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

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:

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

(a) For each of the three loan types find (a) the expected time until paid or foreclosed.

(b) the probability the loan is paid.