Customers shift between variable rate loans (V), thirty year fixed-rate loans

(30), fifteen year fixed-rate loans (15), or enter the states paid in full (P), or foreclosed according to the following transition matrix:

(a) For each of the three loan types find

(a) the expected time until paid or foreclosed.

(b) the probability the loan is paid.

V 30 15 P F V.55.35 0.05.05 30.15.54.25.05.01 15.20 0.75.04.01 P000 10 F 0 0 0 0 1