Question 1192450: This is a problem I have, I have tried everything to solve it and can't. I have one answer spot left. Thank you
Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days long. (Round your answer to the nearest cent.)
$625 balance, 18%, $575 payment; average daily balance method
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
It really depends on when the payment was made. Unfortunately your teacher didn't provide this info.
The longer the person delays payment, the higher the finance charge will be.
This is because the average daily balance (ADB) will be larger since the individual daily balances themselves are larger for longer, until the payment is made of course.
It's a very good idea to always pay off the balance as soon as possible.
I'm going to assume that the person made the payment on day 1 and it took 10 days for the payment to be fully processed.
This will ensure that the ADB is as small as possible to lead to the smallest possible finance charge.
If that assumption is correct, then we can make a chart like this
| Balance | Number of days | Start and End Date | | $625 | 10 | Day 1 to Day 10 | | $50 | 20 | Day 11 to Day 30 |
The $50 is from subtracting the payment of $575 from the original balance $625
625 - 575 = 50
Multiply each balance with their respective day count
625*10 = 6250
50*20 = 1000
Then add the products
6250+1000 = 7250
This is then divided over the 30 days to find the average daily balance (ADB)
ADB = 7250/30 = 241.67 dollars approximately
For more information, check out the concept of a weighted mean.
We use this to calculate the finance charge F
F = (ADB*APR*n)/365
F = (241.67*0.18*30)/365
F = 3.57539178082191
F = 3.58
The n = 30 refers to the number of days in the billing cycle.
I'm using the decimal form of the APR 18% to get 0.18
I'll assume that the credit card company uses a 365 day year (rather than a 360 day year).
Another way to think of it is to recall the simple interest formula
i = P*r*t
The interest (i) is the finance charge
P = 241.67 is the ADB
r = 0.18 is the decimal form of the APR of 18%
t = 30/365 is the time in years that the simple interest is being computed for.
You should find that:
i = P*r*t
i = 241.67*0.18*(30/365)
i = 3.57539178082191
i = 3.58
Or you can think of it like this
finance charge = (ADB)*(daily periodic rate)*(number of days in billing cycle)
finance charge = (241.67)*(0.18/365)*(30)
finance charge = 3.57539178082191
finance charge = $3.58
Effectively it's nearly the same formula as before, but a few things have been rearranged somewhat.
Answer: $3.58
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