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/3ó 0 day count.)