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## Credit cards and loans

# Annual percentage rate (APR) and effective APR

## Video transcript

Voiceover: Easily the most quoted number people give you when they're
publicizing information about their credit cards is the APR. I think you might guess
or you might already know that it stands for annual percentage rate. What I want to do in this
video is to understand a little bit more detail
in what they actually mean by the annual percentage
rate and do a little bit math to get the real or the
mathematically or the effective annual percentage rate. I was actually just
browsing the web and I saw some credit card that had
an annual percentage rate of 22.9% annual percentage rate, but then right next to it, they say that we have 0.06274% daily periodic rate, which, to me, this right here
tells me that they compound the interest on your credit
card balance on a daily basis and this is the amount that they compound. Where do they get these numbers from? If you just take .06274
and multiply by 365 days in a year, you should get this 22.9. Let's see if we get that. Of course this is percentage, so this is a percentage here
and this is a percent here. Let me get out my trusty
calculator and see if that is what they get. If I take .06274 - Remember, this is a percent,
but I'll just ignore the percent sign, so as a
decimal, I would actually add two more zeros here, but
.06274 x 365 is equal to, right on the money, 22.9%. You say, "Hey, Sal,
what's wrong with that? "They're charging me .06274% per day, "they're going to do
that for 365 days a year, "so that gives me 22.9%." My reply to you is that
they're compounding on a daily basis. They're compounding this
number on a daily basis, so if you were to give them
$100 and if you didn't have to pay some type of a minimum
balance and you just let that $100 ride for a year,
you wouldn't just owe them $122.9. They're compounding this much every day, so if I were to write
this as a decimal ... Let me just write that as a decimal. 0.06274%. As a decimal this is the
same thing as 0.0006274. These are the same thing, right? 1% is .01, so .06% is .0006 as a decimal. This is how much they're
charging every day. If you watch the
compounding interest video, you know that if you wanted
to figure out how much total interest you would be
paying over a total year, you would take this number, add it to 1, so we have 1., this thing
over here, .0006274. Instead of just taking this
and multiplying it by 365, you take this number and you
take it to the 365th power. You multiply it by itself 365 times. That's because if I have $1 in my balance, on day 2, I'm going to
have to pay this much x $1. 1.0006274 x $1. On day 2, I'm going to have to pay this much x this number again x $1. Let me write that down. On day 1, maybe I have $1 that I owe them. On day 2, it'll be $1 x
this thing, 1.0006274. On day 3, I'm going to have to pay 1.00 - Actually I forgot a 0. 06274 x this whole thing. On day 3, it'll be $1,
which is the initial amount I borrowed, x 1.000, this number, 6274, that's just that there and
then I'm going to have to pay that much interest on
this whole thing again. I'm compounding 1.0006274. As you can see, we've kept
the balance for two days. I'm raising this to the second
power, by multiplying it by itself. I'm squaring it. If I keep that balance for
365 days, I have to raise it to the 365th power and
this is counting any kind of extra penalties or
fees, so let's figure out - This right here, this number,
whatever it is, this is - Once I get this and I subtract 1 from it, that is the mathematically
true, that is the effective annual percentage rate. Let's figure out what that is. If I take 1.0006274 and I
raise it to the 365 power, I get 1.257. If I were to compound
this much interest, .06% for 365 days, at the end
of a year or 365 days, I would owe 1.257 x my
original principle amount. This right here is equal to 1.257. I would owe 1.257 x my
original principle amount, or the effective interest rate. Do it in purple. The effective APR, annual percentage rate, or the mathematically correct
annual percentage rate here is 25.7%. You might say, "Hey, Sal,
that's still not too far off "from the reported APR,
where they just take "this number and multiply
by 365, instead of taking "this number and taking
it to the 365 power." You're saying, "Hey, this is roughly 23%, "this is roughly 26%, it's
only a 3% difference." If you look at that
compounding interest video, even the most basic one
that I put out there, you'll see that every
percentage point really, really, really matters, especially
if you're going to carry these balances for a long period of time. Be very careful. In general, you shouldn't
carry any balances on your credit cards,
because these are very high interest rates and you'll
end up just paying interest on purchases you made many, many years ago and you've long ago lost all
of the joy of that purchase. I encourage you to not even keep balances, but if you do keep any balances, pay very close attention to this. That 22.9% APR is still probably not the full effective interest
rate, which might be closer to 26% in this example. That's before they even
count the penalties and the other types of
fees that they might throw on top of everything.