In an amual-pay cap, the Black volatilities for caplets with maturities 1, 2, 3, and 5 yours are 18%, 20%, 22%, and 20%, respectively. Estimate the volatility of a 1-year forward rate in the LIBOR Market Model when the time to maturity is

(a) 0 to 1 year,

(b) 1 to 2 years,

(c) 2 to 3 years, and

(d) 3 to 5 years. Assume that the zero curve is flat at 5% per annum (annually compounded). Use DerivaGem to estimate fiat volatilities for 2, 3, 4, 5, and 6-year caps.