(a) The finance charge for May is $1.37
(b) Joe's new balance is $609.76
Explanation: The finance charge is the fee charged by your financial institution for offering you a credit facility. Basically, when yoiu are allowed to spend more than you have earned (with the intent to repay in the future of course), you pay a finace charge usually reffered to as an APR (annual percentage rate). To derive your finance charge for the month you need to calculate the APR per day, which is derived as:
APR/365.
This is then multiplied by the daily balance on your credit account to arrive at your monthly finance charge. Note also that every debit entry is deducted while every credit entry is added to the available balance.
Joes' APR has been given as 15% (or 0.15) and the APR per day is now;
Daily APR = 0.15/365
Daily APR = 0.00041096
Daily APR = 0.00041 (approximately)
A look at the transaction history shows the following;
Opening balance = 1216.88 Bal)
May 10 - 270 (debit) 946.88 (bal)
May 15 - 86.50 (credit) 1033.38 (bal)
May 19 - 300 (debit) 733.38 (bal)
May 25 - 122.25 (credit) 611.13 (bal)
As you can see from the figures above, the daily balances have been derived from the transactions recorded and therefore the daily APR can now be calculated as
May 10 - $0.39
May 15 - $0.43
May 19 - $0.30
May 25 - $0.25
The total finance charge for the month of May is the addition of all the above results and that is a total of $1.37.
Note that the finance charge would be debited to Joe's account and that means a deduction. Therefore his new balance is 611.13 minus 1.37 which gives you 609.76.
Please note the correction in the Answers at the beginning. That was an error. The correct answer for option b is $609.76