Customers shift between variable rate loans (V), 30 year fixed-rate loans

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

V 30 15 P f V 0:55 0:35 0 0:05 0:05 30 0:15 0:54 0:25 0:05 0:01 15 0:20 0 0:75 0:04 0:01 P 0 0 0 1 0 F 0 0 0 0 1

(a) For each of the three loan types find

(a) the expected time until paid or foreclosed.

(b) the probability the loan is paid.