Here we want to try to calculate the finance charge on a credit card so here’s our scenario carrie has a target credit card with a balance of 672.89 her current billing period goes from january 10th to february 9th and below is her activity during this billing period find the monthly finance charge if charges apr annual percentage rate is 18.9 percent so as we

Can see her she’s starting out with the balance of 672.89 she makes a payment that’s going to go down it’ll stay there for a little while until the next time she makes a purchase which is january 27th she buys gas for 45.78 it’ll go up it’ll stay at that value for a little while and then it’ll go up again when she buys groceries on february 3rd for 178 53 and

Then whatever the balance is after that it’s going to stay there until the end of the billing period which we know is on february 9th so what we need to figure out is her balance is constantly changing so how do we find a finance charge on what balance and what we do is actually calculate the average daily balance so that’s what the first part of this video is on

Is calculating the average daily balance so what i want to do first is let’s add in the starting point the starting date of her period so it’s um january 10th and we know that the balance is 672.89 from here we can calculate the balance as we go down from uh the payment to the purchase to the next purchase so if we take 50 away from 672.89 that’s going to be

622.89 i need to now add 45.78 so that’s going to give me 668.67 and finally add in her last purchase of 178.53 that gives me a balance of 847.20 and let’s also put in the last date of her billing period of february 9th so here’s our february 9th this is the ending of her billing period now from here we want to calculate her average daily balance but let’s look

At a different much simpler scenario so down below let’s create a new scenario so for average daily balance and let’s consider um maybe the month of september because there’s 30 days in september that makes it a little bit easier so let’s let’s do a scenario kind of like a similar to above but with a nicer number so let’s say somebody has a two hundred dollar

Balance and it’s going to stay at two hundred dollars for five days so what we can say is it’s going to be two hundred dollars for five out of the 30 days of september or you could reduce that and say it’s really one-sixth of the time it’s at 200. now let’s say you make a payment um on that sixth day so the balance changes it goes down to 150. let’s say it stays

There for 10 days so 10 out of 30 days it’s going to be at 150 so that’s one third of the month and finally let’s make a big purchase of 200 so we’re going to go up to 350 and it’s going to stay there until the end of the month so that’s the last 15 days so 15 out of 30 is half half of the month is at 350. if we add all of these up we get what’s called the average

Daily balance and on this one it’s really and 258.33 cents now when we actually do our calculations up above here we want to make it a little bit simpler so what i can actually do is i can factor out this dividing by 30 at the and really just multiply the balance by the number of days in each of these situations and then divide the total by 30. so if i take

200 times 5 150 times 10 350 times 15 add it up and then divide by 30 i get the same average daily balance so the tricky part usually on these calculations of every daily balance is really being able to accurately calculate the number of days it’s at each balance so that’s what we’ll work on on our top part so let’s calculate the number of days between january

10th and january 16th and an easy way to do it is just to bite do by tally marks so start out with the 10th and just tally mark up don’t include 16 because on the 16th it the balance changes so it’s really only only going to stay at this 670 289 for the 10th up to the 15th so if we tally mark those off we’ll get a tally mark for the 10th 11th 12th 13th 14th and

15th which really turns out to just be six days so the number of days um at that first balance is six an easy way to do that to figure out how many days from like the 10th up to the 16th but not including we can just do 16 minus 10 which gives me 6. so for the next one if i want to know how many days there are from the 16th up to the 27th but not in counting

The 27 that’s just 27-16 so we should have 11 days there the next one gets a little trickier because we’re starting in january 27th but we’re running all the way through up to february 3rd so since there’s 31 days in january you might be tempted just to go 31 minus 27 is 4 and then i’ve got 4 days i have to add to it february first and second but not the third

So it sounds like six but what we’re missing is one actual day because if we do our tally marks and look at how many days are there from the 27th up through the 31st we’re going to have the 27th 28th 29th 30 and 31 so that’s a total of five which means then when we add up the february 1st and 2nd that does give us a total of seven days from the 27th up through

The uh february 3rd but not counting the third so when you cross over a month it’s really tricky you have to think about adding a one to that subtraction just to include that last day of the month similar for the very last period we go from the ninth down to the third you might say well nine minus three is six but again we wanna include this nine so it’s really

If we if you count tally marks from the third fourth fifth sixth seventh eighth and ninth again we get seven so all the way through is seven now before i do any of my calculations i always add up this column of dates just to make sure you have the same number as the number of days in the month you’re starting with in january so we should get 31 and yep 6 plus 11

Plus 7 plus 7 does give me 31. so from here all i need to do now is multiply the balance times the number of days at that balance so that’s like calculating up this part of our simpler problem the balance times the number of days keep on doing that and then we’ll add those up so on this first one we’re going to get 672.89 times six is four thousand thirty seven

Thirty four the next one six twenty two point eight nine times eleven is six thousand eight fifty one seventy nine the next one i’ll multiply out and i get forty six eighty point sixty nine and finally the last one is fifty nine hundred thirty dollars and forty cents i can add these up and i get 21 500.22 and to turn this into an average daily balance i just need

To divide by the number of days in my month which in this case is 31. so if i divide by 31 i’m going to get my average daily balance to be 21 522 let me get rid of this stuff divide by 31 and that gives me an average daily balance of 693 dollars and 56. so lastly we can calculate our finance charge so how do we calculate the finance charge finance charge is

Really just simple interest so our simple interest is interest is p times r times t where t is the length of time r is your annual percentage rate p is normally principal but we’re going to call the principal in this case our average daily balance and so let’s call that fc for finance charge so my finance charge is going to be the principal or the average daily

Balance 693.56 i need to multiply that by my interest rate of 0.189 so multiplied by 0.189 and then i need to multiply by the length of time or the term of the loan is how we’ve also set it and so you might be tempted to say well we’re looking at one month out of 12 months out of the year so maybe this is 1 12 but the problem with that is each month has different

Number of days february sometimes says 28 september has 30. january has 31. so to get a more accurate length of time or part of a year we actually have to multiply by 31 out of 365. so what this gives me then if i do all of this multiplication my finance charge turns out to be 11. and 13 cents so when kerry makes a payment right off the top of that payment 11

And 13 cents goes to interest kind of just right out the window and if we actually take this one step further credit card companies to usually calculate your minimum payment by somewhere between two and three percent of your ending balance so if we did this if we take three percent of our ending balance which was eight forty seven twenty if we got a statement from

Our credit card company they would say the payment the minimum payment is three percent of that balance which turns out to be 25.42 a lot of times if this payment is less than 25 let’s say it turned out to be eleven dollars they might say well your minimum payment is a fixed twenty dollars but in this case let’s go with the 2542 and so she makes a payment of

25.42 the problem is 11 of that just again goes out the window it’s like burning up 11 the only amount that actually goes towards the balance is going to be 2542 minus 11 13 which turns out to be 1429 so out of that 25 dollar payment 14 of it knocks her balance down a little bit 11 gets burned up and so this is why they always say never just make that minimum

Payment because if i made an additional five dollars all of that five dollars would go towards my balance or if i doubled my payment i would get a knock that balance down quite a bit so it’s sad to only make that minimum payment so hopefully this gives you a good idea of first how to calculate the average daily balance use that to calculate the finance charge and

Just really pay attention to the number of days that each balance is actually staying at that’s the hardest part so hopefully we’ll be able to do another one of these in class

Transcribed from video

Average Daily Balance and Finance Charge By chazs2000