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The bank calculated how much was refunded in service fees for all its customers over the following months:

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
& Jan & Feb & Mar & Apr & May & Jul & Aug & Sep & Oct & \begin{tabular}{l}
Total \\
to date
\end{tabular} \\
\hline
\begin{tabular}{l}
Refund \\
(Rand)
\end{tabular} & 60000 & 78000 & 30000 & 34000 & 40000 & 15000 & 18000 & 19000 & 20000 & 314000 \\
\hline
\begin{tabular}{l}
Number \\
of refunds
\end{tabular} & 1200 & 1800 & 800 & 600 & 500 & 300 & 300 & 300 & 300 & 6100 \\
\hline
\end{tabular}

4.1. What trend can you identify and what could the reason be? (2)

4.2. Calculate for each of the months the refunds due, expressed as a percentage proportion (rounded off to two decimals). (3)

January
February
March



Answer :

GinnyAnswer
Sure, let's address the questions step-by-step.

4.1. Trend Identification and Possible Reasons

From the data provided:

[tex]\[ \begin{tabular}{|c|c|c|} \hline Month & Refund (Rand) & Number of Refunds \\ \hline Jan & 60000 & 1200 \\ Feb & 78000 & 1800 \\ Mar & 30000 & 800 \\ Apr & 34000 & 600 \\ May & 40000 & 500 \\ Jul & 15000 & 300 \\ Aug & 18000 & 300 \\ Sep & 19000 & 300 \\ Oct & 20000 & 300 \\ Total & 314000 & 6100 \\ \hline \end{tabular} \][/tex]

Trend Identified:
1. There is a general trend of high refunds in the earlier months (January and February) and a decline in the number of refunds and refund amounts in subsequent months.
2. The number of refunds also follows a similar trend, being higher in the earlier months and then tending to decrease or stabilize.

Possible Reasons:
1. Seasonal Factors: The beginning of the year might have a higher refund rate due to annual service renewals or issues that customers notice at the start of the year.
2. Policy Changes: The bank might have updated its refund policies or processes after February, resulting in fewer refunds being issued.
3. Customer Behavior: Customers may be more vigilant about checking and disputing fees at the beginning of the year following holiday spending.

4.2. Calculate Each Month's Refunds as a Percentage

We want to calculate the refunds due for January, February, and March, expressed as a percentage of the total refunds to date.

To find the percentage proportion for each month:
[tex]\[ \text{Percentage for a month} = \left(\frac{\text{Refund for the month}}{\text{Total refunds}}\right) \times 100 \][/tex]

For January:
[tex]\[ \text{Percentage for January} = \left(\frac{60000}{314000}\right) \times 100 \approx 19.11\% \][/tex]

For February:
[tex]\[ \text{Percentage for February} = \left(\frac{78000}{314000}\right) \times 100 \approx 24.84\% \][/tex]

For March:
[tex]\[ \text{Percentage for March} = \left(\frac{30000}{314000}\right) \times 100 \approx 9.55\% \][/tex]

Therefore, the refunds for January, February, and March as a percentage of the total refunds to date are approximately:

- January: 19.11%
- February: 24.84%
- March: 9.55%

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