The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%.

Now consider a capped 1-year floater indexed to the short rate with a face value of $100 and a 3.4% cap rate.

a) What is the payout to this capped floater at time t=0.5 (units: dollars)?

b) What is the payout to this capped floater at time t=1.0 if the up state is realized at time t=0.5 (units: dollars)?

c) What is the payout to this capped floater at time t=1.0 if the down state is realized at time t=0.5 (units: dollars)?