To calculate the forward rate from year 3 to year 4:

Step 1: Calculate the 3-year and 4-year spot rates

• 3-year bond price = 85.16
• 4-year bond price = 79.81

For zero-coupon bonds: Price = 100 / (1 + r)^n

3-year spot rate: 85.16 = 100 / (1 + r₃)³ (1 + r₃)³ = 100 / 85.16 = 1.174 1 + r₃ = 1.174^(1/3) = 1.0549 r₃ = 5.49%

4-year spot rate: 79.81 = 100 / (1 + r₄)⁴ (1 + r₄)⁴ = 100 / 79.81 = 1.253 1 + r₄ = 1.253^(1/4) = 1.0581 r₄ = 5.81%

Step 2: Calculate forward rate from year 3 to year 4 (1 + r₄)⁴ = (1 + r₃)³ × (1 + f₃,₄) (1.0581)⁴ = (1.0549)³ × (1 + f₃,₄) 1.253 = 1.174 × (1 + f₃,₄) 1 + f₃,₄ = 1.253 / 1.174 = 1.067 f₃,₄ = 6.7%

The forward rate from year 3 to year 4 is 6.7%.