How Do Credit Card Companies Calculate Interest?

Date: 02/05/2004 at 03:58:50
From: Amanda
Subject: How do I Determine Credit Card Monthly Interest Calculation

I have a balance of 426.92 on my credit card with an annual interest 
rate of 23.73% and a compounded daily interest rate of .06501% with 
a continuus minimum payment of $15.  My bill states that the total 
interest for the month was $8.49 and that after my payment of 41.92 
my balance was 393.49.  

I would like to know if there is an equation that would determine the
total amount of interest each month so that I can figure out the best
payment monthly for my bills.  I can use the same equation for each
credit card.

Date: 02/05/2004 at 09:53:27
From: Doctor Vogler
Subject: Re: How do I Determine Credit Card Monthly Interest Calculation

Hi Amanda,

First of all, the "best payment" for your bills is the full balance on 
the bill.  If your card has a grace period (which most do), do this 
every month and you will never pay *any* interest.

Also, the formulas on our "loans and interest" FAQ assume that you 
will not be charging additional payments to the loan, which is normal 
for credit cards.  You have to factor in how much you are buying, too.

That said, you would like to know how the credit card company 
calculates how much interest you owe.  The first thing to do is pull 
out your credit card's "user agreement" or whatever they call the 
booklet of rules and regulations that they go by.  Perhaps you threw 
it away, but they are required by law to tell you the formulas that 
they use, and some companies will use somewhat different formulas.

My card uses the "average daily balance," which means that they record 
the balance at a certain time of day (such as midnight) every day in 
the month.  Then they average them all together (add them all up and 
divide by the number of days) and consider this to be your "month's 
balance" on which they will charge interest.  Then they multiply this 
by your monthly interest rate, which is the daily interest rate times 
the number of days.  For example, a 30-day month with a daily rate of 
23.73%/365 = 0.06501% or 0.0006501 (remember that "percent" means 
"divided by 100") has a monthly interest rate of 30*0.06501% = 1.95%, 
so that you would be charged interest that is 0.0195 times your 
"average daily balance."

But you said "compounded daily" which (if this is the method your card 
uses) means that they charge interest every day.  So, at some time 
(such as midnight) every day, they take the current balance on your 
card, multiply it by 0.06501% (or 0.0006501) and add that amount of 
interest.  Notice that they will then charge interest on this little 
bit on top of your previous balance when they charge interest 
tomorrow.  That is "compounded interest," meaning interest on your 
interest.  So if you have a balance of $393.49, then they will charge 
you $393.49 * 0.0006501 = 26 cents of interest on the first day of the 
month, then $393.75 * 0.0006501 = 26 cents again on the second day, 
and so on.  Your "user agreement" will probably also say how much they 
round (to the nearest cent each day, or to the nearest hundredth of a 
cent each day, or perhaps exactly until the end of the month, and then 
they round off to the nearest cent).

If you have any questions or need more help, please write back and 
show me what you have been able to do, and I will try to offer further 
suggestions.

- Doctor Vogler, The Math Forum
  http://mathforum.org/dr.math/