Consider a floorlet on a three-month LIBOR rate in nine month's time, with a notional principal amount of \(\$ 10,000\) per interest rate percentage point. The term structure is flat at \(3.95 \%\) per year with discrete compounding, the volatility of the forward LIBOR rate in nine months is \(10 \%\), and the floor rate is \(4.5 \%\).

a) What are the key assumptions on the LIBOR rate in nine month in order to apply Black's formula to price this floorlet?

b) Compute the price of this floorlet using Black's formula as an application of Proposition 19.7 and (19.21), using the functions \(\Phi\left(d_{+}\right)\)and \(\Phi\left(d_{-}\right)\).