2. Please, again, help me help my son -- His dad's the math whiz but is currently in Iraq.....?

Question

A customers charge account shows a balance of $1,242.42 on August 1. A purchase of $49.95 was made on August 7. A payment of $350 was made on August 10. A purchase of $122.50 was made on August 21. An annual rate of 18.5% is applied to the account.

A) What is the average daily balance?
a. $1,967.78
b. $2,076.78
c. $1,067.76
d. $1,077.78

B) What is the finance charge on this account?
a. $18.50
b. $16.61
c. $19.40
d. $17.30

Thank you so much for your help. Like I mentioned in my other similiar question, my husband is our household math whiz....... but unfortunately he is serving in Iraq. Any and all help will be greatly appreciated.

Please explain your answer if you can.

TIA

Answer 1

August 1-6 (6 days): balance is $1,242.42
August 7-9 (3 days): balance is $1,242.42 + $49.95 = $1,292.37.
August 10-20 (11 days): balance is $1,292.37 - $350 = $942.37.
August 21-31 (11 days): balance is $942.37 + $122.50 = $1,064.87.
The average daily balance is therefore
(6×$1,242.42 + 3×$1,292.37 + 11×$942.37 + 11×$1,064.87) / 31
= $1,077.78 to the nearest cent.

Assuming the finance charge is calculated on a monthly basis, it will be $1,077.78 × 18.5/100 × 1/12 = $16.62 to the nearest cent, so go with $16.61 as the answer. (More normally the finance charge would be calculated on a daily rate to give you $1,077.78 × 18.5/100 × 31/365 = $16.93, but this isn't one of the options given.)