Question

From the historical data, the firm has determined the following transition matrix:
  

	New Account	1M Overdue	2M Overdue	3M Overdue	Paid	Bad Debt
New Account	0.0	0.6	0.0	0.0	0.4	0.0
1M Overdue	0.0	0.0	0.5	0.0	0.5	0.0
2M Overdue	0.0	0.0	0.0	0.4	0.6	0.0
3M Overdue	0.0	0.0	0.0	0.0	0.7	0.3
Paid	0.0	0.0	0.0	0.0	1.0	0.0
Bad Debt	0.0	0.0	0.0	0.0	0.0	1.0

  
For example, if an account is two months overdue at the beginning of a month, there is a 40% chance that at the beginning of next month, the account will not be paid up (and therefore be three months overdue) and a 60% chance that the account will be paid up. It is assumed that after three months, a debt is either collected or written off as a bad debt. Once a debt is paid up or written off as a bad debt, the account is closed, and no further transitions occur.

What is the probability that a new account will eventually be collected?

	A.	0.700
	B.	0.964
	C.	0.880
	D.	0.036
	E.	0.940

Answer 1

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