Sally
This is a convoluted answer. I only know of one state (VA) where a judge has agreed that a bank credit card is an open account.
To understand you must look at the history of the industry and the development of statutes. Long before there were credit cards, there was a thing called an open account. This was a credit account that facilitated the sale of goods and services. A good example would be charging groceries at the local grocery store (long before Safeway). Historically, an open account was pretty informal and documented by a ledger sheet and the customer's signature across the face of the sales receipt or cash register ticket.
A department store charge card is also considered an open account (Dillards, for example). The key is that the credit is extended directly by the merchant for the purpose of facilitating the sale of goods and services. In other words, an open account is best understood as a "charge card". Only two parties are involved -- the merchant and the debtor.
Legislatures wrote the statutes in contemplation of charge cards and bank loans. A bank loan is the classical "written agreement". All this took place before the invention of the "credit card" in the 1950s.
A credit card is different than a charge card. A credit card is money you borrow from the issuer to pay a third party. A credit card involves three parties -- the bank, the service provider and the debtor. Typically, credit cards are documented with formal agreements that technically constitute a "written agreement" very similar to a bank loan.
There is lots of confusion caused by a misunderstanding of a federal statute that talks about "open-ended accounts" and gives credit card as an example. But, an "open account" and an "open-ended account" are not the same thing. The opposite of an open-ended account is a closed-end account. A mortgage or car loan is an example of a closed-end account.
I suspect that you are going to disagree with me on this. Fine, lots of people do. But, my 35 years of banking experience has taught me a thing or two.
By the way, just to correct some errors by previous posters.
1. A few states have a statute of repose. That means the debt literally dies after a certain date. If you state does not have a statute of repose, then the debt lives forever.
2. The passage of the state SOL does not mean that you cannot be sued. SOL is merely an affirmative defense to the lawsuit. I see people all the time sued on SOL debts. Sometimes they blow it off because the debt is SOL. Failure to assert your defense in a timely and correct fashion will result in a judgement. Once the judgment is granted, the consumer loses the SOL as a defense. This is true even in those cases where the consumer "never got notified of the lawsuit" unless the consumer can prove the plaintiff failed to follow state law -- sometimes they can and sometimes they cannot. I've seen a lot of very unhappy folks when they figure out their ignorance of the law has a price.
3. A cease and desist is only binding on a third party collection agency. Original creditors are not subject to FDCPA and thus can ignore the whole thing.
4. A cease and desist is binding on the 3rd party CA only to the degree that you are willing to enforce it. There are no FDCPA cops and you would have to sue the CA for violation. Most consumers could not find the courthouse let alone find their way around the filings, motions, hearings, pre-trial, etc.
5. A C&D on a debt that is within SOL is an invitation to be sued. When you take away the collector's opportunity to rattle your cage by phone, all they have left is to go nuclear.
6. Dispute letters and C&D letters you find on the internet are mostly worthless. The CA is not impressed that you can recite the requirements of the law and threaten to take away their toys if they violate. They see zillions of these things that have been copied off the internet. Personally, I suggest you keep it simple. You don't need more than two short sentences to invoke your rights. Just keep a good paper trail.
7. Gumshoe is trying hard but his/her actual knowledge is way down on the curve --many opinions and misunderstandings but little substance.
Good luck. Let me know how it goes.