Questions: Suppose your VISA card calculates interest using the average daily balance method, and the monthly interest rate is 2.95 %. The itemized billing for the month of April is shown below. Detail Date Amount --------- Unpaid balance April 1 845 Charge April 3 455 Charge April 11 1055 Charge April 15 815 Payment received April 28 125 Last day of billing period April 30 Payment due date May 7 (a) Find the average daily balance. (b) Find the interest due for this month. (c) Find the total balance owed on the last day of the billing period. (d) This credit card requires a 20 minimum payment or 1/36 of the amount due, whichever is higher. What is the minimum monthly payment due for this month?

Suppose your VISA card calculates interest using the average daily balance method, and the monthly interest rate is 2.95 %. The itemized billing for the month of April is shown below. Detail Date Amount --------- Unpaid balance April 1 845 Charge April 3 455 Charge April 11 1055 Charge April 15 815 Payment received April 28 125 Last day of billing period April 30 Payment due date May 7 (a) Find the average daily balance. (b) Find the interest due for this month. (c) Find the total balance owed on the last day of the billing period. (d) This credit card requires a 20 minimum payment or 1/36 of the amount due, whichever is higher. What is the minimum monthly payment due for this month?
Transcript text: Suppose your VISA card calculates interest using the average daily balance method, and the monthly interest rate is $2.95 \%$. The itemized bilting for the month of April is shown below. \begin{tabular}{|r|c|r|} \hline \multicolumn{1}{|c|}{ Detail } & Date & Amount \\ \hline Unpaid balance & April 1 & 845 \\ \hline Charge & April 3 & 455 \\ \hline Charge & April 11 & 1055 \\ \hline Charge & April 15 & 815 \\ \hline Payment received & April 28 & 125 \\ \hline Last day of billing period & April 30 & \\ \hline Payment due date & May 7 & \\ \hline \end{tabular} (a) Find the average daily balance. \$ $\square$ (b) Find the interest due for this month. \$ $\square$ (c) Find the total balance owed on the last day of the billing period. \$ $\square$ (d) This credit card requires a $\$ 20$ minimum payment or $1 / 36$ of the amount due, whichever is higher. What is the minimum monthly payment due for this month? \$ $\square$ Question Help: Video Message instructor Submit Question
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Solution

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Solution Steps

Solution Approach

(a) To find the average daily balance, calculate the balance for each day of the billing period, sum these daily balances, and then divide by the number of days in the billing period.

(b) To find the interest due for the month, multiply the average daily balance by the monthly interest rate.

(c) To find the total balance owed on the last day of the billing period, add the interest due to the balance on the last day of the billing period.

Step 1: Calculate the Average Daily Balance

To find the average daily balance, we sum the daily balances over the billing period and divide by the number of days. The calculated average daily balance is:

\[ \text{Average Daily Balance} = \frac{2293.6667}{30} \approx 2293.67 \]

Step 2: Calculate the Interest Due

The interest due for the month is calculated by multiplying the average daily balance by the monthly interest rate:

\[ \text{Interest Due} = 2293.6667 \times 0.0295 \approx 67.6632 \]

Step 3: Calculate the Total Balance Owed

The total balance owed on the last day of the billing period is the sum of the current balance and the interest due:

\[ \text{Total Balance Owed} = 3045 + 67.6632 \approx 3112.6632 \]

Final Answer

The answers to the sub-questions are as follows:

  • (a) Average Daily Balance: \( \boxed{2293.67} \)
  • (b) Interest Due: \( \boxed{67.6632} \)
  • (c) Total Balance Owed: \( \boxed{3112.6632} \)
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