Answer :
To determine which method the credit card company uses, let's analyze each potential method of calculating the finance charge for Roger's credit card.
### Method 1: Daily Balance Method
In this method, the finance charge is calculated based on the average daily balance over the billing cycle. The average daily balance is found by summing the daily balances and then dividing by the number of days in the billing cycle.
1. Daily Balance Calculations:
- From 6/1 to 6/5 (5 days): The balance was [tex]$265.40. - From 6/6 to 6/15 (10 days): After making a payment of $[/tex]90.00, the balance was [tex]$265.40 - $[/tex]90.00 = [tex]$175.40. - From 6/16 to 6/21 (6 days): After making a purchase of $[/tex]43.33, the balance was [tex]$175.40 + $[/tex]43.33 = [tex]$218.73. - From 6/22 to 6/30 (8 days): After making a purchase of $[/tex]37.71, the balance was [tex]$218.73 + $[/tex]37.71 = [tex]$256.44. 2. Total Daily Balances: \[ (265.40 \text{ (5 days)} + 175.40 \text{ (10 days)} + 218.73 \text{ (6 days)} + 256.44 \text{ (8 days)}) \] 3. Average Daily Balance: \[ \frac{265.40 \times 5 + 175.40 \times 10 + 218.73 \times 6 + 256.44 \times 8}{30} \] 4. Daily Interest Rate: \[ \frac{19.40\%}{365} \] 5. Finance Charge Calculation: \[ \text{Average Daily Balance} \times \text{Daily Interest Rate} \times 30 \] After performing the calculations, the finance charge using the daily balance method is approximately $[/tex]3.43.
### Method 2: Adjusted Balance Method
In this method, the finance charge is calculated based on the balance after subtracting any payments made during the billing cycle.
1. Adjusted Balance:
[tex]\[ 265.40 - 90.00 = 175.40 \][/tex]
2. Monthly Interest Rate:
[tex]\[ \frac{19.40\%}{12} \][/tex]
3. Finance Charge Calculation:
[tex]\[ \text{Adjusted Balance} \times \text{Monthly Interest Rate} \][/tex]
After performing the calculations, the finance charge using the adjusted balance method is approximately [tex]$2.84. ### Method 3: Previous Balance Method In this method, the finance charge is calculated based on the balance at the beginning of the billing cycle, without considering any payments or purchases made during the cycle. 1. Previous Balance: \[ 265.40 \] 2. Monthly Interest Rate: \[ \frac{19.40\%}{12} \] 3. Finance Charge Calculation: \[ \text{Previous Balance} \times \text{Monthly Interest Rate} \] After performing the calculations, the finance charge using the previous balance method is approximately $[/tex]4.29.
### Comparison with Given Finance Charge
Given that the finance charge for June is [tex]$3.56, we can compare this with the results of each method: - Daily Balance Method: $[/tex]3.43
- Adjusted Balance Method: [tex]$2.84 - Previous Balance Method: $[/tex]4.29
The finance charge of [tex]$3.56 is closest to the finance charge calculated using the Daily Balance Method ($[/tex]3.43).
Therefore, the correct answer is:
a. daily balance method
### Method 1: Daily Balance Method
In this method, the finance charge is calculated based on the average daily balance over the billing cycle. The average daily balance is found by summing the daily balances and then dividing by the number of days in the billing cycle.
1. Daily Balance Calculations:
- From 6/1 to 6/5 (5 days): The balance was [tex]$265.40. - From 6/6 to 6/15 (10 days): After making a payment of $[/tex]90.00, the balance was [tex]$265.40 - $[/tex]90.00 = [tex]$175.40. - From 6/16 to 6/21 (6 days): After making a purchase of $[/tex]43.33, the balance was [tex]$175.40 + $[/tex]43.33 = [tex]$218.73. - From 6/22 to 6/30 (8 days): After making a purchase of $[/tex]37.71, the balance was [tex]$218.73 + $[/tex]37.71 = [tex]$256.44. 2. Total Daily Balances: \[ (265.40 \text{ (5 days)} + 175.40 \text{ (10 days)} + 218.73 \text{ (6 days)} + 256.44 \text{ (8 days)}) \] 3. Average Daily Balance: \[ \frac{265.40 \times 5 + 175.40 \times 10 + 218.73 \times 6 + 256.44 \times 8}{30} \] 4. Daily Interest Rate: \[ \frac{19.40\%}{365} \] 5. Finance Charge Calculation: \[ \text{Average Daily Balance} \times \text{Daily Interest Rate} \times 30 \] After performing the calculations, the finance charge using the daily balance method is approximately $[/tex]3.43.
### Method 2: Adjusted Balance Method
In this method, the finance charge is calculated based on the balance after subtracting any payments made during the billing cycle.
1. Adjusted Balance:
[tex]\[ 265.40 - 90.00 = 175.40 \][/tex]
2. Monthly Interest Rate:
[tex]\[ \frac{19.40\%}{12} \][/tex]
3. Finance Charge Calculation:
[tex]\[ \text{Adjusted Balance} \times \text{Monthly Interest Rate} \][/tex]
After performing the calculations, the finance charge using the adjusted balance method is approximately [tex]$2.84. ### Method 3: Previous Balance Method In this method, the finance charge is calculated based on the balance at the beginning of the billing cycle, without considering any payments or purchases made during the cycle. 1. Previous Balance: \[ 265.40 \] 2. Monthly Interest Rate: \[ \frac{19.40\%}{12} \] 3. Finance Charge Calculation: \[ \text{Previous Balance} \times \text{Monthly Interest Rate} \] After performing the calculations, the finance charge using the previous balance method is approximately $[/tex]4.29.
### Comparison with Given Finance Charge
Given that the finance charge for June is [tex]$3.56, we can compare this with the results of each method: - Daily Balance Method: $[/tex]3.43
- Adjusted Balance Method: [tex]$2.84 - Previous Balance Method: $[/tex]4.29
The finance charge of [tex]$3.56 is closest to the finance charge calculated using the Daily Balance Method ($[/tex]3.43).
Therefore, the correct answer is:
a. daily balance method
