Explanation

To calculate the 1-year forward rate three years from today with continuous compounding, we use the formula:

$F = \frac{R_4 \times T_4 - R_3 \times T_3}{T_4 - T_3}$

Where:

• $R_3 = 4.6\%$ (3-year zero rate)
• $R_4 = 5.0\%$ (4-year zero rate)
• $T_3 = 3$ years
• $T_4 = 4$ years

Substituting the values:

$F = \frac{0.05 \times 4 - 0.046 \times 3}{4 - 3}$ $F = \frac{0.20 - 0.138}{1}$ $F = \frac{0.062}{1}$ $F = 0.062 = 6.2\%$

Therefore, the correct answer is 6.2% (Option A).

Alternative Method Using Continuous Compounding Formula:

For continuous compounding, the forward rate can also be calculated using:

$e^{R_3 \times 3} \times e^{F \times 1} = e^{R_4 \times 4}$ $R_3 \times 3 + F \times 1 = R_4 \times 4$ $0.046 \times 3 + F = 0.05 \times 4$ $0.138 + F = 0.20$ $F = 0.20 - 0.138$ $F = 0.062 = 6.2\%$

Both methods confirm that the forward rate is 6.2%.