Annual percentage rate (APR) and effective APR (video) | Khan Academy

Video transcript

Voiceover : well the most quote 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 share rate. What I want to do in this video recording is to understand a small morsel more detail in what they actually mean by the annual percentage rate and do a short moment mathematics to get the substantial or the mathematically or the effective annual percentage rate. I was actually good browsing the web and I saw some credit rating circuit board that had an annual share rate of 22.9 % annual share rate, but then right future to it, they say that we have 0.06274 % daily periodic rate, which, to me, this right here tells me that they compound the matter to on your credit circuit board balance on a casual basis and this is the sum that they compound. Where do they get these numbers from ? If you good take .06274 and multiply by 365 days in a year, you should get this 22.9. Let ‘s see if we get that. Of path this is percentage, so this is a share here and this is a percentage here. Let me get out my trusty calculator and see if that is what they get. If I take .06274 – Remember, this is a percentage, but I ‘ll just ignore the percentage sign, so as a decimal, I would actually add two more zeros here, but .06274 x 365 is peer to, right on the money, 22.9 %. You say, “ Hey, Sal, what ‘s amiss with that ? “ They ‘re charging me .06274 % per day, “ they ‘re going to do that for 365 days a year, “ sol that gives me 22.9 %. ” My reply to you is that they ‘re compounding on a daily basis. They ‘re compounding this total on a casual footing, so if you were to give them $ 100 and if you did n’t have to pay some character of a minimum balance and you fair let that $ 100 ride for a year, you would n’t good owe them $ 122.9. They ‘re compounding this much every day, so if I were to write this as a decimal fraction … Let me just write that as a decimal. 0.06274 %. As a decimal this is the lapp thing as 0.0006274. These are the lapp thing, right ? 1 % is .01, therefore .06 % is .0006 as a decimal fraction. This is how much they’re charging every day. If you watch the compound concern video recording, you know that if you wanted to figure out how much total interest you would be paying over a sum class, you would take this number, add it to 1, so we have 1., this matter over here, .0006274. rather of just taking this and multiplying it by 365, you take this number and you take it to the 365th exponent. 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 ten $ 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, possibly 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 ten this wholly thing. On day 3, it ‘ll be $ 1, which is the initial come 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 excess penalties or fees, so lashkar-e-taiba ‘s figure out – This justly 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 share rate. Let ‘s figure out what that is. If I take 1.0006274 and I raise it to the 365 might, I get 1.257. If I were to compound this much interest, .06 % for 365 days, at the end of a class or 365 days, I would owe 1.257 x my original principle amount. This correct here is adequate to 1.257. I would owe 1.257 x my master rationale amount, or the effective sake rate. Do it in purple. The effective APR, annual percentage rate, or the mathematically correct annual share rate here is 25.7 %. You might say, “ Hey, Sal, that ‘s still not excessively far off “ from the reported APR, where they equitable take “ this issue and multiply by 365, alternatively of taking “ this issue and taking it to the 365 office. ” You ‘re saying, “ Hey, this is approximately 23 %, “ this is approximately 26 %, it’s only a 3 % difference. ” If you look at that compounding interest video recording, tied the most basic matchless that I put out there, you ‘ll see that every percentage orient truly, truly, truly matters, particularly if you ‘re going to carry these balances for a hanker period of time. Be very careful. In general, you shouldn’t carry any balances on your recognition cards, because these are very high interest rates and you’ll end up barely paying matter to on purchases you made many, many years ago and you ‘ve long ago lost all of the joy of that leverage. 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 however probably not the broad effective interest rate, which might be closer to 26 % in this case. That ‘s before they even count the penalties and the other types of fees that they might throw on top of everything.

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