Answer :
To determine which method of calculating the finance charge Dennis's credit card company uses, let's analyze the three common methods: adjusted balance method, previous balance method, and daily balance method. We will compare each method's result to the given finance charge of [tex]$3.82.
1. APR and Billing Cycle Details:
- APR (Annual Percentage Rate): 10.14%
- Days in a Year: 365
- Billing Cycle Days: 30
2. Converting APR to a Daily Rate:
- Daily Rate \( = \frac{10.14\%}{365} = \frac{10.14}{100 \times 365} \)
- Daily Rate \( = \frac{0.1014}{365} \approx 0.00027808 \)
3. Calculating Cycle Rate:
- Cycle Rate \( = \text{Daily Rate} \times \text{Billing Cycle Days} \)
- Cycle Rate \( = 0.00027808 \times 30 \approx 0.0083424 \)
### Method 1: Previous Balance Method
Under the Previous Balance Method, the finance charge is calculated based on the balance at the beginning of the billing cycle.
- Previous Balance: $[/tex]517.87
- Finance Charge: Previous Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 517.87 \times 0.0083424 \approx 4.32 \)[/tex]
### Method 2: Adjusted Balance Method
Under the Adjusted Balance Method, the finance charge is calculated based on the balance after all payments are made.
- Balance Adjustments:
- Starting with the Previous Balance: [tex]$517.87 - November 9: Purchase of $[/tex]31.63
- New Balance: [tex]\( 517.87 + 31.63 = 549.50 \)[/tex]
- November 23: Purchase of [tex]$64.10 - New Balance: \( 549.50 + 64.10 = 613.60 \) - November 26: Payment of $[/tex]65.75
- New Balance: [tex]\( 613.60 - 65.75 = 547.85 \)[/tex]
- Finance Charge: Adjusted Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 547.85 \times 0.0083424 \approx 4.57 \)[/tex]
### Method 3: Daily Balance Method
Under the Daily Balance Method, the finance charge is calculated based on the average daily balance throughout the billing cycle.
- Daily Balances:
- 1st to 8th (8 days): [tex]\( 517.87 \)[/tex]
- 9th to 22nd (14 days): [tex]\( 517.87 + 31.63 = 549.50 \)[/tex]
- 23rd to 25th (3 days): [tex]\( 549.50 + 64.10 = 613.60 \)[/tex]
- 26th to 30th (5 days): [tex]\( 613.60 - 65.75 = 547.85 \)[/tex]
- Sum of Daily Balances:
- [tex]\( 8 \times 517.87 + 14 \times 549.50 + 3 \times 613.60 + 5 \times 547.85 \)[/tex]
- [tex]\( = 4142.96 + 7693 + 1840.80 + 2739.25 = 16415.51 \)[/tex]
- Average Daily Balance:
- [tex]\( = \frac{16415.51}{30} \approx 547.18 \)[/tex]
- Finance Charge: Average Daily Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 547.18 \times 0.0083424 \approx 4.57 \)[/tex]
By comparing the calculated finance charges with the given finance charge of [tex]$3.82, we see that none of the typical methods (Previous Balance, Adjusted Balance, Daily Balance) match the given finance charge exactly. However, the comparison leads us to observe that the standard finance charges calculated are over $[/tex]4. Hence, we conclude:
Which method of calculating the finance charge does the credit card company use?
d. there is not enough information to determine which method was used
- Finance Charge: Previous Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 517.87 \times 0.0083424 \approx 4.32 \)[/tex]
### Method 2: Adjusted Balance Method
Under the Adjusted Balance Method, the finance charge is calculated based on the balance after all payments are made.
- Balance Adjustments:
- Starting with the Previous Balance: [tex]$517.87 - November 9: Purchase of $[/tex]31.63
- New Balance: [tex]\( 517.87 + 31.63 = 549.50 \)[/tex]
- November 23: Purchase of [tex]$64.10 - New Balance: \( 549.50 + 64.10 = 613.60 \) - November 26: Payment of $[/tex]65.75
- New Balance: [tex]\( 613.60 - 65.75 = 547.85 \)[/tex]
- Finance Charge: Adjusted Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 547.85 \times 0.0083424 \approx 4.57 \)[/tex]
### Method 3: Daily Balance Method
Under the Daily Balance Method, the finance charge is calculated based on the average daily balance throughout the billing cycle.
- Daily Balances:
- 1st to 8th (8 days): [tex]\( 517.87 \)[/tex]
- 9th to 22nd (14 days): [tex]\( 517.87 + 31.63 = 549.50 \)[/tex]
- 23rd to 25th (3 days): [tex]\( 549.50 + 64.10 = 613.60 \)[/tex]
- 26th to 30th (5 days): [tex]\( 613.60 - 65.75 = 547.85 \)[/tex]
- Sum of Daily Balances:
- [tex]\( 8 \times 517.87 + 14 \times 549.50 + 3 \times 613.60 + 5 \times 547.85 \)[/tex]
- [tex]\( = 4142.96 + 7693 + 1840.80 + 2739.25 = 16415.51 \)[/tex]
- Average Daily Balance:
- [tex]\( = \frac{16415.51}{30} \approx 547.18 \)[/tex]
- Finance Charge: Average Daily Balance [tex]\( \times \)[/tex] Cycle Rate
- Finance Charge: [tex]\( 547.18 \times 0.0083424 \approx 4.57 \)[/tex]
By comparing the calculated finance charges with the given finance charge of [tex]$3.82, we see that none of the typical methods (Previous Balance, Adjusted Balance, Daily Balance) match the given finance charge exactly. However, the comparison leads us to observe that the standard finance charges calculated are over $[/tex]4. Hence, we conclude:
Which method of calculating the finance charge does the credit card company use?
d. there is not enough information to determine which method was used
