Math Problem Statement

Compute the average daily balance based on the given credit card transactions and balances for each period in the billing cycle.

Solution

To solve for the average daily balance, we need to calculate the daily balance over each period in the billing cycle and divide the total by the number of days in the cycle.

Here's how to approach it with the given dataTo solve for the average daily balance, we need to calculate the daily balance over each period in the billing cycle and divide the total by the number of days in the cycle.

Here's how to approach it with the given

  1. List the Balance and Days: Based on the image, each transaction changes the balance, and each new balance lasts for a certain number of days.

    DateBalanceDays
    Nov 1-7$5,0006
    Nov 7-20$5,14313
    Nov 20-21$5,1991
    Nov 21-24$5,3753
    Nov 24-26$5,4342
    Nov 26-30$5,5894
  2. Calculate the Balance Over Each Period: Multiply each balance by the corresponding number of days to get the balance-days.

    • Nov 1-7: 5,000×6=30,0005,000 \times 6 = 30,000
    • Nov 7-20: 5,143×13=66,8595,143 \times 13 = 66,859
    • Nov 20-21: 5,199×1=5,1995,199 \times 1 = 5,199
    • Nov 21-24: 5,375×3=16,1255,375 \times 3 = 16,125
    • Nov 24-26: 5,434×2=10,8685,434 \times 2 = 10,868
    • Nov 26-30: 5,589×4=22,3565,589 \times 4 = 22,356
  3. Sum the Balance-Days: Add all these values together.

    30,000+66,859+5,199+16,125+10,868+22,356=151,40730,000 + 66,859 + 5,199 + 16,125 + 10,868 + 22,356 = 151,407

  4. Divide by the Total Number of Days: There are 30 days in November, so we divide the total balance-days by 30.

    151,40730=5,046.90\frac{151,407}{30} = 5,046.90

Therefore, the Average Daily Balance is $5,046.90.

Would you like additional details or have any questions?


Here are some follow-up questions to deepen your understanding:

  1. How would the calculation change if there were additional transactions?
  2. What is the importance of calculating the average daily balance in credit card billing?
  3. How does the average daily balance method impact interest charges compared to other methods?
  4. What other factors, besides the average daily balance, can affect the amount of interest charged?
  5. Could this method be applied to other forms of credit, and if so, how?

Tip: Always double-check the days and balance for each period to ensure accuracy when calculating the average daily balance.

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Math Problem Analysis

Mathematical Concepts

Average Daily Balance
Credit Card Balances
Interest Calculation

Formulas

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

Theorems

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Suitable Grade Level

Grades 10-12