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# Annual percentage rate (APR) and effective APR

## Video transcript

easily the most quoted number people give you and they're publicizing information about their credit cards is the APR and I think you might guess or you might already know that it stands for annual percentage rate annual percentage rate percentage rate and what I want to do in this video is to understand a little bit more detail on 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 so I was actually just browsing the web and I saw some credit card that had an annual percentage rate of they say it's a twenty two point nine percent annual percentage rate but then right next to it they say that we have zero point zero six two seven four percent daily daily periodic rate periodic rate which to me this right here this piece 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 so where do they get these numbers from well if you just take point zero six if you just point take point O six two seven four and multiply by 365 days in a year you should get this twenty two point nine and let's see if we get that and 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 so if I take if I take point O six two seven four and remember this is a percent but I'll just ignore the percent sign so so as a decimal I would actually add two more zeros here but 0.06 two seven four times 365 is equal to right on the right on the money twenty two point nine percent would say hey Sal what's wrong with that that's you know they're charging me 0.06 two seven four percent per day they're going to do that for 365 days a year so that gives me twenty two nine point twenty two point nine percent and 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 go them one hundred twenty two point nine dollars they're compounding this much every day so if I were to write this as a decimal so let me just write that as a decimal so point zero point zero six two seven four percent if I as a decimal this is the same thing as zero point zero zero oh six two seven four these are the same thing right one percent is 0.01 so 0.06 percent is point zero zero zero six as a decimal now this is how much they're charging every day and if you watch the compounding interest video you know that if you if you wanted to figure out how much you how much total interest you would be paying over total year you would take this number add it to one add it to one so we have one point this thing over here point zero zero zero six two seven four and instead of so instead of just taking this and multiplying it by 365 you take this number and you take it to the 360 fifth to the 360 fifth power you multiply it by itself 365 times that's because if I have one dollar in my balance on day two I'm going to have to pay this much times one dollar 1.000 six two seven four times a dollar on day two I'm gonna have to pay this much times that times this number again times the one dollar so let me write that down on day one on day one on day one maybe I have one dollar that I owe them on day to day two it'll be one dollar times this thing 1.00 six to seven four on day three on day three I'm going to have to pay 1.00 actually I forgot to zero oh six to seven four times this whole thing so on day three will be one dollar which is the initial amount I borrow times 1.000 this number six to seven four that's just that there and I want to pay that much interest on this whole thing again I'm compounding 1.000 six to seven four so as you can see we've kind of kept the balance for two days and I'm raising this to the second power if I'm multiplying it by itself I'm squaring it so if I keep that balance for 365 days I have to raise it to the 360 fifth power and this isn't counting any kind of extra penalties or fees so let's figure out and this right here this number whatever it is this is if I once I get this and I subtract one from it that is the mathematically true that is the effective annual percentage rate so let's figure out what that is so if I take one point zero zero zero six two seven four and I raise it I raise it to the to the 365 power I get one point two five seven so if I were to compound this much interest 0.06 percent for 365 days at the end of a year I would or the 365 days I would oh one point two five seven times my original prints all about so that's so this right here this right here is equal to one point two five seven so I would a one point two five seven times my original principal amount or the effective interest rate let me do it in purple the effective interest rate effective APR annual percentage rate or the mathematically correct annual percentage rate here is twenty five point seven percent and you might say hey Sal you know that's still not too far off from the reported APR where they just take 22 when they just take this number and multiply by 365 instead of taking this number and taking to the 365 power you're saying hey this is only a this is roughly 23% this is roughly 26 percent it's only a three percent difference but if you look at that compounding interest video even the most basic one that I've put out there you'll see that every percentage point really really really really matters especially if you're going to carry these balances for a long period of time so be very careful in general you shouldn't carry any on your credit cards because these are very high interest rates and you'll end up just being paying interest on purchases you made many many years ago and you've long ago lost all of the joy of that purpose so I encourage you to not even keep balances but if you do keep any balances pay very close attention to this that that 22.9% APR is still probably not the full effective interest rate which might be closer to 26% in this example and that's before they even count the penalties and the other types of fees that they might throw on top of everything