I had a same experience. So I researched what people are saying about this problem and solved it. This is what I did. I opened my account at my PC, changed payment credit card from Visa to Amex. Then updated the info at my iPhone. Sorry, this may not help if you do not use PC or do not have other credit card.
Hi, my problem was solved.
First, you need to check the balance on your bank account.
Then, you need to open the itunes on your laptop and sign in. There, you can see "purchase history". Click on that.
Under the purchase history, you can see the amount you owe to Apple. If your balance is lower than the amount you owe, then you need to top up some money to your bank account.
Make sure the amount you want to top up is higher than the amount you owe.
Then, open your apple id account and click payment information..insert back your debit card info and your billing address. Then, click "Done".
That's all.. After you complete this step, under payment method you can see "None" option appears. Try this out!
(Sorry for my bad english, hope you can undertand what I want to share)
I'm have the same problem I'm in able to download any apps or games or music to my new I phone 5s because when I go to iTunes or Apple store it's saying there was a problem with your last purchase, so update payment method. Then I put my debit card information in the phone, but then my old payment method information keeps coming up, halfway filled out!! How can I just but in a new payment method?? So I can down load my apps and music I've already purchased??
Try signing out of the iTunes & App Store. Then close the app: double-click the Home key and swipe up on the iTunes & App Store thumbnail. Then go back to Settings>iTunes & App Store and sign back in, then select View Account, then go in and change your billing again and see if you have any luck!