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Sagot :
To determine which method of calculating Yvonne's finance charge will result in a greater finance charge, let's break down the steps for both the daily balance method and the previous balance method.
Step-by-step calculation:
### 1. Identify the relevant information:
- APR (Annual Percentage Rate): 17.79%
- Billing cycle: 30 days
- Transactions:
- June 1: Beginning balance [tex]$925.43 - June 7: Payment $[/tex]62.74
- June 11: Purchase [tex]$28.27 - June 21: Purchase $[/tex]50.00
### 2. Calculate the finance charge using the daily balance method:
- Convert APR to a decimal: [tex]\( \frac{17.79}{100} = 0.1779 \)[/tex]
- Daily rate: [tex]\( \frac{0.1779}{365} \approx 0.000487945 \)[/tex]
- Track balances over the 30-day billing cycle considering each transaction.
- Define each day's balance and calculate average daily balance:
1. From June 1 to June 6 (6 days): [tex]$925.43 2. From June 7 to June 10 (4 days): \( 925.43 - 62.74 = 862.69 \) 3. From June 11 to June 20 (10 days): \( 862.69 + 28.27 = 890.96 \) 4. From June 21 to June 30 (10 days): \( 890.96 + 50.00 = 940.96 \) - Sum of daily balances: \[ 6 \times 925.43 + 4 \times 862.69 + 10 \times 890.96 + 10 \times 940.96 = 5552.58 + 3450.76 + 8909.60 + 9409.60 = 27322.54 \] - Average daily balance: \[ \frac{27322.54}{30} \approx 910.75 \] - Finance charge using the daily balance method: \[ 910.75 \times 0.000487945 \times 30 \approx 204.799 \] ### 3. Calculate the finance charge using the previous balance method: - Beginning balance: $[/tex]925.43
- Finance charge:
[tex]\[ 925.43 \times 0.000487945 \times 30 = 13.5316 \][/tex]
### 4. Calculate the difference between the two methods:
- Daily balance finance charge: [tex]$204.80 (rounded) - Previous balance finance charge: $[/tex]13.53 (rounded)
- Difference in finance charges:
[tex]\[ 204.80 - 13.53 = 191.27 \][/tex]
Based on given options and final rounding conventions in finance calculations.
### Final result:
The daily balance method will result in a higher finance charge than the previous balance method by approximately [tex]$\$[/tex]191.28[tex]$ Among the options: a. The daily balance method will have a finance charge \$[/tex]0.21 greater than the previous balance method.
b. The daily balance method will have a finance charge \[tex]$0.53 greater than the previous balance method. c. The previous balance method will have a finance charge \$[/tex]0.45 greater than the daily balance method.
### Conclusion:
None of these options match exactly.
Based on given options there seems issue 191.28, true option should be "the daily balance method will have a finance charge \\( \[tex]$ 191.28$[/tex] greater than the previous balance method."
Step-by-step calculation:
### 1. Identify the relevant information:
- APR (Annual Percentage Rate): 17.79%
- Billing cycle: 30 days
- Transactions:
- June 1: Beginning balance [tex]$925.43 - June 7: Payment $[/tex]62.74
- June 11: Purchase [tex]$28.27 - June 21: Purchase $[/tex]50.00
### 2. Calculate the finance charge using the daily balance method:
- Convert APR to a decimal: [tex]\( \frac{17.79}{100} = 0.1779 \)[/tex]
- Daily rate: [tex]\( \frac{0.1779}{365} \approx 0.000487945 \)[/tex]
- Track balances over the 30-day billing cycle considering each transaction.
- Define each day's balance and calculate average daily balance:
1. From June 1 to June 6 (6 days): [tex]$925.43 2. From June 7 to June 10 (4 days): \( 925.43 - 62.74 = 862.69 \) 3. From June 11 to June 20 (10 days): \( 862.69 + 28.27 = 890.96 \) 4. From June 21 to June 30 (10 days): \( 890.96 + 50.00 = 940.96 \) - Sum of daily balances: \[ 6 \times 925.43 + 4 \times 862.69 + 10 \times 890.96 + 10 \times 940.96 = 5552.58 + 3450.76 + 8909.60 + 9409.60 = 27322.54 \] - Average daily balance: \[ \frac{27322.54}{30} \approx 910.75 \] - Finance charge using the daily balance method: \[ 910.75 \times 0.000487945 \times 30 \approx 204.799 \] ### 3. Calculate the finance charge using the previous balance method: - Beginning balance: $[/tex]925.43
- Finance charge:
[tex]\[ 925.43 \times 0.000487945 \times 30 = 13.5316 \][/tex]
### 4. Calculate the difference between the two methods:
- Daily balance finance charge: [tex]$204.80 (rounded) - Previous balance finance charge: $[/tex]13.53 (rounded)
- Difference in finance charges:
[tex]\[ 204.80 - 13.53 = 191.27 \][/tex]
Based on given options and final rounding conventions in finance calculations.
### Final result:
The daily balance method will result in a higher finance charge than the previous balance method by approximately [tex]$\$[/tex]191.28[tex]$ Among the options: a. The daily balance method will have a finance charge \$[/tex]0.21 greater than the previous balance method.
b. The daily balance method will have a finance charge \[tex]$0.53 greater than the previous balance method. c. The previous balance method will have a finance charge \$[/tex]0.45 greater than the daily balance method.
### Conclusion:
None of these options match exactly.
Based on given options there seems issue 191.28, true option should be "the daily balance method will have a finance charge \\( \[tex]$ 191.28$[/tex] greater than the previous balance method."
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