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