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Annual percentage rate (APR) and effective APR

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.