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How credit card interest is calculated

Learn about average daily balance, grace period, and credit card interest. Created by Sal Khan.

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Video transcript

Let's think a little bit deeper about how interest on your credit card is actually calculated for a given billing cycle. And a billing cycle is just a period of time over which the credit card company will give you a statement. And so let's just say, for the sake of argument, your billing cycle is from the first of the month to until the first of the next month, and we'll just assume that it's October, to use as an example. So let's just say, going into October, you had $100 balance on your credit. So you have $100 balance in your credit card and you continue to have $100 balance. You don't do any spending nor do you pay down the card until October 6th. So let's say that's the sixth right over there, and that's where you go and you buy yourself a nice sweater for $100. And so now, you have a $200 balance on your credit card. And once again, that $200 balance, it continues. You don't do any more spending or paying down. But you had sent a check in a couple of days ago and it finally gets registered with the credit card company on the 20th. And that check was for a $150, and so it pays down your balance. Your balance would now go down from 200, since you paid 150, it would go down to 50. It would go down to 50. And then you don't do any more paying nor do you do any more spending until the end of the billing cycle, just like that. So let's think about how much interest you would have to pay for that period. And just to make things a little bit concrete, let's say that your annual percentage rate, APR, it's typically called, let's say that that is 22.99%. I just looked at one of my credit cards and that is what the APR was, and they always tend to put this .99%. I guess they feel like it makes you, it looks better than saying 23%. So let's think about what the interest charge would be for the spending in this period. And the way that it's typically calculated is using the average daily balance method. Let me write this down. Average daily balance. And one way of thinking about it is it is exactly what it says. It averages your daily balance for every day in the billing period. So for example, right over here, we had five days from October 1st until the beginning, I guess you could say from midnight October 1st, until midnight October 6th where we had a balance of $100, so we could write that down. We have five days where we had a balance of, let me write it like this. We have five days where we had a balance of $100. And then we go from the 6th to the 20th, so that is 14 days when we have a balance of $200. So, plus 14 times $200. And then finally, going from the 20th to the 1st, you could almost see the 1st as the 32nd, so this is another, this right over here would be 12 days. This is going to be 12 days where we have a balance of $50. And we're gonna divide this, we're gonna divide this by the total number of days of our billing cycle. And once again, in October, we had 31 days. This would be a different number if we were going from the 1st of February to the 1st of March. And just to make it clear that this is the average daily balance, I could have written down 100 plus 100 plus 100 five times. So I could have done 100 plus 100 plus 100 five times and then I could have done 200 plus 200 plus 200. So literally for each day that I'm at a hundred, I would have written a hundred, but there's five of those. And for each day that I'm at 200, I could have added 200 to this, to the top part of this fraction. Remember, there's 14 of those, so I just multiply it 14 times 200. And the same thing, there are 12 days when I was at 50. I could have said 50 plus 50 plus 50, done that 12 times, but that's just going to be 12 times 50. So our average daily balance is going to be, let's think about this. This would be $500. 14 times 200 is 2800 or 2,800. And then 12 times 50 is $600. So let's see, 500 plus 600 is 1100, plus 2800 is $3,900, and we're going to divide that into 31 days. So if you summed up your balance for each day, you would get 3900. And so let's divide. So $3,900 divided by 31 gets us $125.8, I guess if we round to the nearest penny, 81. So that is equal to, let me give myself some space here, $125.81 or $125 and 81 cents. This is what your average daily balance would be. Now your credit card company, based on this, can actually calculate what your interest charge should be for that billing cycle. So they'll take the $125 and 81 cents, and then they're going to multiply it by your APR, but adjusted for the number of days in the billing cycle. So you'll say, "What fraction of the year "was this billing cycle?" So they'll multiply it. So let's assume that there are 365 days in this year, this billing cycle has 31 days, so 31 divided by 365. And then that times the annual percentage rate. So, times 22.99%, and that is going to give us, get the calculator out again. And so I could take this previous answer that I had and multiply that. That just means the previous answer that I just had, times 31 divided by 365 times 22.99%, that's the same thing as 0.2299, and we get an interest charge of $2, I guess we could say $2 and 46 cents. So $2 and 46 cents in interest. Now, if we pay the entire, that's what we'll have to pay in interest if we don't pay the entire balance off in full. But you usually have a grace period so that if you pay your credit card fully off and the grace period only applies for a traditional credit transactions, not necessarily things like cash advances or not necessarily things like balance transfers, but typically, you have a grace period of 21 to 25 days, sometimes it might be even longer than that where if you pay off your balance in that period, so in the grace period, so if you completely pay this off, so if you pay off the $50 in this period, then you won't have to pay this. If you pay anything less than the complete balance, then some of your payment will go to this interest charge.