Explanation

This question appears to be incomplete as it cuts off at the calculation. However, I can complete the calculation and provide the full solution.

Given:

• Notional principal: $400 million
• Fixed rate paid: 3.0% per annum (semi-annual payments)
• Receive: LIBOR
• Remaining life: 9 months (0.75 years)
• Next payments: 0.25 and 0.75 years from today
• LIBOR zero rate (risk-free rate): 2.20% (flat curve)
• Forward rate F(0.25, 0.75): 2.20% with continuous compounding

Calculation of forward rate with semi-annual compounding:

$$F(0.25, 0.75) = 2 \times \left[ e^{0.0220/2} - 1 \right]$$ $$F(0.25, 0.75) = 2 \times \left[ e^{0.0110} - 1 \right]$$ $$F(0.25, 0.75) = 2 \times \left[ 1.011055 - 1 \right]$$ $$F(0.25, 0.75) = 2 \times 0.011055 = 0.02211 = 2.211\%$$

This forward rate represents the 6-month LIBOR rate that will prevail 3 months from now, expressed with semi-annual compounding.

To value the swap, we would:

1. Calculate the present value of fixed payments
2. Calculate the present value of floating payments using the forward rate
3. The swap value = PV(floating) - PV(fixed)

Since the question is cut off, I cannot provide the final numerical answer, but the calculation above shows how to convert the continuously compounded forward rate to a semi-annually compounded rate.