Answer :
To determine the financial details of Hu's credit card for the March billing cycle, we need to follow several steps involving calculations of average daily balance, interest, total balance due, and minimum payment due. Here is how we can break down these steps:
### 1. Calculate the Average Daily Balance
To find the average daily balance, we need to account for the balance on each day and how long each balance persisted.
- Previous Balance (March 1): \[tex]$987.00 - March 2 Payment: \$[/tex]100.00 credit
- March 12 Charge: \[tex]$84.00 - March 24 Charge: \$[/tex]287.00
- March 29 Charge: \[tex]$8.00 We assume the balances on the following days: - From March 1 to March 1: \$[/tex]987.00 for 1 day
- From March 2 to March 11: \[tex]$887.00 (987 - 100) for 9 days - From March 12 to March 23: \$[/tex]971.00 (887 + 84) for 12 days
- From March 24 to March 28: \[tex]$1258.00 (971 + 287) for 5 days - From March 29 to March 31: \$[/tex]1266.00 (1258 + 8) for 3 days
Now, we calculate the average daily balance using these amounts and durations:
[tex]\[ \text{Average Daily Balance} = \frac{(987 \times 1) + (887 \times 9) + (971 \times 12) + (1258 \times 5) + (1266 \times 4)}{31} \][/tex]
Calculating this step-by-step:
[tex]\[ \text{Aggregate Balance} = 987 \times 1 + 887 \times 9 + 971 \times 12 + 1258 \times 5 + 1266 \times 4 = 987 + 7983 + 11652 + 6290 + 5064 = 31976 \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{31976}{31} = 1031.48 \][/tex]
The average daily balance for March is \[tex]$1031.48. ### 2. Calculate the Interest for April 1 Interest is calculated using the average daily balance and the monthly interest rate. Given monthly interest rate: 7.31% or 0.0731 \[ \text{Interest} = \text{Average Daily Balance} \times \text{Monthly Interest Rate} = 1031.48 \times 0.0731 = 75.40 \] The interest required to be paid on April 1 is \$[/tex]75.40.
### 3. Calculate the Total Balance Due on April 1
To find the total balance due on April 1, we add the end balance of March and the interest calculated:
[tex]\[ \text{End Balance for March} = \text{Previous Balance} - \text{Payment Credit} + \text{Total Charges} \][/tex]
Where:
Previous Balance: \[tex]$987.00 Payment Credit: \$[/tex]100.00
Total Charges: \[tex]$84.00 + \$[/tex]287.00 + \[tex]$8.00 = \$[/tex]379.00
[tex]\[ \text{End Balance} = 987.00 - 100.00 + 379.00 = 1266.00 \][/tex]
Now, add the interest:
[tex]\[ \text{Total Balance Due} = 1266.00 + 75.40 = 1341.40 \][/tex]
The total amount due on April 1 is \[tex]$1341.40. ### 4. Determine the Minimum Monthly Payment The minimum monthly payment is: - \$[/tex]25 if the balance due is less than \[tex]$200. - $[/tex]\frac{1}{32}[tex]$ of the total balance due, rounded up to the nearest dollar, if the balance due is greater than \$[/tex]200.
Since the total balance due (\[tex]$1341.40) is greater than \$[/tex]200:
[tex]\[ \text{Minimum Monthly Payment} = \left\lceil \frac{1341.40}{32} \right\rceil = \left\lceil 41.91 \right\rceil = 42 \][/tex]
The minimum monthly payment owed by Hu that is due by April 3 is \$42.
Through these detailed calculations, we reached the financial summary for Hu's credit card statement for March.
### 1. Calculate the Average Daily Balance
To find the average daily balance, we need to account for the balance on each day and how long each balance persisted.
- Previous Balance (March 1): \[tex]$987.00 - March 2 Payment: \$[/tex]100.00 credit
- March 12 Charge: \[tex]$84.00 - March 24 Charge: \$[/tex]287.00
- March 29 Charge: \[tex]$8.00 We assume the balances on the following days: - From March 1 to March 1: \$[/tex]987.00 for 1 day
- From March 2 to March 11: \[tex]$887.00 (987 - 100) for 9 days - From March 12 to March 23: \$[/tex]971.00 (887 + 84) for 12 days
- From March 24 to March 28: \[tex]$1258.00 (971 + 287) for 5 days - From March 29 to March 31: \$[/tex]1266.00 (1258 + 8) for 3 days
Now, we calculate the average daily balance using these amounts and durations:
[tex]\[ \text{Average Daily Balance} = \frac{(987 \times 1) + (887 \times 9) + (971 \times 12) + (1258 \times 5) + (1266 \times 4)}{31} \][/tex]
Calculating this step-by-step:
[tex]\[ \text{Aggregate Balance} = 987 \times 1 + 887 \times 9 + 971 \times 12 + 1258 \times 5 + 1266 \times 4 = 987 + 7983 + 11652 + 6290 + 5064 = 31976 \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{31976}{31} = 1031.48 \][/tex]
The average daily balance for March is \[tex]$1031.48. ### 2. Calculate the Interest for April 1 Interest is calculated using the average daily balance and the monthly interest rate. Given monthly interest rate: 7.31% or 0.0731 \[ \text{Interest} = \text{Average Daily Balance} \times \text{Monthly Interest Rate} = 1031.48 \times 0.0731 = 75.40 \] The interest required to be paid on April 1 is \$[/tex]75.40.
### 3. Calculate the Total Balance Due on April 1
To find the total balance due on April 1, we add the end balance of March and the interest calculated:
[tex]\[ \text{End Balance for March} = \text{Previous Balance} - \text{Payment Credit} + \text{Total Charges} \][/tex]
Where:
Previous Balance: \[tex]$987.00 Payment Credit: \$[/tex]100.00
Total Charges: \[tex]$84.00 + \$[/tex]287.00 + \[tex]$8.00 = \$[/tex]379.00
[tex]\[ \text{End Balance} = 987.00 - 100.00 + 379.00 = 1266.00 \][/tex]
Now, add the interest:
[tex]\[ \text{Total Balance Due} = 1266.00 + 75.40 = 1341.40 \][/tex]
The total amount due on April 1 is \[tex]$1341.40. ### 4. Determine the Minimum Monthly Payment The minimum monthly payment is: - \$[/tex]25 if the balance due is less than \[tex]$200. - $[/tex]\frac{1}{32}[tex]$ of the total balance due, rounded up to the nearest dollar, if the balance due is greater than \$[/tex]200.
Since the total balance due (\[tex]$1341.40) is greater than \$[/tex]200:
[tex]\[ \text{Minimum Monthly Payment} = \left\lceil \frac{1341.40}{32} \right\rceil = \left\lceil 41.91 \right\rceil = 42 \][/tex]
The minimum monthly payment owed by Hu that is due by April 3 is \$42.
Through these detailed calculations, we reached the financial summary for Hu's credit card statement for March.
