In this thread I had discussed how mortgage lenders calculate interest. I want to bring up the same question with regard to credit card companies.
For example, for simplicity suppose my credit card has an APR of 10%. Now I take APR of 10% to mean if you had an initial balance of B on, say, Jan 1, made no payments whatsoever for a year, then on Jan 1 of the following year your balance would be B x 1.10. (This would be, of course, disregarding any other fees.) So my first question is whether this assumption about the meaning of APR is valid or not.
However, my credit card does not compound yearly, but daily. The daily rate is gotten from the APR by simply dividing by 365. So if my balance before interest is B, then the total balance including interest in a month with 30 days would be
B x (1 + R/365)[sup]30[/sup]
However, this is NOT equivalent to the APR as I have described it. If I had a balance of, say, $1000 on Jan 1, then one year later at 10% you would expect the total to be $1100, right? Not so. From the way they actually calculate it, it would be
$1000 x (1 +.1/365)[sup]365[/sup] = $1105.55
The correct way to compound daily so that it is equivalent to the APR is just as easy for them to calculate. It is
B x (1 + R)[sup]days/365[/sup]
= $1000 x (1 + .1)[sup]365/365[/sup]
= $1100
(and putting in 30 for days above would give a month’s worth)
But it is clearly in the advantage of the company to use the former. Sure, it is only 5 bucks in this case, but when you consider how many cards a company may have in use, it really adds up.
So is this legit? Is it just taken to be common knowledge that your “APR” is not really APR, but is really the daily compounding method used? Or perhaps simply no one has called the companies on this somewhat misleading practice?