1. Ling has received been approved for a Visa credit card with a $2000 credit limit, however he has not charged that much since opening the account. On April 24, he discovers a monthly statement from March that had accidentally slid down between his desk and the wall. Because he has been busy at work, he has not had time to carefully review his monthly statements, but is spending the weekend catching up on paying bills and organizing his desk. He is particularly interested in how much he still owes the credit card company.
He reviews the statement and discovers that there is a page missing – the one with the unpaid balance. He can see that his beginning balance for March (March 1 through March 31) was $700 and that he paid $250 on March 12, charged purchases of $50 on March 5, $100 on March 20, and $50 on March 30. Ling remembers that the Annual Percentage Rate (APR) on the credit card is 16% of the unpaid balance and interest is charged using the average daily balance method, including current purchases.
a. (5 points) Find the unpaid balance for the March statement (before interest was charged).
Answer:
b. (5 points) Find the average daily balance for the month of March (assume 31 days):
Answer:
c. (5 points) Calculate how much interest Ling must pay in addition to the minimum payment.
Answer:
To find the unpaid balance for the March statement (before interest was charged), we can start with the beginning balance and then subtract the payments made and add the charges made during the month.
a. Unpaid balance = Beginning balance - (Payments - Charges)
= $700 - ($250 - $50 - $100 - $50)
= $700 - $150
= $550
So the unpaid balance for the March statement is $550.
To find the average daily balance for the month of March, we need to calculate the balance at the end of each day and then find the average of these daily balances.
b. Average daily balance = (Sum of daily balances) / (Number of days in the month)
= (Beginning balance x number of days) + (Charge 1 x number of days) + (Charge 2 x number of days) + (Charge 3 x number of days) + (Charge 4 x number of days) / (Number of days in the month)
= ($700 x 31) + ($50 x 31) + ($100 x 31) + ($50 x 31) / 31
= $21700 + $1550 + $3100 + $1550 / 31
= $28000 / 31
= $903.23 (approx)
So the average daily balance for the month of March is approximately $903.23.
To calculate how much interest Ling must pay in addition to the minimum payment, we need to multiply the average daily balance by the APR (in decimal form) and by the number of days in the billing cycle. Then we subtract the minimum payment made.
c. Interest = (Average daily balance x APR x Number of days) - Minimum payment
= ($903.23 x 0.16 x 31) - $250
= $455.24 - $250
= $205.24
So Ling must pay an additional $205.24 in interest, in addition to the minimum payment.