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Annual Percentage Rate (APR) and effective APR | Finance & Capital Markets | Khan Academy

October 19, 2019

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.

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  • Reply xoLEADFOOTox September 29, 2013 at 7:33 am


  • Reply Supsup516 November 28, 2013 at 1:34 am

    Thank you sir!

  • Reply Xeno May 2, 2014 at 3:56 am

    So in other words the APR is the Nominal Interest Rate and Effective APR is, well, the Effective Interest Rate? Thanks!!

  • Reply BliBlaBloo January 24, 2015 at 4:28 pm


  • Reply Sonya The Singer June 25, 2015 at 9:51 pm

    do you use a pen, or do you write with the mouse? Because your hand writing looks really neat

  • Reply JonnyBeoulve September 16, 2015 at 9:34 pm

    Damn great explanation.

  • Reply Arsenal FC Fan January 31, 2016 at 1:51 am

    Why dont we teach this in high school?

  • Reply James Hanley April 11, 2016 at 5:29 pm

    Isn't this only correct if the card issuer is applying interest daily? A lot of issuers will use a daily rate but will calculate it at the end of the statement period. Therefore, the compound element comes from the time between statement date and payment date.

  • Reply mehmet coskun June 6, 2016 at 1:29 pm

    how did he get 25.7% effective apr ?

  • Reply Quantum Mechanics July 31, 2016 at 2:36 am

    I still don't understand how he got 25.7%

  • Reply Zack Vance September 23, 2016 at 12:29 am

    Slow down Sal, explain how you calculated the effective APR….. D:

  • Reply dinsdins27 February 2, 2017 at 1:05 am

    Do I still pay apr if I always make payments on time?

  • Reply Shaolin Tex Chris Lightning a.k.a. tox May 5, 2017 at 3:20 pm

    I don't even try.

  • Reply Shaolin Tex Chris Lightning a.k.a. tox May 5, 2017 at 3:24 pm


  • Reply Shaolin Tex Chris Lightning a.k.a. tox May 5, 2017 at 3:27 pm

    I saw costs.

  • Reply David Reames May 27, 2017 at 1:40 pm

    so the day1, day2 calculations are based on a $100 balance or a $1 balance? He said $100 then $1.

  • Reply Việt Phùng November 8, 2017 at 7:20 pm

    Can you tell me where can you get the effective annual rate is 25,7% ? Is it from a calculation or something ? I'm still confused of this part. Thank you

  • Reply Einsatzgruppen Commander February 27, 2018 at 12:29 pm

    So if the effective APR is actually 25.7%, even with no late fees or penalties. What exactly does a 22.9% represent? Would that be your actual APR, only if you paid interest every day? (0.0006274% every day, instead of paying all interest on day 365?)

  • Reply Float Circuit November 10, 2018 at 6:44 pm

    Daing, I almost set up a “certificate” that my bank offered me because APR (and effective APR) sounded like a good thing. Glad I immediately went online to learn about it. Thanks Sal, for saving me some needless heartache. Wishing you the best!

  • Reply Tin Do December 19, 2018 at 3:17 am

    Man credit card is such a scam.

  • Reply Rodri A Cruz February 16, 2019 at 10:03 pm

    thanks once again, Sal! you're the man

  • Reply taxacher April 3, 2019 at 7:48 pm

    @ Einsatz…Commander the 22.9% represents a way for the Lender to make you think you are paying less of an APR than the (mathematically correct) APR which is actually the 25.7%. Banks in particular don't like you to find out what you're really paying. It's more convenient to gently? lie to the customer. As another example, probably most of the good folks on this comment stream actually think that their savings or checking account money is actually in the bank, lololol….. NOT!!! Your money is loaned out almost as quickly as it lands in your account, using something called "leverage" otherwise known as the "reserve ratio". This ratio is carefully determined by years of experience with human behavior as to how many cents on the dollar they must still keep at the bank, to cover withdrawals. They loan the rest of it at high rates like 8,9, 10% APR for a car loan, then pay you .08% annually on your savings account for using your money. I believe this to be essentially correct. The banks then cover each other with a process known as "overnight lending" which is the way they can maximize leverage without revealing how little money is kept in the bank vault. I would get into how mortgages are financed by the bank when you buy a house, but I don't want to make your blood boil / push you over the edge!!

  • Reply JimmyBoom April 4, 2019 at 4:53 am

    i cant believe im just learning this

  • Reply Never lose sleep over the small stuff October 18, 2019 at 8:37 am

    How did he go from 1.257 to 25.7%? Can someone please explain

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