The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 1.5% of the average daily balance. Calculate parts a-d using the statement on the right.
| Transaction Description | Transaction Amount |
|---|---|
| Previous balance, $6330.00 |
| March 1 Billing date |
| March 5 Payment | $250.00 credit |
| March 7 Charge: Restaurant | $50.00 |
| March 12 Charge: Groceries | $80.00 |
| March 21 Charge: Car Repairs | $280.00 |
| March 31 End of billing period |
| Payment Due Date: April 9 |
a. Find the average daily balance for the billing period. Round the nearest cent.
The average daily balance for the billing period is $ [ ]. (Round to the nearest cent as needed.)
Answer (2)
Calculate the balance for each period based on transactions.
Multiply each balance by the number of days it remained the same.
Sum the results from the previous step.
Divide the sum by the number of days in the billing cycle (31) to find the average daily balance: $\frac{$195410.00}{31} = 6303.55 .
The average daily balance for the billing period is $\boxed{ 6303.55} .
Explanation
Understanding the Problem We need to calculate the average daily balance for the billing period. The average daily balance is calculated by summing the daily balances and dividing by the number of days in the billing cycle. In this case, the billing cycle is 31 days (March 1 to March 31).
Calculating Daily Balances First, let's calculate the balance for each period:
March 1-4 (4 days): Previous balance = $6330.00
March 5-6 (2 days): Payment of $250.00, so balance = $6330.00 - $250.00 = $6080.00
March 7-11 (5 days): Charge of $50.00, so balance = $6080.00 + $50.00 = $6130.00
March 12-20 (9 days): Charge of $80.00, so balance = $6130.00 + $80.00 = $6210.00
March 21-31 (11 days): Charge of $280.00, so balance = $6210.00 + $280.00 = $6490.00
Multiplying Balances by Number of Days Now, we multiply each balance by the number of days it remained the same:
$6330.00 * 4 = $25320.00
$6080.00 * 2 = $12160.00
$6130.00 * 5 = $30650.00
$6210.00 * 9 = $55890.00
$6490.00 * 11 = $71390.00
Summing the Results Next, we sum these results:
$25320.00 + $12160.00 + $30650.00 + $55890.00 + $71390.00 = $195410.00
Calculating the Average Daily Balance Finally, we divide the sum by the number of days in the billing cycle (31):
$\frac{$195410.00}{31} = 6303.548387...
Rounding to the nearest cent, we get $6303.55.
Final Answer Therefore, the average daily balance for the billing period is $$6303.55.
Examples
Understanding average daily balance is crucial for managing credit card expenses. For instance, if you want to minimize interest charges, knowing how the average daily balance is calculated helps you plan your payments and purchases strategically. Paying off your balance before the end of the billing cycle or making more frequent payments can lower your average daily balance, thus reducing the interest you owe. This concept extends to other financial products like loans, where understanding the balance calculation method can save you money.
The average daily balance for the billing period is calculated to be $6303.55 by summing the calculated daily balances for the respective periods and dividing by the total number of days. Each balance reflects the transactions that occurred throughout March 2023. This method ensures an accurate representation of spending and payments over the month.
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