Average Daily Balance

This video shows how to calcluate the finance charge on a credit card using the average daily balance method.

Hi this is dr. dave what we’re gonna look at now is how to calculate a finance charge on a credit card using the average daily balance method in a previous video we use the unpaid balance method which is not very much in use anymore however the average daily balance is probably used by most credit cards so suppose that on january 1st you have a credit card balance

Of six hundred and twenty dollars on january 10th you purchase a magazine subscription for twenty dollars on january 12th you return an item to target for a credit of $34.50 on january 22nd you make a payment of $500 on january 25th you make a purchase at safeway of one hundred and twelve dollars the annual interest rate on the credit card is twenty one percent

And calculate the finance charge for january that will appear on next month’s statement using the average daily balance method so the key here is in order to be able to calculate an average daily balance i need to know what the balance is on each and every day of the month so from january 1st through january 31st so it says on january 1st i have a balance of six

Hundred and twenty dollars the next transaction i have is on january 10th that means on the first the second the third the fourth the fifth the sixth the seventh the eighth all of those days and the ninth i’m going to have that balance now on january 10th there’s a transaction all right so this transaction is the subscription and it’s gonna reeled a change in balance

It’s gonna increase my balance by $20.00 because it’s a purchase so plus 20 that means after that transaction my balance will be six hundred and forty dollars so the next transaction is on january 12th so i’ll have that balance of 640 on the 10th and on the 11th on the 12th i returned an item to target so that’s a return and that’s going to be reduce my balance by

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$34.50 so i’m going to subtract 3450 so when i go ahead and subtract 3450 we have a balance of 640 and it’s going to be reduced by the return by 3450 so that gives my new balance of 605 dollars so that gives my new balance of 605 dollars and 50 cents now remember i made that transaction on the 12th the one after that is on the 22nd so i’m gonna have that balance

On the 13th the 14th the 15th the 16th 17th 18th the 19th the 20th and the 21st on the 22nd is where my next transaction occurs and that one is a payment and a payment is going to reduce my balance by $500 so from the $605 and $0.50 balance it’s going to reduce it by 500 that’s going to leave me with a balance of 105 50 the next transaction is on january 25th so

I’m going to have that balance on the 22nd the 23rd the 24th and the 29th the 25th because that’s where the next one is so the next one goes down here on the 25th and that’s a purchase at safeway and it purchase of a hundred and twelve dollars so that’s gonna add to my balance a hundred and twelve dollars so my 105 fifty when i add one hundred and twelve dollars

That gives me a new balance of two hundred and seventeen dollars and fifty cents and now i’m gonna have that balance through the end of the month because that’s my last transaction so twenty-six twenty-seven the 28th the 29th the 30th and the 31st all right so now we need to figure out our average daily balance and to do that i need to know how many days i had

That balance and what the balance was so for this first one the first second third fourth fifth sixth seventh eighth night that’s nine days we had the balance of 644 two days the balance of 605 let’s see one two three four five six seven eight nine ten for ten days the balance of 105 fifty for three days and then the balance of two seventeen fifty one two three

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Four five six seven days so if i’ve done this correctly these should add up to being 31 days so 9 plus 2 is 11 plus ten is 21 another 10 is 31 so i’ve accounted for the entire month so now i need to work out my average daily balance and the way i do that is i need to add up the balances on all 31 days i could say 620 plus 6 26 29 times and then 640 plus 6 4605 50

10 times in my sum to but to make it easier i’m going to go ahead and take advantage and say 620 times 9 instead of adding up 629 times i’m gonna add that 640 times the two days plus 605 0.5 0 times the 10 days the 105 50 times the 3 days and finally the 217 50 times seven days that’s going to account for all 31 days so then i divide it by 31 when i work out that

Top it comes out to be fourteen thousand seven hundred fifty-four divided by 31 and so when i work out that division i get a number that is approximately four hundred seventy five point nine four that’s to the nearest penny now look at my numbers here if i make a mistake here if i were to do this incorrectly and a lot of the time i’ll see people go oh there’s five

Lines to this table i’m gonna divide by five if you do that you get a number that is much much larger in fact it’s a number in the thousands but look at these numbers the lowest ones 105 50 the highest one 640 the average daily balance has to be somewhere in between those two numbers so if you work out this division and get something that is way bigger than your

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Highest balance or way lower than your lowest balance you know you’ve made some kind of a mistake all right so now i have the average daily balance i need to work out the finance charge and i’m going to do that the same way i did with the unpaid balance method i’m gonna use simple interest so i’m gonna take the average daily balance i’m gonna multiply it times the

21% so it’s the present value which in this case is the average daily balance times the rate and now i’m going to multiply it by time but since we’re doing everything here on a daily basis i’m gonna multiply it by 31 over 365 because a year or a month in this case of january 31 days out of a total of 365 so that’s the fraction of the year for january when i put that

Into my calculator and work it out so 475 0.94 times 0.2 one times 31 divided by three six five so i get eight point four eight eight six rounded to the nearest penny that’s eight dollars and 49 cents so that would be the finance charge corresponding to the january bill so the key thing here i find is when i do these average daily balance to make a table lists out the

Days don’t say one through nine because if you say one through nine you have a tendency say that’s eight days i like to list out the actual days so then i could count them up to get my nine days off to the side but then it’s balanced times the day’s balance times the days you add those all up that’s the top part of the average daily balance and then divide by the total number of days

Transcribed from video
Average Daily Balance By MathFAQ