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I have a credit card and I'm trying to calculate future interest charges per month. I have 4 months of statements that I have had to reverse engineer their math for. It took me a few days, but I finally figured out this banks algorithms for calculating their interest (I tried to get their help, but nobody could figure it out lol... yeah...).

However I am stuck on one part I can't figure out. They break apart the payment into proportional parts. According to them, they're putting the majority towards the soonest promotional end date is all I got from them. It seems that each charge/balance has it's own weight to it.

So it's deferred interest, so the payment amount is not tied to any interest\interest calculations. Just focusing on one month, we have the following:

$$ \text{Payment Amount:}\quad \text{\$25.00}\quad\qquad\qquad \qquad\qquad\qquad \qquad\qquad$$

$$ \text{Before payment:} \quad \text{\$975,}\quad \quad \; \text{\$800,} \qquad\text{\$17.98,} \qquad \text{\$74.99} $$

$$ \text{After payment:}\; \quad \text{\$961.94,} \quad \text{\$789.30,}\quad\text{\$17.74,} \qquad \text{\$73.99} $$

$$ \text{Difference of:}\; \qquad \text{\$13.06,} \quad \text{\$10.70,}\qquad\text{\$0.24,} \qquad \text{\$1.00} $$

The $975's deferment date ends 9/15/2018. All the rest end on 10/16/2018. I can't even think of where to start with this one, maybe my mind is zapped from figuring out their crazy system for their interest, but any help is greatly appreciated.

Thanks!

(Probably not needed for this calculation, but this months statement is from 10/17/2018 to the end of 11/15/2018, with the payment on 11/08/2018.)

intwarrior
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1 Answers1

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They've paid off the same proportion (rounded to the nearest cent) of each. Specifically, for a total payment of $p$, and amounts owing $x_1, \ldots, x_n$, they've subtracted $$\frac{px_k}{\sum\limits_{i=0}^nx_i}$$ from each (rounding to the nearest penny, possibly with some check in there to make sure that the rounding all cancels out). Whatever they say about "putting the majority towards the soonest promotional end date", they aren't. Feel free to check the other months to be sure that this pattern holds up.

user3482749
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  • You are awesome, thank you! I can sleep peacefully tonight and finish my Excel sheet tomorrow. I likely won't get charged interest, but I'd still like to know to be able to project a just in case model. It's good practice/skill. And now I can make a full model that should match their statements. – intwarrior Dec 22 '18 at 02:44
  • Just out of curiosity, can you point me in the right direction to figure out how to do a similar checker to make sure they add up? Being a penny off isn't the end of the world, but I'd like to increase my programming skills too. – intwarrior Dec 22 '18 at 02:51
  • There's a few ways to do it, and I'm not sure which one your bank is doing. The easiest is probably to notice that if we round everything down to start with, the four remainders must add up to either 0 cents, 1 cent, 2 cents, or 3 cents (it has to be a whole number of cents, and you can't reach 4 cents). If it's 0 cents, then everything else adds up perfectly, so we don't need to do anything. If it's 1 cent, add 1 cent to the amount with the largest remainder. If it's 2 cents, add 1 cent to each of the 2 largest. If it's 3 cents, add one cent to each of the 3 largest. – user3482749 Dec 22 '18 at 11:49
  • That's not quite what your bank is doing (they're a penny high on the first payment and a penny low on the second), but it's one of the more sensible ways to do it. – user3482749 Dec 22 '18 at 11:51