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Annual percentage rates. What's really behind those confusing little numbers? A lot of math. Find out how banks and credit card companies use both APR and effective APR to calculate how much interest you'll pay on your debt over time.
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Easily the most quoted number people give you when 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 of 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 22.9 percent annual percentage rate but then right next to it they say that we have 0.06274 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 .06, if you just point, take .06274 and multiply by 365 days in a year, you should get this 22.9, 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, I if take, if I take .06274 and remember, this is percent but I'll just ignore the percent sign so as a decimal I would actually add two more zeros here. But .06274 times 365 is equal to, right on the, right on the money, 22.9 percent, and you would say, hey Sal, what's wrong with that? That's, you know, they're charging me .06274 percent per day. They're going to do that for 365 days a year, so that gives me 22.9, 22.9 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 owe them $122.90, 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 .06274 percent, if I, as a decimal this is the same thing as 0.0006274, these are the same thing, right? One percent is .01, so .06 percent is .0006 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 a total year you would take this number, add it to one, add it to one, so we have one point this thing over here, .0006274, and instead of, so instead of just taking this and multiplying it be 365 you take this number and you take it to the 365th, to the 365th 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, 1.0006274, times a dollar. On day two I'm going to 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 two, day two it'll be one dollar times this thing, 1.006274. On day three, on day three, I'm going to have to pay 1.00, actually, I forgot a zero, 06274 times this whole thing. So, on day three it'll be one dollar, which is the additional amount I borrowed times 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. 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, I if keep that balance for 365 days I have to raise it to the 365th 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 have, 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 1.0006274, and I raise it, I raise it to the, to the 365 power, I get 1.257. So, if I were to compound this much interest, .06 percent for 365 days, at the end of a year I would, or the 365 days, I would owe 1.257 times my original principal balance. So, that's, so this right here, this right here, is equal to 1.257. So, I would owe 1.257 times my original principal amount or the effective interest rate, let me do it in purple, the effective interest rate, the effective APR, annual percentage rate, or the mathematically correct annual percentage rate here is 25.7 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, where they just take this number and multiply it by 365 instead of taking this number and taking it to the 365 power. You say, hey, this is only a, this is roughly 23 percent, 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 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 balances on your credit card 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 purchase. So I encourage you to not even keep balances but if you do keep any balances pay very close attention to this, at that 22.9 percent APR is still probably not the full effective interest rate, which might be closer to 26 percent in this example, that's before they even count the penalties and the other, uh, types of fees that they might throw on top of everything.