Calculate the price of a cap on the 90-day LIBOR rate in 9 months' time when the principal amount is $1,000. Use Black's model and the following information:
(a) The quoted 9-month Eurodollar futures price = 92. (Ignore differences between futures and forward rates.)
(b) The interest rate volatility implied by a 9-month Eurodollar option = 15% per annum.
(c) The current 12-month interest rate with continuous compounding = 7.5% per annum.
(d) The cap rate = 8% per annum. (Assume an actual/360 day count.)