Today the market shows that the three-month interest rate is 3% per annum, the six-month interest rate is 5% per annum, and the nine-month interest rate is 6% per annum. An investor is looking into a six-month forward rate agreement (FRA) with the notional principal of $1,000,000 for a loan period of three months. The investor is trying to figure out what should be the fixed-rate specified in the FRA, and the amount of cash settlement at the expiry date of the FRA. Assuming that after six months, the market rate for this loan is 9% and the investor uses continuous rates for discounting cash flows (All interest rates are continuously compounded).

Calculate the amount of cash settlement?