Understanding Annual Profit Increase

The question asks us to identify the period with the maximum percentage increase in annual profit compared to the previous year. To do this, we need to calculate the percentage increase for each period where a comparison is possible, based on the provided profit data.

Analyzing the Annual Profit Data Table

First, let's look at the annual profit data given in the table:

Calculating Percentage Increase in Profit

The formula for calculating the percentage increase is:

$$ \text{Percentage Increase} = \left( \frac{\text{Profit in Current Period} - \text{Profit in Previous Period}}{\text{Profit in Previous Period}} \right) \times 100\% $$

We will calculate the percentage increase for each period starting from 2015-2016:

Percentage Increase for 2015-2016

Compared to 2014-2015:

• Profit in 2015-2016 = 690
• Profit in 2014-2015 = 625

$$ \text{Percentage Increase}_{2015-2016} = \left( \frac{690 - 625}{625} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2015-2016} = \left( \frac{65}{625} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2015-2016} = 0.104 \times 100\% = 10.4\% $$

Percentage Increase for 2016-2017

Compared to 2015-2016:

• Profit in 2016-2017 = 725
• Profit in 2015-2016 = 690

$$ \text{Percentage Increase}_{2016-2017} = \left( \frac{725 - 690}{690} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2016-2017} = \left( \frac{35}{690} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2016-2017} \approx 0.0507 \times 100\% \approx 5.07\% $$

Percentage Increase for 2017-2018

Compared to 2016-2017:

• Profit in 2017-2018 = 775
• Profit in 2016-2017 = 725

$$ \text{Percentage Increase}_{2017-2018} = \left( \frac{775 - 725}{725} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2017-2018} = \left( \frac{50}{725} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2017-2018} \approx 0.0689 \times 100\% \approx 6.89\% $$

Percentage Increase for 2018-2019

Compared to 2017-2018:

• Profit in 2018-2019 = 815
• Profit in 2017-2018 = 775

$$ \text{Percentage Increase}_{2018-2019} = \left( \frac{815 - 775}{775} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2018-2019} = \left( \frac{40}{775} \right) \times 100\% $$

$$ \text{Percentage Increase}_{2018-2019} \approx 0.0516 \times 100\% \approx 5.16\% $$

Comparing Percentage Increases

Let's summarize the percentage increases calculated for each period:

• 2015-2016: 10.4%
• 2016-2017: 5.07%
• 2017-2018: 6.89%
• 2018-2019: 5.16%

Comparing these values, we can see that the maximum percentage increase in profit over the previous year occurred in the period 2015-2016, with an increase of 10.4%.

Conclusion

The period with the maximum percentage increase in profit over the previous year is 2015-2016.

Revision Table: Annual Profit Analysis

Additional Information: Understanding Percentage Change

Percentage change is a fundamental concept used in finance, economics, and many other fields to show how much a value has changed relative to its original value. It is useful for comparing changes across different quantities or periods, as it standardizes the change relative to the starting point.

• A positive percentage change indicates an increase.
• A negative percentage change indicates a decrease.
• The formula can be used for both increase and decrease; if the value decreases, the numerator $(\text{New Value} - \text{Old Value})$ will be negative, resulting in a negative percentage change.

In business analysis, tracking percentage changes in metrics like profit, revenue, or expenses helps in understanding growth trends, evaluating performance, and making informed decisions.