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%.