Answer: 6.7%

## Calculation Explanation The implied forward rate from year 3 to year 4 can be calculated using the formula: \[ (1 + f_{3,4}) = \frac{(1 + r_4)^4}{(1 + r_3)^3} \] Where: - \( r_3 \) is the 3-year spot rate - \( r_4 \) is the 4-year spot rate - \( f_{3,4} \) is the forward rate from year 3 to year 4 **Step 1: Calculate the spot rates** For zero-coupon bonds: \[ P = \frac{100}{(1 + r)^n} \] For 3-year bond: \[ 85.16 = \frac{100}{(1 + r_3)^3} \] \[ (1 + r_3)^3 = \frac{100}{85.16} = 1.1743 \] \[ 1 + r_3 = 1.1743^{1/3} = 1.055 \] \[ r_3 = 5.5\% \] For 4-year bond: \[ 79.81 = \frac{100}{(1 + r_4)^4} \] \[ (1 + r_4)^4 = \frac{100}{79.81} = 1.2530 \] \[ 1 + r_4 = 1.2530^{1/4} = 1.058 \] \[ r_4 = 5.8\% \] **Step 2: Calculate the forward rate** \[ (1 + f_{3,4}) = \frac{(1.058)^4}{(1.055)^3} = \frac{1.2530}{1.1743} = 1.067 \] \[ f_{3,4} = 6.7\% \] Therefore, the one-year implied forward rate from year 3 to year 4 is **6.7%**.

Author: LeetQuiz .