Can't get the accounts department to close an account!

Accounts department can't close an account in 6 months and they phone everyday asking when the payment will be made for all the charges they keep adding every month since it was settled! My husband has written 8 letters and responded everyday to the calls again in writing but low and behold the next day he will get another call asking when he's going to pay and they know nothing about all the correspondence. And the amounts continue to be charged and the calls keep coming! He called in March and said he wanted to close the account and they told him what amount to pay, which he did. They did not close the account as discussed on that day and still haven't. How does this get resolved? He's tried everything and nothing happens.