Gregory has a credit card with a 30-day billing cycle and an APR of [tex]$11.95 \%$[/tex]. The following table shows Gregory's 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 method of computing Gregory's April finance charge will result in a greater finance charge, and how much greater will it be?
a. The daily balance method will have a finance charge 90.09 greater than the adjusted balance method.
b. The daily balance method will have a finance charge [tex]$0.54[/tex] greater than the adjusted balance method.
c. The adjusted balance method will have a finance charge [tex]$1.40[/tex] greater than the daily balance method.
Answer (1)
Calculate the adjusted balance by subtracting the payment from the beginning balance.
Determine the monthly interest rate from the APR and calculate the finance charge using the adjusted balance method.
Calculate the average daily balance by summing the daily balances and dividing by the number of days in the billing cycle, then calculate the finance charge using the daily balance method.
Compare the finance charges from both methods to find the difference: $0.54 .
Explanation
Problem Analysis Let's analyze Gregory's credit card transactions to determine which method, the adjusted balance method or the daily balance method, results in a greater finance charge. We will calculate the finance charge for each method and then compare the results.
Adjusted Balance Method Calculation First, we calculate the finance charge using the adjusted balance method. The beginning balance is $622.82 , and a payment of $45.45 is made on April 4. The adjusted balance is calculated as: 622.82 − 45.45 = 577.37 The APR is 11.95% , so the monthly interest rate is: 12 0.1195 = 0.009958333 The finance charge using the adjusted balance method is: 577.37 × 0.009958333 = 5.7496
Daily Balance Method Calculation Next, we calculate the finance charge using the daily balance method. We need to determine the daily balances for each period:From April 1 to April 3 (3 days): $622.82 From April 4 to April 9 (6 days): 622.82 − 45.45 = $577.37 From April 10 to April 24 (15 days): 577.37 + 78.91 = $656.28 From April 25 to April 30 (6 days): 656.28 + 16.36 = $672.64 The sum of the daily balances is: ( 622.82 × 3 ) + ( 577.37 × 6 ) + ( 656.28 × 15 ) + ( 672.64 × 6 ) = 1868.46 + 3464.22 + 9844.2 + 4035.84 = 19212.72 The average daily balance is: 30 19212.72 = 640.424 The daily interest rate is: 365 0.1195 = 0.000327397 The finance charge using the daily balance method is: 640.424 × 0.000327397 × 30 = 6.2902
Comparison and Conclusion Now, we compare the finance charges calculated using both methods:Adjusted balance method: $5.7496 Daily balance method: $6.2902 The difference between the finance charges is: 6.2902 − 5.7496 = 0.5406 Therefore, the daily balance method results in a finance charge that is approximately $0.54 greater than the adjusted balance method.
Examples
Understanding credit card finance charges is essential for managing personal finances. For instance, if you're planning to make a large purchase on your credit card and want to minimize interest, knowing how different calculation methods affect your finance charges can help you strategize your payments. By understanding these calculations, you can make informed decisions about when to make payments and how much to pay, potentially saving money on interest charges. This knowledge is also useful when comparing different credit card offers, as APR and calculation methods can vary significantly.
