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

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.

L&S

Thank you sir!

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

THANK YOU SO MUCH YOU HAVE A NATURAL GIFT

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

Damn great explanation.

Why dont we teach this in high school?

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.

how did he get 25.7% effective apr ?

I still don't understand how he got 25.7%

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

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

I don't even try.

Account.

I saw costs.

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

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

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?)

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!

Man credit card is such a scam.

thanks once again, Sal! you're the man

@ 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!!

i cant believe im just learning this

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