Hi I tried to answer this question by post multiplying the original distribution vector (1,0,0,0) by the transition matrix twice but for some reason this didn't work. The solution calculated the answer by using P^2 and taking the relevant number from that. I thought both methods would work. Should both methods work in this case? Maybe I got my maths wrong on the post multiplying method. Or maybe I needed to do it a third time...Or maybe only calculating P^2 works... Thanks Adam,
At 1/1/15, Mike (the policyholder) is in the 20% discount state. So to use your approach you need to start with the original distribution vector (0,1,0,0). Then it works fine.
