Credit cards and loans
Annual Percentage Rate (APR) and Effective APR The difference between APR and effective APR
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- Usually 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.
- 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.
- 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 a 0.06274
- percent daily periodic rate.
- Which to me, this piece 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 0.06274 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 if I take 0.06274-- and remember this is a percent,
- but I'll just ignore the percent sign, so as a decimal
- I would actually add 2 more 0's here.
- But 0.06274 times 365 is equal to 22.9%.
- And you say, hey Sal, what's wrong with that?
- They're charging me 0.06274% per day.
- They're going to do that for 365 days a year, so
- that gives me 22.9%.
- And my reply to you is that they're
- compounding 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 is a decimal.
- So let me just write that as a decimal.
- So 0.06274% as a decimal this is the same thing as 5 These
- are the same thing.
- 1% is 0.01.
- So 0.06% is 0.0006 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 want 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 1.0006274.
- So 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 times one dollar $1.
- 1.0006274 times $1.
- On day 2, I'm going to have to pay this much, times this
- number again, times the $1.
- So let me write that down.
- On day 1 maybe I have $1 that I owe them.
- On day 2, it'll be $1 times this thing, 1.006274.
- On day 3, I'm going that have to pay 1.0006274 times this
- whole thing.
- So on day 3 it'll be $1 times 1.0006274.
- Then I'm going to have to pay that much interest on this
- whole thing again.
- I'm compounding, 1.0006274.
- So you can see we've kind of kept the balance for 2 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 365th power.
- And this isn't counting any kind of extra
- penalties or fees.
- This number, whatever it is, once I get this and I subtract
- 1 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 to the 365
- power, I get 1.257.
- So if I were to compound this much interest, 0.06% for 365
- days, at the end of a year I would owe 1.257 times my
- original principal balance.
- So this right here is equal to 1.257.
- So I would owe 1.257 times my original principal amount.
- Or the effective interest rate, APR, annual percent
- rate, or the mathematically correct annual percentage rate
- here, is 25.7%.
- And 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.
- But 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, 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 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 a 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.
- A 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.
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