The 2-year forward rate starting in 3 years is calculated using the formula:

$_3F_2 = \frac{(R_5 \times 5 - R_3 \times 3)}{(5 - 3)}$

Where:

• $R_3 = 3\text{-year zero rate} = 2.50\%$
• $R_5 = 5\text{-year zero rate} = 3.50\%$
• $_3F_2 = \text{2-year forward rate in year 3}$

Calculation: $_3F_2 = \frac{(3.50\% \times 5 - 2.50\% \times 3)}{(5 - 3)} = \frac{(17.50\% - 7.50\%)}{2} = \frac{10\%}{2} = 5.00\%$

Why other options are incorrect:

• A (3.50%): This is the zero rate (spot rate) for a 5-year investment, not the forward rate.
• B (4.17%): This would be the annualized 3-year forward rate starting in 2 years, calculated using the wrong formula: $_3F_2 = \frac{(R_5 \times 5 - R_3 \times 2)}{(5 - 2)}$.
• D (6.09%): This results from applying the wrong formula: $(1 + _3R_2) = (1 + R_5) \times (1 + R_3)$.