I believe interest is calculated on the average daily balance for the period. Paying the minimum may cause your balance to actually increase slightly, depending on your balance and rate.
Whenever I've had to carry a balance, I usually transfer to a new card which offers a 0% intraductory rate on balance transfers. Then I can pay it off quickly without shelling out extra cash on interest.
If you've regularly paid your balance, you've already learned the best credit strategy. Outstanding balances are a tool of the devil!
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