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Answer: Calculation incomplete in source text
## 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.
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Suppose that some time ago, a financial institution entered into a swap where it agreed to make semi-annual payments at a rate of 3.0% per annum and receive LIBOR on a notional principal of $400.0 million. The swap now has a remaining life of only nine months (0.75 years). Payments will therefore be made 0.25 and 0.75 years from today. The risk-free rates with continuous compounding is assumed to be the LIBOR zero rate, and currently, it is 2.20% for all maturities. Because the LIBOR zero rate curve is flat at 2.20%, the six-month forward rate beginning in three months, F(0.25, 0.75), is also 2.20% with continuous compounding and therefore is equal to $2 \times \left[ e^{0.0220/2} - 1 \right] =$
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Calculation incomplete in source text
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