Consider a world where the 6-month short rate is governed by the Black-Derman-Toy with constant volatility. Suppose that the mean growth rate of the short rate is 2% and the volatility of the growth in the short-rate is 20%. Further assume that the current short rate is 2.5% per year.

a) What will be the short rate 6 months from now following an up-state realization (units: percent per year)?

b) What will be the short rate 1 year from now following two up-state realizations (units: percent per year)?

c) What will be the short rate 1 year from now following one up-state realization and one down-state realization (units: percent per year)?

d) What will be the short rate 1 year from now following one down-state realization and then one up-state realization (units: percent per year)?