Suppose a company just negotiated a FRA(forward rate agreement) with a bank to receive a fixed interest rateRKand pay LIBOR for a period of 3-month starting 1 year from now. The notional principal

on the FRA is $100 million. The LIBOR forward rate for the corresponding period(namely the period starts in one year and ends in 1.25 years) is 3% per annum now. The risk-free rates for all maturities are 2.5% per annum with continuously compounding.All other interest rates are measured with quarterly compounding.

(a). Assume no arbitrage opportunity exists, what should be the fixed rateRKthe company just negotiated to receive in the future and what is the value of the FRA now?

(b). Suppose 6 month passed, the LIBOR forward rate for the corresponding period is 2.8% with quarterly compounding now. The risk-free rate remains at 2.5%. What is the value of the contract now?