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:
a. To find the unpaid balance for the March statement, you need to calculate the total charges made during March and subtract the payments made.
Starting balance (March 1): $700
Charges Made: $50 + $100 + $50 = $200
Payments Made: $250
Unpaid Balance = Starting balance + charges - payments
Unpaid Balance = $700 + $200 - $250 = $650
Therefore, the unpaid balance for the March statement is $650.
b. To find the average daily balance for the month of March, you need to take into account the balance at the beginning of each day and calculate the average of those balances.
To calculate the average daily balance, you need to determine the balance at the end of each day, and then add them up and divide by the number of days in the month.
Here's a step-by-step calculation:
1. March 1: Starting balance = $650
2. March 2-4: No changes, balance remains $650
3. March 5: Charged $50, new balance = $650 + $50 = $700
4. March 6-11: No changes, balance remains $700
5. March 12: Payment of $250, new balance = $700 - $250 = $450
6. March 13-19: No changes, balance remains $450
7. March 20: Charged $100, new balance = $450 + $100 = $550
8. March 21-29: No changes, balance remains $550
9. March 30: Charged $50, new balance = $550 + $50 = $600
10. March 31: No changes, balance remains $600
Total of all daily balances = $650 + $650 + $650 + $700 + $700 + $700 + $700 + $450 + $450 + $450 + $550 + $550 + $550 + $550 + $550 + $550 + $550 + $600 + $600
= $11,500
Average Daily Balance = Total of all daily balances / Number of days in the month
Average Daily Balance = $11,500 / 31 = $370.97 (rounded to the nearest cent)
Therefore, the average daily balance for the month of March is approximately $370.97.
c. To calculate how much interest Ling must pay in addition to the minimum payment, you need to apply the APR and average daily balance.
Interest = APR * Average Daily Balance
Interest = 16% * $370.97 = $59.36 (rounded to the nearest cent)
Therefore, Ling must pay approximately $59.36 in addition to the minimum payment.