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Does a credit company need to show you how they calculated your interest?
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            To answer your question directly, no. They don't have to "show" you. All they have to do is charge it in line with their T+Cs. If you apply the method agreed in the T+Cs and come up with a different result, then you can challenge it. Ultimately a judge might insist they "show" how they came up with the result if it comes wrong. I suppose the ombudsman might consider if unfair if they refused to assist you in understanding their calculation.
Also, it has been known for mistakes to be made. A few years ago I got a credit from Barclaycard. It was less than £1, but they had discovered an error in their software. When I've been charged interest in the past, I've always done a rough calculation in my head to double check.I paid the £500 the day of my last statement, one month ago today. My current statement was dated today so I should have been paying a lot less interest for a month exactly, the whole of the current statement period. I just want to know if I can get them to tell me exactly how they calculated the interest?
You mentioned in your first post that this was half of your balance. But we don't know exactly how long the full balance was outstanding for. It could be that interest for a full month on the £500 is more than interest on the full amount for a shorter time.
If you wish someone here to have a second look, it would be best to post a transaction history - ie precise dates of transactions, payments, and statements etc...0 
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