Main content

# Annual percentage rate (APR) and effective APR

APR stands for Annual Percentage Rate. It's the yearly interest rate you pay on a loan or credit card. However, a credit card's advertised APR isn't the true interest rate because it compounds daily. Learn how to calculate the effective APR to find a card's true interest rate. Created by Sal Khan.

## Want to join the conversation?

- sal compounds the multiplier (which is 1.006274) by 365 times in a year. But shouldnt he compound the multiplier by 364 times/ year instead? I think this because he says that he receives his money on day 1, and on day one, he doesnt multiply the money by anything because he just received the money on that day. And so, if he doesnt compound the money on the first day, there are only 364 days left in the year, so why doesnt he compound the money by 364 times instead??(62 votes)
- Good catch. Technically yes, if you include day one (where no interest was charged), then at the end of 365 days, only 364 days of compounding would have taken place. Sal's goal was to calculate a year of compounding, so that's why he raised 1.0006274 to the 365th power (which means that the 365 days start after day one). But you're right: if you count day one as the day you put the money on the card like he did, the number should be raised to the 364th power.(52 votes)

- In the last step, how come it goes from 1.257 to 25.7%. Shouldn't it be 125.7%? What happens with the 1, can someone explain to me? Thanks(11 votes)
- The 1 represents the original amount of money over which you pay the interest. So its 100% of capital and 25.7% of iterest, 125.7% total.(22 votes)

- What is the difference between APR and APY?(6 votes)
- APR is the rate of interest you are being paid. APY is the
**actual**return you are getting once you factor in compounding.

For example, suppose you have two different investment vehicles, and they both pay 4% interest (APR). However, one compounds daily and the other one monthly. The APY will be higher for the vehicle that compounds daily.(19 votes)

- Why does he say he would 1.257 times his original principal amount, and then he says his effective interest rate would be 25.7%? Wouldn't it be 125.7%? I don't understand where he got that 25.7% from. If he was using that initial 1.257, if you change that into a percentage, it wouldn't be 25.7%, would it?(8 votes)
- Jacob, great question!. You are correct that 1.257 = 125.7%, but here we are just trying to find the interest or the amount added to the principal. So we just look at the amount above 100%, which is the 25.7%. So in these types of problems, we find some result (which is 1 + interest rate) and then subtract the 1 to isolate the interest rate.(10 votes)

- Please, clarify understanding.

APR - is something wierd.

Hope I get an idea of compound interests, so, it's all about applying some interest from cycle to cycle, but why do we have compound interest's interpritation here?

If somebody state to me, that my annual percentage rate is 22.9% and it all dividing into parts by day,

a will think that in looks something like dividing percents by 365 parts and then applying to my initial credit, likewise our credit is 1000, so bank got it and take 22,9 percent out, then divide into 365 days and charge off day by day. It's even sounds so, APR, the first word here - ANNUAL, hence if I got 1000, to the next year I'll must pay off 229$ that exactly 22.9% from my initial loan. I can't understand how they can apply compound interests when somebody states about 22.9% per year, or, to state 22.9% per year when has compound interests and some rate per day that eventually doesn't equal to annual...(6 votes)- Great question Mark. I think you are asking "why do they have a simple interest calculation like APR represent compound interest? Why not just use effective APR?"

I have thought about this quite a bit and I am wondering the same thing. I can only note that there are different types of APRs and many different types of loans, so an APR must be an effective tool in certain situations.(6 votes)

- I do not understand how Sal went from 0.6724% to a decimal of 0.0006724. Could someone please explain how he got the latter?(4 votes)
- Sami, he got the 0.06724% by dividing the 22.9% by 365, the number 0.06724% is how much the bank compounds the principal daily. Now that you have the 0.06724%, Sal then turns this number into a decimal by moving the decimal point over two places to the left, thus giving you the latter of 0.0006724 (which is the decimal notation of 0.06724%).(5 votes)

- at 3,22 why does Sal adds 1 to 000,6274?(3 votes)
- It is the principle + 1 period of interest.(7 votes)

- So after you find the effective interest rate, do you just multiply it to the principle to get the true final cost?(3 votes)
- apr is annual percentage rate. If you barrow money from a credit card company you will end up spending more money paying them back then you borrowed from them.(4 votes)

- So I appreciate this video! I thought they compounded monthly not daily so I assumed I was not paying interest on the 30 days after I make a purchase. I checked my credit card information and found that there is no charge to the first 25 days after the after the billing cycle and YTD I have paid $0.00. So I am glad that I am not automatically paying interest. However, do most companies offer a grace period?(4 votes)
- The grace period only applies if you paid your bill in full the prior month, and if you take no cash advances.(2 votes)

- According to the other interest videos, Sal stated that the equation for compound interest compounding monthly for a year would be something like this A= P(r/12+1)^12. Now here, the interests are being compounded daily, and by his lecture, the equation was A=P(R+1)^365. My question is that shouldn't we divide the rate by 365 as well because the other videos, he divided the rate by the compounding period. If it compounds annually, then we wouldn't have to do anything with the rate because it's a year. If it compounds semi-annually, then we would have to divide the rate by 2, because its compounding every 6 months, and therefore, would compound TWICE per year. If it compounds quarterly, we would have to divide the rate by 4 because it would be compounding every 3 months, and FOUR times per year. However, in this problem, even though it says that this interest compounds daily, meaning you would have to divide the rate by 365, he didn't do that. Can somebody tell me why is that?(3 votes)
- in your second equation R would be the daily rate, not the annual rate.(3 votes)

## 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.