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For people trying to pay down balances on two or more cards, the usual advice is to make the biggest possible payment for the card with the highest rate, paying only the minimums on everything else.

But imagine this scenario (based very loosely on my own situation):

Card #1 has a 8K balance at 9.99% To make the math easy, assume that the minimum payment is $100/month.

Card #2 has a 4K balance at 0$ until April. But if it's not completely paid off before April 2, then a 20% APR will apply retroactively to October 1 of 2013.

If I have $4000 right now, and will be able to pay $1100K /month toward debt reduction, how should I allocate that $4K lump sum and the $1100 monthly to minimize my interest payments?

I suspect the smart thing would be to pay the $4K toward the 9.9% card today, then make the minimum payments on that and allocate the rest to the card that's currently at 0%. But that's based on instinct, not logic.

(I vaguely remember learning how to calculate minimums & maximums in an advanced algebra class I took years ago, but I don't remember enough to figure out how to solve this problem.
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