Question 4.87

4.87 Credit card defaults.

The credit manager for a local department store is interested in customers who default (ultimately failed to pay entire balance). Of those customers who default, 88% were late (by a week or more) with two or more monthly payments. This prompts the manager to suggest that future credit be denied to any customer who is late with two monthly payments. Further study shows that 3% of all credit customers default on their payments and 40% of those who have not defaulted have had at least two late monthly payments in the past.

  1. What is the probability that a customer who has two or more late payments will default?
  2. Under the credit manager's policy, in a group of 100 customers who have their future credit denied, how many would we expect not to default on their payments?
  3. Does the credit manager's policy seem reasonable? Explain your response.

4.87

(a) 0.0637. (b) Out of 100, we would expect 93 or 94 not to default. (c) The manager’s policy seems unreasonable. Because only 3% of customers default, and while it’s true that percent more than doubles to 6.37% if they are late, the vast majority of these customers still do not default, and it is bad business to deny them credit.