Question
A credit union classifies car loans into one of four categories: the loan has been paid in full (F), the account is in good standard
A credit union classifies car loans into one of four categories: the loan has been paid in full (F), the account is in good standard (G) with all payments up to date, the account is in arrears (A) with one or more missing payments, or the account has been classified as a bad debt (B) and sold to a collection agency. Past records indicated that each month,
20%
of the accounts in good standing pay the loan in full,
70%
remain in good standing, and
10%
become in arrears. Furthermore,
10%
of the accounts in arrears are paid in full,
40%
become accounts in good standing,
40%
remain in arrears, and
10%
are classified as bad debts. Complete parts (A) through (C) below.
(A) In the long run, what percentage of the accounts in arrears will pay their loan in full?Present the given information in a standard form matrix. Within the group of absorbing states and within the group of nonabsorbing states, from left to right and top to bottom, list F before A, B, and G; list B before A and G; and list G before A.
Now determine the limiting matrix P.
In the long run, ___________%
of the accounts in arrears will pay their loan in full.
In the long run, what percentage of the accounts in good standing will become bad debts?
(C) What is the average number of months that an account in arrears will remain in this system before it is either paid in full or classified as a bad debt?
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