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Sagot :
Let's analyze and solve the problem step-by-step to determine which method results in a greater finance charge for Gregory's card transactions in April.
### Step 1: Understanding and Recording the Transactions
We have the following transactions:
1. April 1: Beginning balance of \[tex]$622.82. 2. April 4: A payment of \$[/tex]45.45.
3. April 10: A purchase of \[tex]$78.91. 4. April 25: A purchase of \$[/tex]16.36.
### Step 2: Adjusted Balance Method
The adjusted balance method subtracts any payments made throughout the month from the initial balance before computing finance charges. For April:
- Starting balance (April 1): \[tex]$622.82 - Payment (April 4): \$[/tex]45.45
Adjusted balance = \[tex]$622.82 - \$[/tex]45.45 = \[tex]$577.37 Next, we calculate the finance charge using the adjusted balance. - Annual Percentage Rate (APR) is 29.99%, hence the daily rate \( \frac{29.99\%}{365} = \frac{0.2999}{365} \approx 0.00082 \) - Finance charge for the month using adjusted balance method: \[ 14.231775041095892 \] ### Step 3: Daily Balance Method The daily balance method involves calculating the balance each day, accounting for transactions as they occur. We then average these daily balances over the month and calculate the finance charge based on this average. Daily balances: - April 1-3: \$[/tex]622.82 (for 3 days)
- April 4-9: \[tex]$577.37 (for 6 days, after the payment) - April 10-24: \$[/tex]656.28 (for 15 days, after the first purchase)
- April 25-30: \[tex]$672.64 (for 6 days, after the second purchase) The total balance-days are computed as follows: \[ \text{Total balance-days} = (622.82 \times 3) + (577.37 \times 6) + (656.28 \times 15) + (672.64 \times 6) = 19212.72 \] Average daily balance for 30 days: \[ \text{Average daily balance} = \frac{19212.72}{30} \approx 640.42 \] Finance charge using the daily balance method: \[ 15.78601295342466 \] ### Step 4: Comparing the Finance Charges We now compare the finance charges obtained from both methods: - Adjusted balance method: \$[/tex]14.23
- Daily balance method: \[tex]$15.79 The difference between the two methods: \[ 15.78601295342466 - 14.231775041095892 = 1.5542379123287677 \] ### Step 5: Determining the Correct Answer Given the finance charge difference, \( 1.5542379123287677 \), doesn't correspond to any of the choices provided. However, since we must choose one of the given options: a. \$[/tex]0.09 difference
b. \[tex]$0.54 difference c. \$[/tex]1.40 difference
d. \$0.86 difference
None of these options exactly match the [tex]\(1.5542379123287677\)[/tex] difference calculated. However, the numerical solution indicates the following labels: [tex]\( -1 \)[/tex], which suggests none of the given options match the computed result.
Thus, the final conclusion is the computed difference of [tex]\(1.5542379123287677\)[/tex] does not match any of the provided answers exactly based on calculations. Therefore, it shows an error or misinformation.
### Step 1: Understanding and Recording the Transactions
We have the following transactions:
1. April 1: Beginning balance of \[tex]$622.82. 2. April 4: A payment of \$[/tex]45.45.
3. April 10: A purchase of \[tex]$78.91. 4. April 25: A purchase of \$[/tex]16.36.
### Step 2: Adjusted Balance Method
The adjusted balance method subtracts any payments made throughout the month from the initial balance before computing finance charges. For April:
- Starting balance (April 1): \[tex]$622.82 - Payment (April 4): \$[/tex]45.45
Adjusted balance = \[tex]$622.82 - \$[/tex]45.45 = \[tex]$577.37 Next, we calculate the finance charge using the adjusted balance. - Annual Percentage Rate (APR) is 29.99%, hence the daily rate \( \frac{29.99\%}{365} = \frac{0.2999}{365} \approx 0.00082 \) - Finance charge for the month using adjusted balance method: \[ 14.231775041095892 \] ### Step 3: Daily Balance Method The daily balance method involves calculating the balance each day, accounting for transactions as they occur. We then average these daily balances over the month and calculate the finance charge based on this average. Daily balances: - April 1-3: \$[/tex]622.82 (for 3 days)
- April 4-9: \[tex]$577.37 (for 6 days, after the payment) - April 10-24: \$[/tex]656.28 (for 15 days, after the first purchase)
- April 25-30: \[tex]$672.64 (for 6 days, after the second purchase) The total balance-days are computed as follows: \[ \text{Total balance-days} = (622.82 \times 3) + (577.37 \times 6) + (656.28 \times 15) + (672.64 \times 6) = 19212.72 \] Average daily balance for 30 days: \[ \text{Average daily balance} = \frac{19212.72}{30} \approx 640.42 \] Finance charge using the daily balance method: \[ 15.78601295342466 \] ### Step 4: Comparing the Finance Charges We now compare the finance charges obtained from both methods: - Adjusted balance method: \$[/tex]14.23
- Daily balance method: \[tex]$15.79 The difference between the two methods: \[ 15.78601295342466 - 14.231775041095892 = 1.5542379123287677 \] ### Step 5: Determining the Correct Answer Given the finance charge difference, \( 1.5542379123287677 \), doesn't correspond to any of the choices provided. However, since we must choose one of the given options: a. \$[/tex]0.09 difference
b. \[tex]$0.54 difference c. \$[/tex]1.40 difference
d. \$0.86 difference
None of these options exactly match the [tex]\(1.5542379123287677\)[/tex] difference calculated. However, the numerical solution indicates the following labels: [tex]\( -1 \)[/tex], which suggests none of the given options match the computed result.
Thus, the final conclusion is the computed difference of [tex]\(1.5542379123287677\)[/tex] does not match any of the provided answers exactly based on calculations. Therefore, it shows an error or misinformation.
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