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. **Given:** - 1-year spot rate (r₁) = 1.50% - 2-year spot rate (r₂) = 2.00% - 3-year spot rate (r₃) = 2.25% **Formula:** The forward rate from year 1 to year 3 (a 2-year forward rate starting in 1 year) can be calculated as: (1 + r₃)³ = (1 + r₁)¹ × (1 + f(1,2))² Where: - r₃ = 3-year spot rate = 2.25% - r₁ = 1-year spot rate = 1.50% - f(1,2) = 2-year forward rate starting in 1 year **Calculation:** (1 + 0.0225)³ = (1 + 0.015)¹ × (1 + f(1,2))² (1.0225)³ = (1.015) × (1 + f(1,2))² 1.0690 = 1.015 × (1 + f(1,2))² (1 + f(1,2))² = 1.0690 / 1.015 = 1.0532 1 + f(1,2) = √1.0532 = 1.02625 f(1,2) = 0.02625 = 2.625% **Alternative calculation using the 2-year and 3-year rates:** We can also calculate this using: (1 + r₃)³ = (1 + r₂)² × (1 + f(2,1)) Where f(2,1) is the 1-year forward rate in 2 years, but this is not what we're looking for. **For the 2-year forward rate in one year:** We need the rate that would apply for years 2 and 3, starting in year 1. Actually, let me recalculate more carefully: We want the forward rate for years 2 and 3 (a 2-year period starting in year 1). (1 + r₃)³ = (1 + r₁)¹ × (1 + f(1,2))² Where f(1,2) is the 2-year forward rate starting in 1 year. Plugging in: (1.0225)³ = 1.015 × (1 + f)² 1.0690 = 1.015 × (1 + f)² (1 + f)² = 1.0690 / 1.015 = 1.0532 1 + f = √1.0532 = 1.02625 f = 0.02625 = 2.625% This rounds to 2.63%, which corresponds to option B. Wait, let me check my initial answer. Looking at the options: A. 2.50% B. 2.63% C. 2.75% My calculation gives 2.625%, which is closest to 2.63% (option B). **Therefore, the correct answer is B. 2.63%.** **Key Concept:** Forward rates are implied by spot rates through the no-arbitrage condition. The forward rate represents the interest rate that would make an investor indifferent between investing for the entire period versus investing for shorter periods and reinvesting at the forward rate.

Author: LeetQuiz .