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I have a credit card with an outstanding balance and I am trying to work out when I will complete paying it off.

It is a UK credit card (where I am based) and I do not spend on it. I pay 150 per month.

I cannot for the life of me work out how the interest figures are calculated. Here are the details from a recent statement.

Statement date:   10 Sep 2012

Opening balance:                                3176.59
Payment received on 3 Sep 2012:                  150.00
Interest on balance transfers at 0.032% per day:  27.73
Interest on purchases at 0.032% per day:           5.74
Closing balance:                                3060.06

The interest for both components of the balance is stated as 0.032% per day or 12.45% per annum.

I have tried multiple methods and simply cannot reach the figures quoted as interest charges however I try.

Anyone care to have a go? I'd be most grateful.

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2  
Have you tried calculating it by the "Daily average balance" method? –  Mechaflash Sep 17 '12 at 19:52
    
Trivial calculation brings 32.58 as the result, they calculated 33.47, the 0.89 can probably be attributed to the daily averaging and compounding components of the calculation. –  littleadv Sep 17 '12 at 20:36

2 Answers 2

up vote 2 down vote accepted

The interest calculation is straightforward daily compounding at a daily rate of 12.45%/365 which is a tad more than 0.03410% per day. Note that this is larger than the stated daily rate of 0.032% per day which, when compounded daily, gives an APR of 12.3873...% per annum.
I get that for the first 25 days, compounding

3176.59*(1+.1245/365)^25 = 3203.79

Payment of 150.00 reduces the balance to 3053.79

Over the next 6 days (August 31 makes the period between statements to be 31 days), interest compounding gives

3052.79*(1+.1245/365)^6 = 3060.05

This is off by .01 from the bank's 3060.06 as the final balance which I attribute to the fact that I rounded off the numbers to two decimal places just twice, whereas the bank's computers may well be rounding off the daily balance each and every day (cf. the comment by @littleadv on the OP's question).

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Fantastic, thanks. –  tomfanning Sep 19 '12 at 21:34

With the comment in the OP being said...

Calculating interest by the "Daily average balance" is a popular method nowadays. See HERE for reference on how this works.

In a nutshell, you take the sum of each day's ending balance for the billing cycle divided by the days in the billing cycle. Then, multiply it by the APR, then multiply it by the days in your billing cycle, then divide it all by 365.

You will then have your calculated interest payment based on the "Daily average balance" method.

Example: 30 day cycle. 15% APR. Starting balance 0. Day 10 you charge $100. Day 20 you charge another $100. Your balance between days 1 and 9 are $0, 10 and 19 $100, 20 and 30 $200.

0*9 + 100*10 + 200*11 = 3200
3200 / 30 = 106.66
106.66 * .15 = 15.99
15.99 * 30 = 479.70
479.70 / 365 = 1.31
$1.31 Interest

Now if you were to charge back to $200 on day 1 of the next billing cycle, and left the balance at $200 the entire length of the billing cycle:

200 * 30 = 6000
6000 / 30 = 200
200 * .15 = 30
30 * 30 = 900
900 / 365 = 2.46
$2.46 Interest

EDIT: Derp...

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Would it be possible for you to work out the details with the numbers given and claims made by the OP and what can be inferred (e.g. no new charges during the month, balance was 3176.59 from 10 August through September 3 (25 days) and then went down by 150 till Sept 10 (6 days) etc and see what you actually get and whether it matches the numbers computed by the credit card company? –  Dilip Sarwate Sep 18 '12 at 19:42
    
One bit of information that isn't 100% clear is the start date of the billing cycle. Different creditors range from a 28-day cycle to a 31-day cycle. However, I will calculate it with all 4 instances and see if I hit. –  Mechaflash Sep 18 '12 at 20:00
    
I came the closest based on a 31 day cycle calculating the end of the billing cycle on the 9th (10th being the statement date). So 24 days @ 3176.59 and 7 days @ 3026.59, came out to 33.23 –  Mechaflash Sep 18 '12 at 20:15

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