Generally speaking, your refund is going to go to whatever payment method you used to make the purchase. So if you used a credit card, you’ll get a credit on your credit card account. Your checking account is irrelevant to the purchase.
How your credit card company deals with the return will vary – they’ll either send you a refund or apply the credit to your next bill.
For example:
1) You buy something from Amazon for $20. You pay with your Visa card.
2) You pay your Visa bill from your checking account.
3) You return your item to Amazon.
4) Amazon issues a credit to your Visa account. Assuming you haven’t bought anything else in the interim, the balance on your Visa account is now $20 in your favor.
Most of the time, that $20 would then get deducted from whatever you owe Visa in the next billing cycle but there are situations where they’d pay it back to you. (For example, if you closed the account.)
Your credit card can go negative, which will just stay negative until you respend it (so, if you’re $100 negative, and use it to buy something for $100, you’ll be back to zero).
If you’re still negative on the next billing cycle or 30 days or whatever (this can vary on the bank), they’ll mail you a check for the negative balance
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