Answer :
Alright, let's go through the steps to determine the requested values based on Veronica's credit card statement for November.
Step 1: Calculate the Average Daily Balance
To determine the average daily balance, we need to account for the balance changes occurring throughout the billing cycle. Here’s how the balance changes over the month based on the transactions:
- November 1 to November 6:
* Balance = previous balance = \[tex]$4,224.00 * Number of days = 6 - November 7 to November 12: Balance for these days = \$[/tex]4,224.00 - \[tex]$100.00 = \$[/tex]4,124.00
Number of days = 6
- November 13 to November 27:
* Balance for these days = \[tex]$4,124.00 + \$[/tex]74.00 = \[tex]$4,198.00 * Number of days = 15 - November 28: Balance for this day = \$[/tex]4,198.00 + \[tex]$77.00 = \$[/tex]4,275.00
Number of days = 1
- November 29 and November 30:
* Balance for these days = \[tex]$4,275.00 + \$[/tex]199.00 = \[tex]$4,474.00 * Number of days = 2 Now, we add up the daily balances for each period: - Total from November 1-6: \(6 \times 4224.00 = 25344.00\) - Total from November 7-12: \(6 \times 4124.00 = 24744.00\) - Total from November 13-27: \(15 \times 4198.00 = 62970.00\) - Total from November 28: \(1 \times 4275.00 = 4275.00\) - Total from November 29-30: \(2 \times 4474.00 = 8948.00\) Sum of daily balances for the billing cycle: \[ 25344.00 + 24744.00 + 62970.00 + 4275.00 + 8948.00 = 126281.00 \] To find the average daily balance: \[ \text{Average daily balance} = \frac{126281.00}{30} = 4209.37 \] Therefore, the average daily balance for November is \( S = 4209.37 \). Step 2: Calculate the Interest to Be Paid Next, we use the average daily balance to calculate the interest. The annual interest rate is \(3.93\%\). \[ \text{Monthly interest rate} = \frac{3.93\%}{12} = 0.3275\% \] The interest to be paid is: \[ \text{Interest to be paid} = 4209.37 \times 0.003275 = 13.79 \] Therefore, the interest required to be paid on December 1 is \( \$[/tex] 13.79 \).
Step 3: Calculate the Total Balance Due on December 1
To find the total balance due, we need to add the interest to the previous balance adjusted for payments and new transactions:
[tex]\[ \text{Total balance due} = \$4224.00 - \$100.00 + \$74.00 + \$77.00 + \$199.00 + \$13.79 = 4487.79 \][/tex]
Therefore, the total amount due on December 1 is [tex]\( \$ 4487.79 \)[/tex].
Step 4: Calculate the Minimum Monthly Payment
Finally, to determine the minimum monthly payment:
- If the total balance due is less than [tex]\( \$225 \)[/tex], the minimum payment is [tex]\( \$20 \)[/tex].
- If the total balance due is greater than or equal to [tex]\( \$225 \)[/tex], the minimum payment is [tex]\( \lceil \frac{\text{total balance due}}{20} \rceil \)[/tex].
Here,
[tex]\[ \frac{4487.79}{20} = 224.39 \][/tex]
Rounding up to the nearest whole number:
[tex]\[ \text{Minimum monthly payment} = 225 \][/tex]
Therefore, the minimum monthly payment due by December 8 is [tex]\( \$ 225 \)[/tex].
Step 1: Calculate the Average Daily Balance
To determine the average daily balance, we need to account for the balance changes occurring throughout the billing cycle. Here’s how the balance changes over the month based on the transactions:
- November 1 to November 6:
* Balance = previous balance = \[tex]$4,224.00 * Number of days = 6 - November 7 to November 12: Balance for these days = \$[/tex]4,224.00 - \[tex]$100.00 = \$[/tex]4,124.00
Number of days = 6
- November 13 to November 27:
* Balance for these days = \[tex]$4,124.00 + \$[/tex]74.00 = \[tex]$4,198.00 * Number of days = 15 - November 28: Balance for this day = \$[/tex]4,198.00 + \[tex]$77.00 = \$[/tex]4,275.00
Number of days = 1
- November 29 and November 30:
* Balance for these days = \[tex]$4,275.00 + \$[/tex]199.00 = \[tex]$4,474.00 * Number of days = 2 Now, we add up the daily balances for each period: - Total from November 1-6: \(6 \times 4224.00 = 25344.00\) - Total from November 7-12: \(6 \times 4124.00 = 24744.00\) - Total from November 13-27: \(15 \times 4198.00 = 62970.00\) - Total from November 28: \(1 \times 4275.00 = 4275.00\) - Total from November 29-30: \(2 \times 4474.00 = 8948.00\) Sum of daily balances for the billing cycle: \[ 25344.00 + 24744.00 + 62970.00 + 4275.00 + 8948.00 = 126281.00 \] To find the average daily balance: \[ \text{Average daily balance} = \frac{126281.00}{30} = 4209.37 \] Therefore, the average daily balance for November is \( S = 4209.37 \). Step 2: Calculate the Interest to Be Paid Next, we use the average daily balance to calculate the interest. The annual interest rate is \(3.93\%\). \[ \text{Monthly interest rate} = \frac{3.93\%}{12} = 0.3275\% \] The interest to be paid is: \[ \text{Interest to be paid} = 4209.37 \times 0.003275 = 13.79 \] Therefore, the interest required to be paid on December 1 is \( \$[/tex] 13.79 \).
Step 3: Calculate the Total Balance Due on December 1
To find the total balance due, we need to add the interest to the previous balance adjusted for payments and new transactions:
[tex]\[ \text{Total balance due} = \$4224.00 - \$100.00 + \$74.00 + \$77.00 + \$199.00 + \$13.79 = 4487.79 \][/tex]
Therefore, the total amount due on December 1 is [tex]\( \$ 4487.79 \)[/tex].
Step 4: Calculate the Minimum Monthly Payment
Finally, to determine the minimum monthly payment:
- If the total balance due is less than [tex]\( \$225 \)[/tex], the minimum payment is [tex]\( \$20 \)[/tex].
- If the total balance due is greater than or equal to [tex]\( \$225 \)[/tex], the minimum payment is [tex]\( \lceil \frac{\text{total balance due}}{20} \rceil \)[/tex].
Here,
[tex]\[ \frac{4487.79}{20} = 224.39 \][/tex]
Rounding up to the nearest whole number:
[tex]\[ \text{Minimum monthly payment} = 225 \][/tex]
Therefore, the minimum monthly payment due by December 8 is [tex]\( \$ 225 \)[/tex].
