Gregory has a credit card with a 30-day billing cycle and the following credit card transactions for the month of April:
| Date | Amount ($) | Transaction |
| :----- | :--------- | :----------------- |
| 4 / 1 | 622.82 | Beginning balance |
| 4 / 4 | 45.45 | Payment |
| 4 / 10 | 78.91 | Purchase |
| 4 / 25 | 16.36 | Purchase |
Between the adjusted balance method and the daily balance method, which finance charge will result in a greater finance charge, and by how much?
A. The daily balance method will have a finance charge $0.0 method.
B. The daily balance method will have a finance charge $0.54 method.
C. The adjusted balance method will have a finance charge $ method.
Answer (2)
Calculate the average daily balance: Sum the daily balances and divide by the number of days in the billing cycle.
Calculate the finance charge using the daily balance method: Multiply the average daily balance by the monthly interest rate.
Calculate the adjusted balance: Subtract any payments from the beginning balance.
Calculate the finance charge using the adjusted balance method: Multiply the adjusted balance by the monthly interest rate. The daily balance method results in a greater finance charge by $0.95 .
Explanation
Analyzing the Problem First, let's analyze the given information. We have the beginning balance, payment, and purchase transactions for Gregory's credit card in April. We need to calculate the finance charge using both the adjusted balance method and the daily balance method to determine which results in a greater finance charge.
Assuming an APR Since the APR (Annual Percentage Rate) is not provided, let's assume a reasonable APR of 18% (0.18). This will allow us to calculate the finance charges for both methods.
Calculating Average Daily Balance Now, let's calculate the average daily balance. This involves calculating the balance for each day of the billing cycle, summing them up, and dividing by the number of days in the billing cycle (30).
Calculating Daily Balances From April 1 to April 3 (3 days), the balance is $622.82. From April 4 to April 9 (6 days), the balance is $622.82 - $45.45 = $577.37. From April 10 to April 24 (15 days), the balance is $577.37 + $78.91 = $656.28. From April 25 to April 30 (6 days), the balance is $656.28 + $16.36 = $672.64.
So, the sum of the daily balances is ( 3 × 622.82 ) + ( 6 × 577.37 ) + ( 15 × 656.28 ) + ( 6 × 672.64 ) = 1868.46 + 3464.22 + 9844.20 + 4035.84 = 19212.72 .
The average daily balance is $19212.72 / 30 = $640.424.
Calculating Daily Balance Finance Charge Next, calculate the finance charge using the daily balance method. The monthly interest rate is 0.18/12 = 0.015 . The finance charge is $640.424 \times 0.015 = $9.61.
Calculating Adjusted Balance Now, let's calculate the adjusted balance. This is the beginning balance minus any payments made during the billing cycle: $622.82 - $45.45 = $577.37.
Calculating Adjusted Balance Finance Charge Calculate the finance charge using the adjusted balance method. The monthly interest rate is still 0.015 . The finance charge is $577.37 \times 0.015 = $8.66.
Comparing Finance Charges Comparing the finance charges, the daily balance method results in a finance charge of $9.61, while the adjusted balance method results in a finance charge of $8.66. Therefore, the daily balance method results in a greater finance charge by $9.61 - $8.66 = $0.95.
Final Answer Therefore, the daily balance method will have a finance charge $0.95 greater than the adjusted balance method.
Examples
Understanding credit card finance charges is crucial for managing personal finances. For instance, if you're carrying a balance on your credit card, knowing how interest is calculated can help you minimize costs. By comparing different calculation methods like the adjusted balance and daily balance methods, you can choose cards that save you money. This knowledge is also useful when evaluating loan options or investment returns, ensuring you make informed financial decisions.
The daily balance method yields a finance charge of $9.61, compared to $8.66 from the adjusted balance method. This means the daily balance method generates a greater finance charge of $0.95. Thus, option A is the selected answer.
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