There is no specific number of credit cards you should obtain. An average American has from 5 up to 10 credit accounts open. The number depends on the bank and on you. Some people tend to open up to 50 bank accounts while others are cautious about having multiple credit cards.
The number, especially, depends on your ability to manage your credit cards. If there is your first time of applying for a loan, then one card will be enough. A person, who decided to establish the credit history, should also manage one credit card to avoid the risk.
Closing your credit accounts right after you pay off the debt can also be harmful to your credit history as when you apply for a loan you must provide a proof of your creditworthiness. The valid accounts with a good payment history are supposed to increase your chances of getting a loan approved.
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Multiple credit cards obtain different interest rates. If the difference between interest rates is large, you can transfer the funds to the credit card with a lower interest. Having multiple credit cards can affect your credit score up to 30%.