Is there a contract with paypal or can you cancel at any time? It seems like they can shut you down at anytime so does that mean we can cancel our service with them at anytime?

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You can stop using paypal whenever you want but you can NEVER EVER close your account. They will keep ALL your information forever and the only way to protect yourself from paypal to take your money would be to close all bank accounts you ever had linked to your paypal account. Also report any and all cc associated with the account lost or stolen and get new ones.
As per Paypal: You may close your Account at any time by following the instructions in your Account Profile.

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So does that mean that even after I do what I can do to close my account they can still go into my bank account and take money? Is there no way I can delete my information?

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You can't delete the information you have given to paypal. They will keep that forever. What you can do is close your bank account you had linked to paypal and also report all cc associated with paypal as lost or stolen.

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Yes there is a contract when you sign up with paypal but they call it User Agreement.

"This User Agreement ("Agreement" or "User Agreement") is a contract between you and PayPal, Inc. and applies to your use of the PayPal? payment service and any related products and services (collectively the "Service"). This Agreement affects your rights and you should read it carefully. We encourage you to print the Agreement or copy it to your computer's hard drive for your reference"

NOw it does not say that you have to stay with them for a certain time but there is a lot of things in this agreement that are a bit shady. Like for example if you wish to close your account.

From Paypal's user Agreement:

"Closing Your Account. You may close your account at any time by clicking the "Close Account" link in your Profile on the PayPal website. Upon closure of an account, any pending transactions will be cancelled. Any funds that we are holding in custody for you at the time of closure, less any applicable fees, will be paid to you by check, assuming all withdrawal related authentication requirements have been fulfilled (for example, you may not use closure of your account as a means of evading withdrawal limits on new Unverified users). You may not use closure of your account as a means of evading investigation - if an investigation is pending at the time you close your account, PayPal may continue to hold your funds for up to 180 days as appropriate to protect PayPal against the risk of reversals. If you are later determined to be entitled to some or all of the funds in dispute, PayPal will make an additional payment of those funds to you. You will remain liable for all obligations related to your account even after such account is closed."

So basically you can't close your account.

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