Roger has a credit card with an APR of [tex]$19.40 \%$[/tex] and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of June.
| Date | Amount ($) | Transaction |
|---|---|---|
| 6 / 1 | 265.40 | Beginning balance |
| 6 / 6 | 90.00 | Payment |
| 6 / 16 | 43.33 | Purchase |
| 6 / 22 | 37.71 | Purchase |
If Roger's finance charge for June is $ 3.56, which method of calculating the finance charge does Roger's credit company use?
a. daily balance method
b. adjusted balance method
c. previous balance method
d. there is not enough information to determine which method was used
Answer (2)
Calculate the finance charge using the previous balance method: $265.40 \times \frac{0.194}{12} = $4.29.
Calculate the finance charge using the adjusted balance method: $(265.40 - 90.00) \times \frac{0.194}{12} = $2.84.
Calculate the finance charge using the daily balance method: $\frac{(5 \times 265.40) + (10 \times 175.40) + (6 \times 218.73) + (9 \times 256.44)}{30} \times \frac{0.194}{12} = $3.61.
The finance charge of 3.56 i sc l oses tt o t h e d ai l y ba l an ce m e t h o d , so t h e an s w er i s \boxed{a}$.
Explanation
Understanding the Problem We are given Roger's credit card transactions for June and the finance charge of $3.56. We need to determine which method (previous balance, adjusted balance, or daily balance) was used to calculate the finance charge.
Previous Balance Method First, let's calculate the finance charge using the previous balance method. The previous balance is the balance at the beginning of the billing cycle, which is 265.40. T h e A PR i s 19.40 \frac{0.194}{12} . T h e f inan cec ha r g e i sc a l c u l a t e d a s : 265.40 × 12 0.194 = 4.29063333... $
So, the finance charge using the previous balance method is approximately $4.29.
Adjusted Balance Method Next, let's calculate the finance charge using the adjusted balance method. The adjusted balance is the beginning balance minus any payments made during the billing cycle. In this case, the adjusted balance is 265.40 − 90.00 = 175.40 . The finance charge is calculated as: 175.40 × 12 0.194 = 2.83563333... So, the finance charge using the adjusted balance method is approximately $2.84.
Daily Balance Method Now, let's calculate the finance charge using the daily balance method. We need to calculate the average daily balance for the month. From 6/1 to 6/5 (5 days), the balance is $265.40. From 6/6 to 6/15 (10 days), the balance is $265.40 - 90.00 = 175.40. From 6/16 to 6/21 (6 days), the balance is $175.40 + 43.33 = 218.73. From 6/22 to 6/30 (9 days), the balance is 218.73 + 37.71 = 256.44 . The average daily balance is: 30 ( 5 × 265.40 ) + ( 10 × 175.40 ) + ( 6 × 218.73 ) + ( 9 × 256.44 ) = 30 1327 + 1754 + 1312.38 + 2307.96 = 30 6699.34 = 223.311333... The finance charge is calculated as: 223.311333... × 12 0.194 = 3.61127766... So, the finance charge using the daily balance method is approximately $3.61.
Conclusion Comparing the calculated finance charges with the given finance charge of $3.56, we see that the daily balance method ($3.61) is the closest. Therefore, Roger's credit company most likely uses the daily balance method.
Examples
Understanding credit card finance charge calculations is essential for managing personal finances. For example, if you want to minimize interest payments, knowing how each method affects your balance can help you make informed decisions about when to make payments and how much to spend. This knowledge can also help you compare different credit card offers and choose the one that best suits your spending habits and financial goals. By understanding these calculations, you can avoid unnecessary fees and save money in the long run.
Roger's credit company likely uses the daily balance method for calculating the finance charge, as it aligns most closely with the calculated amount of $3.56. The previous balance method yielded about $4.29, and the adjusted balance method yielded about $2.84, making the daily balance method the best match. Thus, the chosen option is a. daily balance method.
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