Math Problem Statement

Find the average daily balance for the billing period using the given transactions. Round to the nearest cent.

Solution

To calculate the average daily balance for the billing period, we need to account for the balance on each day during the billing cycle based on the transactions made.

Step-by-Step Process:

  1. March 1 - March 5 (5 days):

    • Balance starts at $6220.00.
  2. March 5 (Payment of $350):

    • New balance = $6220.00 - $350.00 = $5870.00.
  3. March 5 - March 7 (2 days):

    • Balance = $5870.00.
  4. March 7 (Charge of $50 for Restaurant):

    • New balance = $5870.00 + $50.00 = $5920.00.
  5. March 7 - March 12 (5 days):

    • Balance = $5920.00.
  6. March 12 (Charge of $90 for Groceries):

    • New balance = $5920.00 + $90.00 = $6010.00.
  7. March 12 - March 21 (9 days):

    • Balance = $6010.00.
  8. March 21 (Charge of $240 for Car Repairs):

    • New balance = $6010.00 + $240.00 = $6250.00.
  9. March 21 - March 31 (10 days):

    • Balance = $6250.00.

Calculating the Average Daily Balance:

Now, multiply each balance by the number of days it was held, sum them up, and divide by the total number of days in the billing cycle (31 days).

Average Daily Balance=(6220×4)+(5870×2)+(5920×5)+(6010×9)+(6250×10)31\text{Average Daily Balance} = \frac{(6220 \times 4) + (5870 \times 2) + (5920 \times 5) + (6010 \times 9) + (6250 \times 10)}{31}

=(24880)+(11740)+(29600)+(54090)+(62500)31= \frac{(24880) + (11740) + (29600) + (54090) + (62500)}{31}

=182810315906.77= \frac{182810}{31} \approx 5906.77

Final Answer:

The average daily balance is $5906.77.

Would you like any further details or explanations? Here are some related questions to consider:

  1. How do different transactions affect the average daily balance?
  2. What would be the impact of an additional payment within the billing cycle?
  3. How is the monthly interest calculated using the average daily balance?
  4. How would the average daily balance change if one of the charges was larger?
  5. What is the importance of paying off the balance before the due date?

Tip: Always track your balances carefully during each billing cycle to minimize interest charges.

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Math Problem Analysis

Mathematical Concepts

Average Daily Balance Calculation
Arithmetic
Interest Calculation

Formulas

Average Daily Balance = (Sum of (Balance × Number of Days Held)) / Total Number of Days

Theorems

Arithmetic Operations

Suitable Grade Level

Grades 9-12