Questions: The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 2.5% of the average daily balance. Calculate parts a-d using the statement on the right. Transaction Description Transaction Amount ------ Previous balance, 6280.00 March 1 Billing date March 5 Payment 400.00 credit March 7 Charge: Restaurant 50.00 March 12 Charge: Groceries 90.00 March 21 Charge: Car Repairs 210.00 March 31 End of billing period Payment Due Date: April 9 a. Find the average daily balance for the billing period. Round to the nearest cent. The average daily balance for the billing period is (Round to the nearest cent as needed)

The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 2.5% of the average daily balance. Calculate parts a-d using the statement on the right.

Transaction Description Transaction Amount
------
Previous balance, 6280.00
March 1 Billing date
March 5 Payment 400.00 credit
March 7 Charge: Restaurant 50.00
March 12 Charge: Groceries 90.00
March 21 Charge: Car Repairs 210.00
March 31 End of billing period
Payment Due Date: April 9

a. Find the average daily balance for the billing period. Round to the nearest cent.

The average daily balance for the billing period is (Round to the nearest cent as needed)

Transcript text: The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is $2.5 \%$ of the average daily balance. Calculate parts a-d using the statement on the right. \begin{tabular}{|l|l|} \hline Transaction Description & \begin{tabular}{l} Transaction \\ Amount \end{tabular} \\ \hline Previous balance, $\$ 6280.00$ & \\ \hline March 1 Billing date & \\ \hline March 5 Payment & $\$ 400.00$ credit \\ \hline March 7 Charge: Restaurant & $\$ 50.00$ \\ \hline March 12 Charge: Groceries & $\$ 90.00$ \\ \hline March 21 Charge: Car Repairs & $\$ 210.00$ \\ \hline March 31 End of billing period & \\ \hline Payment Due Date: April 9 & \\ \hline \end{tabular} a. Find the average daily balance for the billing period. Round to the nearest cent. The average daily balance for the billing period is $\$$ (Round to the nearest cent as needed)

Solution

Solution Steps

Step 1: Initialize the Daily Balances

The daily balances array (DB) is initialized with the initial balance (B_0) for each day of the billing period. This represents the balance before any transactions have occurred. Initial daily balances: [6280, 6280, 6280, 6280, 5880]... (showing first 5 days for brevity)

Step 2: Update the Daily Balances for Each Transaction

For each transaction, the daily balance from the day of the transaction (D) to the end of the billing period is updated by adding the transaction amount (A). Transactions and updates are applied as follows:

Transaction of -400 on day 5 affects balances from day 5 onwards.
Transaction of 50 on day 7 affects balances from day 7 onwards.
Transaction of 90 on day 12 affects balances from day 12 onwards.
Transaction of 210 on day 21 affects balances from day 21 onwards.

Step 3: Calculate the Average Daily Balance (ADB)

The ADB is calculated by summing all daily balances in DB and dividing by the number of days in the billing period (L). Calculated ADB before rounding: 6104.516

Step 4: Round the Average Daily Balance

The ADB is rounded to the nearest cent as per financial conventions, resulting in 6104.52.