Background
I wasn't able to answer my question from searching Money.SE by balance amount subject interest calculation apr—admittedly, I probably didn't know enough (or have enough context) to click the right links—but given that, most questions I found were about general APR calculations and certain nuances such as accounting for grace periods. After calling my bank, I found out that Balance Subject To Interest Rate (or Amount Subject To Interest Rate) is more commonly known as (or rather, computed by the method of) Average Daily Balance. With that knowledge I was able to answer my own question. Still, I thought I'd post the question (and my explanation) here in case future users might fumble around as I did, not knowing the proper terminology to search by.
Takeaway (Why This Answer Might Be Useful To Others)
At times I thought maybe it wasn't feasible to calculate the BSTIR/ASTIR/ADB by hand, but after these investigations it seemed not just feasible but even straightforward to calculate these things, once familiar with billing cycles and prorating, as well as the handling of fees.
Answers (High-Level, Descriptive)
The 1st month's transferred balance showed less than the actual amount transferred, due to prorating. That is, my balance transfer for $2,500 was processed about 1/3 of the way through the billing cycle; therefore the $2,500 was subject to interest only during the latter 2/3 of the billing cycle. (This would have been more obvious had the field been called "Average Daily Balance.") See below for actual calcuations.
The 3rd month's transferred balance started decreasing due to payment; the minimum payment is applied to the balance with the lowest APR (in my case, the transferred balance) while the remainder is applied to the balance with the highest APR. This may not be true about every credit card, but I imagine it's very common. To verify, check your card member agreement or the fine print on your statement, or call customer service. Prorating applies here as well, according to the day in the billing cycle you made your payment. See below for actual calculations.
But then, shouldn't the balance have started decreasing in the 2nd month? Why didn't the minimum payment for the 1st month apply to the transferred balance?
Initially, I thought perhaps that payments didn't begin applying to transferred or promotional balances until after a full billing cycle elapsed (or the statement thereafter was provided). However, this wasn't the case. The 2nd month's transferred balance did start decreasing: but what decreased was a hidden portion (the balance transfer fee, hidden because it was not subject to interest). See below for actual calculations.
Answers (Low-Level, Numerical)
This is a Chase Amazon.com Rewards Visa Card.
Statement 1
Opening/Closing Dates (Billing Cycle) 03/02 - 04/01
Number of Days in Billing Cycle 31
Minimum Payment $41
Minimum Payment Due 04/26
Activity
03/11 Balance Transfer $2,500
03/11 Balance Transfer Fee $75
INTEREST CHARGES
--------------------------------------------------------------------
Balance Type APR Expiry BSTIR
--------------------------------------------------------------------
Purchases 18.24
Cash Advances 19.24
Balance Transfers 18.24
Overdrafts 19.24
Balance Transfer Promotions 0.00 05/2014 $1,774.19
Notes:
- All numbers above, including the number of days in the billing cycle, are transcribed from the actual statement, not derived or calculated (though of course reformatted) by me.
- Always count inclusively when counting days in a range, e.g. 03/10 to 03/13 is 4 days.
So, let's get started. The balance transfer was processed on 03/11. To the end of the billing cycle, 04/01, that's 22 days:
Month 03 04
Date 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 01
Days 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22
That means the balance was only subject to interest for 22 out of the 31 days:
$2,500 * 22/31 = $1,774.1935
The numbers check out!
Month 2
Opening/Closing Dates (Billing Cycle) 04/02 - 05/01
Number of Days in Billing Cycle 30
Minimum Payment $68
Minimum Payment Due 05/26
Activity
04/13 Payment $100
INTEREST CHARGES
--------------------------------------------------------------------
Balance Type APR Expiry BSTIR
--------------------------------------------------------------------
Purchases 18.24
Cash Advances 19.24
Balance Transfers 18.24
Overdrafts 19.24
Balance Transfer Promotions 0.00 05/2014 $2,500.00
Here, I paid at least my minimum payment from the previous statement ($41), which should have applied to the transferred balance. So why didn't it? Turns out, it did. The transferred balance includes the balance transfer fee, so my transferred balance was $2,575 and is now $2,534; however since the fee is not subject to interest† while the balance transfer amount is, only the latter shows under "BSTIR."
