Lake Michigan Credit Union finances auto loans for its members. Each loan can be classified into one of four categories: paid in full, good standing, poor standing (with one or more missing payments), and delinquent (where the debt is sold to a collection agency).
Past records indicate that each month 10% of the accounts in good standing are paid in full, 70% stay in good standing, and 20% become poor standing.
Also, 50% of the accounts in poor standing move to good standing, 40% remain in poor standing, and 10% are delinquent.
Construct the transition matrix T for this situation. Be sure to label the states.
Suppose Lake Michigan Credit Union currently has 600 outstanding auto loans, 400 of which are in good standing, and 200 of which are in poor standing. In the long run, approximate how many of these auto loans will be paid in full, and how many will end up as delinquent.