward rate starting in 1 year, which would be the rate for years 1 to 3. Actually, the 2-year implied forward rate in one year's time means the forward rate for the period from year 1 to year 3. Using the formula: $(1 + z_3)^3 = (1 + z_1)^1 \times (1 + f_{1,2})^2$ Where $f_{1,2}$ is the annual forward rate for years 1-3. $(1.0225)^3 = 1.015 \times (1 + f)^2$ $1.0689 = 1.015 \times (1 + f)^2$ $(1 + f)^2 = 1.0689 / 1.015 = 1.0531$ $1 + f = \sqrt{1.0531} = 1.0262$ $f = 0.0262 = 2.62%$ This is closest to option B: 2.63%. Let me verify with an alternative approach: We can also calculate using: $f_{1,2} = \left[\frac{(1 + z_3)^3}{(1 + z_1)^1}\right]^{1/2} - 1$ $f_{1,2} = \left[\frac{(1.0225)^3}{1.015}\right]^{1/2} - 1$ $f_{1,2} = \left[\frac{1.0689}{1.015}\right]^{1/2} - 1$ $f_{1,2} = [1.0531]^{1/2} - 1$ $f_{1,2} = 1.0262 - 1 = 0.0262 = 2.62%$ Given the options, 2.63% is the closest. **Therefore, the correct answer is B: 2.63%.**

Author: LeetQuiz .