Yvonne's credit card has an APR of [tex]$17.79 \%$[/tex] and a 30-day billing cycle. The following table details her credit card transactions in the month of June.
| Date | Amount ($) | Transaction |
| :----- | :--------- | :----------------- |
| 6/1 | 925.43 | Beginning balance |
| 6/7 | 62.74 | Payment |
| 6/11 | 28.27 | Purchase |
| 6/21 | 50.00 | Purchase |
Between the previous balance method and the daily balance method, which method of calculating Yvonne's June 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 [tex]$0.21[/tex] greater than the previous balance method.
B. The daily balance method will have a finance charge [tex]$0.53[/tex] greater than the previous balance method.
C. The previous balance method will have a finance charge [tex]$0.45[/tex] greater than the daily balance method
Answer (1)
Calculate the finance charge using the previous balance method: $925.43 \times (0.1779/365) \times 30 = $13.53
Calculate the finance charge using the daily balance method by finding the average daily balance and applying the APR: Average daily balance = $910.75, Finance charge = $13.32
Find the difference between the two finance charges: $13.32 - $13.53 = -$0.21
The previous balance method results in a finance charge that is $0.21 greater than the daily balance method: $0.21
Explanation
Calculate finance charge using previous balance method First, we need to calculate the finance charge using the previous balance method. The formula is:
Finance charge = Previous balance × (APR/365) × Number of days in billing cycle
In this case: Previous balance = $925.43 APR = 17.79% = 0.1779 Number of days in billing cycle = 30 So, the finance charge using the previous balance method is: Finance charge = $925.43 × (0.1779/365) × 30
Calculate finance charge using daily balance method Now, let's calculate the finance charge using the daily balance method. First, we need to determine the daily balance for each day of the billing cycle:
June 1-6: Balance = $925.43 (6 days) * June 7-10: Balance = $925.43 - $62.74 = $862.69 (4 days)
June 11-20: Balance = $862.69 + $28.27 = $890.96 (10 days) * June 21-30: Balance = $890.96 + $50.00 = $940.96 (10 days)
Next, we calculate the sum of the daily balances:
Sum of daily balances = ($925.43 × 6) + ($862.69 × 4) + ($890.96 × 10) + ($940.96 × 10) Sum of daily balances = $5552.58 + $3450.76 + $8909.60 + $9409.60 = $27322.54 Now, we calculate the average daily balance: Average daily balance = Sum of daily balances / Number of days in billing cycle Average daily balance = $27322.54 / 30 = $910.7513 Finally, we calculate the finance charge using the average daily balance: Finance charge = Average daily balance × (APR/365) × Number of days in billing cycle Finance charge = $910.7513 × (0.1779/365) × 30
Calculating the finance charges Now we calculate the values using the formulas from the previous steps:
Finance charge with previous balance method: 925.43 × 365 0.1779 × 30 = 13.531561397260273
Finance charge with daily balance method: 910.7513 × 365 0.1779 × 30 = 13.316931139726027
Comparing the finance charges and finding the difference Now, we compare the two finance charges and determine the difference:
Difference = Finance charge (daily balance) - Finance charge (previous balance) Difference = $13.316931139726027 - $13.531561397260273 = -$0.21463025753424603 Since the difference is negative, the daily balance method results in a smaller finance charge. The previous balance method has a finance charge that is approximately $0.21 greater than the daily balance method.
Final Answer The previous balance method will have a finance charge $0.21 greater than the daily balance method.
Examples
Understanding credit card finance charges is crucial for managing personal finances effectively. For instance, if Yvonne consistently carries a balance on her credit card, knowing how the finance charge is calculated helps her estimate the interest she'll pay each month. This knowledge enables her to make informed decisions about paying off her balance faster or transferring it to a card with a lower APR, ultimately saving money on interest payments. Understanding these calculations can also help in comparing different credit card offers and choosing the one that best suits her spending habits and financial goals.
