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The question states that you start with a balance of 135.50 on March 1st. Make a $50.00 payment on March 15th. Then make a purchase of $38.60 on March 18th. Find the average daily balance. Assume the billing cycle begins March 1st and ends March 31st.

So we’ve got a question here about average daily balance and about chapter 12 it says supposed to charge account of strong’s mailing service at a local supply store had 18% interest rate per month on the average daily balance we want to find that average daily balance if he had an unpaid balance on this march first one $35.50 he makes a payment on the 15th then

He makes another purchase i’m sorry he makes a payment on the 15th then he makes another purchase on the 18th his cycle ends on the 31st so what we want to do is average find out what the average daily balance is so what you would do then is take the average this is daily balance every day and they just add up to daily balance for all month and then divide by 31

Since there’s 31 days of the month instead of trying to do that though there’s a little bit of a shortcut but that’s basically what we’re going to do so what i like to do for these questions is to write out exactly what happens to the whole month so on the first he’s got a balance of a hundred and thirty five dollars in 50 cent’s that’s what it says in the problem

Now he’s going to carry that balance all the way to the 15th so it says here till the next time if something happens was on the 15th he makes a payment at $50 so that’s and we’ll carry that same balance all the way down to the 15th so that’s the 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th and under 12 thirteenth’s of 14th and the 15th he makes a payment so the daily

Balance changes it’s all 100 $35.50 all the way down to the 15th on the 15th the balance changes he makes a $50 payment so the 100 $35.50 take away 50 bucks because it makes payment of $50 he winds up with $85 in 56 saw the 15th he has this balance now so it changes is all 100 $35.50 all the way down to the 15th then it says he keeps that until the 18th march the

18th it says here that a purchase of $38 and 60 cents posted on the 18th so on the 18th he makes another pain aee we’re going to add 38 dollars and 60 cents to it to the balance that gives you a hundred and twenty-four dollars and ten cents is the new balance he’s going to carry that balance all the way to the 31st to the 19th to 20th 21st 22nd 23rd 24th 25th 26th

27th 8 right 30th 31st he ends the day the month ends on the 31st so he’s going to carry 135 dollars those months he’s gonna carry 85 dollars and 50 cents for these 3 all these days carries this for all these days he carries this balance for the rest of the days so let’s let’s count up how many days that would be because i really don’t want to say i don’t want to

Add in my calculator 135 point five plus 135 point 5 plus 135 plus 0.5 plus i’m thirty nine point five plus plus plus plus plus plus plus 85 50 plus 85 50 plus 85 50 plus one 24 plus 124 124 plus plus plus plus with all the way down to get a total and then divide by 31 to get to average that out i don’t want to average all these numbers that take forever so what

You do you just count out how many days you carry this balance so i’ll see your sheet of paper here he carries $135 balance 50 cents he carries that balance for 1 2 3 4 5 well 14 days kate for 14 days so if i multiply that out i’m going to get how much it would that that basically does it a little shorthand of saying 135 plus itself 14 times okay now he’s going

To carry this balance 8550 for how many days 1 2 4 3 days so he carried a balance of the 85 50 for three days someone multiply that out for three days then he carries 124 dollars and ten cents for how many days well 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a 14 days for 14 days now you know what we could have just simply subtracted the numbers over here we could have

Said 15 minus 1 is 14 we could have said 18 minus 15 is 3 days but here’s the kicker here’s not being where some people get this wrong if you take 31 minus 18 if you take the 31st – the 18th you get 13 not 14 right i’m going to show you right if i take 31 minus 18 i get 13 and when i counted it i counted 14 days so this last piece you better if you’re going to do

It this way you’re gonna subtract the two dates you better add 1 to it – inc you got to count to the 18th ok you got to count the 18th here in this case at the very end okay so that might be where some people are getting this wrong so let’s figure out how much we got here see 135 50 times 14 is 1897 85 50 times three is twenty two fifty six point five 14 times 124

Dollars and ten cents is 17 hundred thirty-seven dollars add those together now i get 38 90.9 now what that just did was if i would get the same number if i took he 20 days added him up this plus this you know 35 135 50 plus itself out of all these all these what he carried his balance he carried everyday i added them all up i get this so to average it you divide

By 31 because there’s 31 days across of march so i take 338 90/30 one that’s 125 51 that’s the average daily balance that he had if you averaged up the daily balance almost long this is the average that you’ll get

Transcribed from video

Business Math: How to calculate the average daily balance. By mcclendonmath