Month 3
Opening/Closing Dates (Billing Cycle) 05/02 - 06/02
Number of Days in Billing Cycle 32
Minimum Payment $71
Minimum Payment Due 06/26
Activity
05/16 Payment $100
INTEREST CHARGES
--------------------------------------------------------------------
Balance Type APR Expiry BSTIR
--------------------------------------------------------------------
Purchases 18.24
Cash Advances 19.24
Balance Transfers 18.24
Overdrafts 19.24
Balance Transfer Promotions 0.00 05/2014 $2,480.87
The last statement's minimum payment was $68. Again, I paid at least that amount, so that amount gets applied to the transferred balance, which, recall, was $2,534 (including the remaining portion of the balance transfer fee), making the new transferred balance $2,466, as of the payment date, 05/16.
And that payment date is important, because that's where the Average Daily Balance method kicks in:
Month 05 06
Date 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 01 02
Days 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
^ ^
BSTIR $2,500 $2,466
Note, again, that since the fee's not subject to interest†, the BSTIR is $2,500 (not $2,534) until it falls below $2,500.
We don't need to draw a calendar to do these calculations; I'm just drawing them in this case to be clear. Counting inclusively, there are 14 days between 05/02 and 05/15, and 18 days between 05/16 and 06/02, so the average daily balance is calculated as follows.
( (14 * $2,500) + (18 * $2,466) ) / 32 = 2480.8750
The numbers check out, again!‡
† Not all credit cards / balance transfer offers consider fees exempt from interest. See further below for one such example.
‡ Unlike any impressions we may have gotten from grade school (American, at least), 2480.875 is neither "closer" to 2480.87 nor to 2480.88. In this case (or perhaps in accounting, in general; I wouldn't know, since I don't have an accounting background) the value seems rounded to the customer's advantage.
Further Examples
Not all cards exempt fees from interest, e.g. the US Airways Dividend Miles Mastercard (Barclays). This doesn't matter of course for promotional 0 APR balance transfers, but it does matter if you're trying to reproduce the numbers on your statements. The following example also demonstrates a case in which a new account was created for the balance transfer (as opposed to transferring balances to an existing account); I had expected things to get screwy with billing cycles, but the calculations remained tame.
Statement 1 (Different Card)
Opening/Closing Dates (Billing Cycle) 11/10/13 - 12/06/13
Number of Days in Billing Cycle 30
Minimum Payment $42.74
Minimum Payment Due 01/03/13
Activity
11/26 Balance Transfer $4,000
11/26 Balance Transfer Fee $120
INTEREST CHARGES
--------------------------------------------------------------------
Balance Type APR Expiry BSTIR
--------------------------------------------------------------------
Purchases 24.99
Balance Transfers 0.00 02/2014 $1,510.66
Cash Advances 25.24
The balance transfer was processed on 11/26. To the end of the billing cycle, 12/06, that's 11 days. That means the balance was only subject to interest for 11 out of the 30 days:
$4,000 * 11/30 = $1,466.6667
(11/30 is not a date; it's 11 divided by 30, in case that's not clear.) But wait, that doesn't check out! That's because this card considers the fee subject to interest rate. Instead, we have to do:
$4,120 * 11/30 = $1,510.6667
Ah, there we go.
As mentioned before, I expected a more complex calculation due to having opened the account on 11/10. Since that's partway through the billing cycle, I thought the denominator should be 27 days rather than 30 days, so that my BSTIR would be higher than what it actually came out to be. Perhaps other credit cards do this; but this card did not, to the customer's advantage.
