Based on the same input parameters as the previous question, price a cap option contract with exercise dates at t = 0.5 and t = 1, at a strike rate of the half-year interest rate of 5%. Assume the notional on the contract to be $100. 

Data in previous question,

The following table summarizes the initial forward curve for three half-year periods and the initial volatility curve at t = 0. Compute the two forward curves at time t = 0.5 and the three forward curves at time t = 1. 

(0, T) (0,0) (0,0.5) (0,1) f(0, T) 0.04 0.045 0.05 o (T) 0.015 0.012