Step 5
The final line in the table will reflect the total amount owed from April 28 to the date of the bill, May 14. Thus, there will be 16 days of the [tex]$540.37$[/tex] balance from April 28.
\begin{tabular}{|l|l|l|l|l|}
\hline Date & Payment or Purchases (in \$) & Balance Each Day (in \$) & Days & Unpaid Balance * No. of Days (in \$)
\hline Apr 14 & & 656 & &
\hline AB/ 17 & 151.56 & [tex]$656+151.56=807.56$[/tex] & 5 & [tex]$5 \cdot 656+151.56=3,431.56$[/tex]
\hline Apr 21 & 26.45 & [tex]$807.56+26.45=834.01$[/tex] & 2 & [tex]$2 \cdot 807.56+26.45=1,641.57$[/tex]
\hline *** 25 & -500 & [tex]$834.01-500=334.01$[/tex] & 4 & [tex]$4 \cdot 834.01-500=2,836.04$[/tex]
\hline Apr 28 & 206.36 & [tex]$334.01+206.36=540.37$[/tex] & 3 & [tex]$3 \cdot 334.01+206.36=1,208.39$[/tex]
\hline & & & 16 & [tex]$16 \cdot 540.37=8645.92 \sim 8,845.92$[/tex]
\hline
\end{tabular}
What is the sum of the number of days in the billing cycle? (Hint: this is the sum of the "Days" column.)
[tex]$70\ \textgreater \ 30$[/tex] day
What is the sum of the total amounts owed (in dollars) for each day of the month? (Find this is the sum of the final column.)
[tex]$51776348 \sim 17,763.48$[/tex]
Step 8
Age - - colate the average datic bolance.
\begin{aligned}
\text { Average daily balance } & =\frac{\text { Sum of the total amounts owed for each day of the month }}{\text { Number of days in the biling cycle }}\\
& =\frac{ s 17, 763, 48 }{ 30 }
\end{aligned}
Divide to calculate the average daily balance in dollars. (Round your result to the nearest cent.)
5592.12
592.12
Answer (2)
Calculate the total number of days in the billing cycle: 5 + 2 + 4 + 3 + 16 = 30 .
Calculate the sum of the 'Unpaid Balance * No. of Days': 3431.56 + 1641.57 + 2836.04 + 1208.39 + 8645.92 = 17763.48 .
Divide the sum of the 'Unpaid Balance * No. of Days' by the number of days in the billing cycle: 30 17763.48 = 592.116 .
Round the result to the nearest cent: 592.12 .
Explanation
Understanding the Problem We are given a table representing a credit card billing cycle. The goal is to calculate the average daily balance. We are provided with the sum of the products of the unpaid balance and the number of days, as well as the total number of days in the billing cycle.
Calculating the Total Number of Days First, we need to verify the sum of the 'Days' column: 5 + 2 + 4 + 3 + 16 = 30 So, the number of days in the billing cycle is 30.
Calculating the Sum of Unpaid Balances Next, we are given that the sum of the 'Unpaid Balance * No. of Days' column is approximately 17 , 763.48. W ec an v er i f y t hi s b ys u mmin g t h e v a l u es : 3431.56 + 1641.57 + 2836.04 + 1208.39 + 8645.92 = 17763.48 $
So, the sum of the total amounts owed for each day of the month is indeed $17,763.48.
Calculating the Average Daily Balance Now, we calculate the average daily balance by dividing the sum of the 'Unpaid Balance * No. of Days' by the number of days in the billing cycle: Average daily balance = Number of days in the billing cycle Sum of the total amounts owed for each day of the month = 30 17763.48 30 17763.48 = 592.116 Rounding to the nearest cent, we get $592.12.
Final Answer Therefore, the average daily balance for the billing cycle is 592.12 .
Examples
Understanding average daily balance is crucial in 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 effectively. Suppose you have a credit card debt and want to reduce the interest you pay. By making larger payments earlier in the billing cycle, you lower your average daily balance, which in turn reduces the interest accrued. This proactive approach can save you money and improve your financial health.
To find the average daily balance, we calculated the total number of days in the billing cycle as 30 days and the sum of the 'Unpaid Balance * No. of Days' as $17,763.48. Dividing the total amount by the number of days gives an average daily balance of $592.12. Hence, the average daily balance is $592.12.
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