Question

The balance on Maria's credit card on May 10, the billing date, was $3,198.23. She sent in a $1,000 payment, which was posted on May 13, and made no other transactions during the billing cycle. Assuming the APR on the card is 7.9%, answer the following.

a) what is the average daily balance for the billing period?
b) how much is the finance charge for the billing period?
c) what will be the new balance when she receives her june 10 statement?

Answer 1

The more I look at this the more confused I get, but here is what I think....

Answer 2

@pphalke This is very similar to the problem we worked on last night.

average daily balance = sum of each day's balance / number of days in billing cycle
sum of each day's balance = (balance day 1 + balance day 2 + ... + balance day 30)
number of days in billing cycle = 30 days

Calculating the sum of each day's balance is made easier because it is the same balance for the first 10 days and then the same new balance for the next 20 days which we can write as the sum of two products
sum of each day's balance = (10*starting balance + 20*(starting balance - payment)

For b, you multiply the average daily balance by the daily interest rate times the number of days in the billing cycle.

The daily interest rate is the APR divided by the number of days in a standard year, 365.

The new balance will be the old balance minus the payment plus the interest.

To summarize that
a) \[AverageDailyBalance = \frac{ (10*3198.23)+(20*(3198.23-1000) }{ 30 }\]
b) \[financecharge=(averagedailybalance)(\frac{ .079 }{ 365 })(30)\]
c) \[NewBalance=(StartingBalance) - (Payment) + (FinanceCharge)\]

Answer 3

I got 2295.00 for the first part

Answer 4

retirEEd, Credit Card accounting has very specific definitions. I looked them up on the internet and they are as I stated above. It is very arbitrary and cannot be figured out from a basic understanding of math. You have to know the specific definitions.

Average Daily Balance is the sum of the balances for each day divided by the number of days in a billing cycle which is 30 for Credit Cards.

APR is the interest rate for the year, but it is calculated daily so you divide the yearly rate by the number of days in a standard year which is 365 by definition.

Answer 5

b is 15.40 and c is 2213.63

Answer 6

Thanks for the information.

That is very complicated seems a little unjust to the consumer. So the consumer gets charged extra, even after paying the bill earlier into the billing cycle.

I am kind of shocked the a credit card company would charge more for a 31 day billing cycle than they would on a 30 day billing cycle.

Answer 7

I also pay my credit cards off in full, since my interest rates are much higher than in this question. :)

Answer 8

You might want to check your math pphalke
(10*$3198.23)+20*$2198.23) = 31982.30 + 43964.6 = $75,946.90
divide that by 30 days gives you $2531.56 how did you get $2295.00?

with that average daily balance b is
(2531.56)(.000216)(30)=$16.40

That would make c
$3198.23-1000+16.40 = $2214.63

Answer 9

@retirEEd LOL, yeah 7.9% APR is a nice rate for Credit Cards.

Answer 10

my book says a) is 2295.00, b is 15.40

Answer 11

I didn't see where @plainntall came up with the 10 days at $3198.23. I thought that was or is some sort of credit card standard charge for the first 10 days of a bill cycle.

I did get $2295 by adding 3198.23 times 3 to 2198.23 times 28 and dividing by 31...