This Week's Problem: "Modern Banking"
An online bank verifies customers’ ownership of external bank accounts by making both a small deposit and a small debit from each customer’s external account, and asking the customer to verify the amounts. In 70% of these exchanges, the deposit and debit are within two cents of one another (for example, a deposit of $0.18 and a debit of $0.16, or a deposit of $0.37 and a debit of $0.38), and the deposit and debit are always within five cents of one another. During one week, the online bank attempts to verify 6,000 accounts in this manner, but 0.5% of the transactions do not go through, and thus no money is transferred. What is the maximum amount, in dollars, that the account verification system could have cost the bank that week?
Go to it. My answer will eventually appear in the comments, although another commenter's answer might appear there first. One remark before I go, though: that's got to be a pretty weird bank if the debit doesn't exactly match the deposit. I certainly wouldn't let any agency take two cents out of my bank account merely to verify that the account is mine!