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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.

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  • blobby green style avatar for user Jeffrey Li
    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??
    (59 votes)
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    • leaf green style avatar for user Christian Borao
      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.
      (50 votes)
  • blobby green style avatar for user Horacio Prado
    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
    (12 votes)
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  • blobby green style avatar for user Letta Bennett
    What is the difference between APR and APY?
    (6 votes)
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    • starky tree style avatar for user melanie
      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.
      (18 votes)
  • blobby green style avatar for user Jacob Elder
    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?
    (9 votes)
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    • male robot hal style avatar for user shaunteaches
      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.
      (11 votes)
  • hopper jumping style avatar for user Mark Ivanovich
    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)
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    • male robot hal style avatar for user shaunteaches
      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)
  • piceratops tree style avatar for user Sami
    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)
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    • male robot donald style avatar for user John
      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)
  • hopper jumping style avatar for user Smart-guy
    at 3,22 why does Sal adds 1 to 000,6274?
    (3 votes)
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  • leafers seed style avatar for user Jazmin Jones
    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)
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  • blobby green style avatar for user Andrew Dvorak
    So after you find the effective interest rate, do you just multiply it to the principle to get the true final cost?
    (3 votes)
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  • piceratops seed style avatar for user rhettb
    I was always under the assumption that if you pay your credit card off monthly, you will never be charged interest. If the interest is compounded daily, do they charge you the daily interest on the balance held at the end of each day? Meaning should I be paying off my credit card daily? Or do they compound the daily balance and only charge it if it's not paid off at the end of the month?
    (3 votes)
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    • leafers seedling style avatar for user Nivas
      @Andrew, you are right! However, theoretically, you'll end up paying less if you pay interests daily that paying it monthly because, there will be new interest calculated for the interest that was unpaid for the 30days! Hope it makes sense!
      (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.