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Percentage change is a measure of the relative difference between two values. The formula for calculating percentage change is:
Percentage change = (difference / original value) * 100, where
- Difference = New value - Original value.
- Original value is the starting point.
- Proportion of change = Difference / Original value.
- Percentage change = Proportion * 100.
Imagine you have 10 candies and you get 5 more, so now you have 10 + 5 = 15 candies.
- Difference = New value (15) - Original value (10) = 15 - 10 = 5.
- Original value is 10 candies.
- Proportion of change = Difference (5) / Original value (10) = 0.5.
- Percentage change = Proportion (0.5) * 100 = 50%.
So, the increase in the number of candies is 50%.
Percentage change is useful in a variety of contexts, including:
- Personal finance: To track the change in the value of investments over time, such as stocks or bonds.
- Business: To track sales growth over time, or to compare market share of different products.
- Economics: To track changes in macroeconomic indicators such as inflation or unemployment rates over time.
Here are some examples example problems that involve calculating percentage change:
Example 1 - An item that was originally priced at $100 is now on sale for $80. What is the percentage decrease in price?
Answer: The difference is $100 - $80 = $20, and the percentage change is
($20 / $100) * 100 = 20%.
Example 2 - A stock was originally priced at $50 per share, and now it is priced at $60 per share. What is the percentage increase in price?
Answer: The difference is $60 - $50 = $10, and the percentage change is ($10 / $50) * 100 = 20%.
Example 3 - A product was originally produced in 100 units, and now it is produced in 120 units. What is the percentage increase in production?
Answer: The difference is 120 - 100 = 20, and the percentage change is (20 / 100) * 100 = 20%.
What you will learn from this article -
- Understanding Percentage Change Formula
- Calculating Percentage Change: Detailed Examples
- Overcoming Common Challenges in Percentage Change Calculation
- Applying Percentage Change in Various Scenarios
Percentage Change
The percentage change formula is used to calculate the difference between two values as a percentage of the original value.
This can be useful when comparing data over time or when comparing different items. To calculate the percentage change, you first need to subtract the original value from the new value. Then, you divide that difference by the original value and multiply by 100 to get the percentage change.
The formula for percentage change is as follows:
% Change = (New Value - Original Value) / Original Value x 100
For example, if the price of a stock was $50 and it has now increased to $60, the percentage change would be: % Change = (60 - 50) / 50 x 100 = 20%. This means that the stock has increased by 20% in value.
It's important to note that the percentage change can be positive or negative. A positive percentage change indicates an increase in value, while a negative percentage change indicates a decrease in value.
It's also important to note that the percentage change can be used to compare different items or data sets. For example, if you wanted to compare the growth of two companies, you could calculate the percentage change in their revenue over the past year.
The percentage change formula is a way to express the difference between two values as a percentage of the original value, it can be positive or negative and it is used to compare different items or data sets over time.
Some Examples on Calculating Percent Change
Calculating the percentage change in the value of a stock
Let's assume the original value of the stock is $50 and the new value is $60. The difference between the new value and the original value is $60-$50 = $10.
To find the percentage change, divide the difference by the original value and multiply by 100: ($10/$50) x 100 = 20%. The stock has increased by 20% in value. Calculating the percentage change in the price of a product:
Calculating the percentage change in the Price of the Product
Let's assume the original price of the product is $100 and the new price is $90. The difference between the new price and the original price is $90-$100 = -$10.
To find the percentage change, divide the difference by the original price and multiply by 100: (-$10/$100) x 100 = -10%. The price of the product has decreased by 10%
Calculating the percentage change in the number of customers
Let's assume the original number of customers is 100 and the new number is 120. The difference between the new number and the original number is 120-100 = 20. To find the percentage change, divide the difference by the original number and multiply by 100: (20/100) x 100 = 20%. The number of customers has increased by 20%
Calculating the percentage change in the height of a building
Let's assume the original height of the building is 100 meters and the new height is 90 meters. The difference between the new height and the original height is 90-100 = -10. To find the percentage change, divide the difference by the original height and multiply by 100: (-10/100) x 100 = -10%. The height of the building has decreased by 10%.
Calculating the percentage change in the weight of a package Let's assume the original weight of the package is 5 kilograms and the new weight is 5.5 kilograms. The difference between the new weight and the original weight is 5.5-5 = 0.5. To find the percentage change, divide the difference by the original weight and multiply by 100: (0.5/5) x 100 = 10%. The weight of the package has increased by 10%.
Overcoming Common Challenges in Percentage Change Calculation
Confusing increase and decrease
It is important to know whether a percentage change is an increase or a decrease and what the sign of the percentage change represents. A positive percentage change represents an increase and a negative percentage change represents a decrease.
Example:
The price of a product increased from $100 to $120. What is the percentage change in the price of the product?
Solution:
- The difference between the new price ($120) and the original price ($100) is $120-$100 = $20.
- To calculate the percentage change, divide the difference ($20) by the original price ($100) and multiply by 100: ($20/$100) x 100 = 20%.
-: The price of the product has increased by 20%.
Not considering the base value
The base value, which is the original value, can greatly affect the calculation of percentage change. A small change in a large base value will result in a smaller percentage change than the same change in a small base value.
Example:
The value of a stock increased from $50 to $60 and then decreased to $55. What is the percentage change in the value of the stock?
Solution:
The stock increased from $50 to $60, resulting in a change of $10.
- The stock then decreased from $60 to $55, resulting in a change of -$5.
- To calculate the percentage change, divide the change by the original value and multiply by 100
- For the first change: ($10/$50) x 100 = 20%. This means the stock increased by 20%.
- For the second change: ($5/$60) x 100 = -8.33%.
-: This means the stock decreased by 8.33%.
Not converting units
Before calculating the percentage change, it is important to make sure the units of the original value and the new value are the same. For example, if the original value is in dollars and the new value is in euros, the values should be converted to the same unit.
Example:
The height of a building increased from 100 meters to 120 feet. What is the percentage change in the height of the building?
Solution: First, the units should be converted to the same unit, in this case, meters. 120 feet is equivalent to 36.58 meters.
The difference between the new height and the original height is 36.58-100 = -63.42. To find the percentage change, divide the difference by the original height and multiply by 100: (-63.42/100) x 100 = -63.42%. The height of the building has decreased by 63.42%.
Misunderstanding percent:
Percent is often confused with percentage points. For example, a change from 10% to 20% is a 100% increase, not a 10% increase.
Example:
The interest rate increased from 10% to 20%. What is the percentage change in the interest rate?
Solution:
- The difference between the new interest rate (20%) and the original interest rate (10%) is 20%-10% = 10 percentage points.
- To calculate the percentage change, divide the difference (10 percentage points) by the original interest rate (10%) and multiply by 100: (10/10) x 100 = 100%.
-: The interest rate increased by 100%.
Forgetting to multiply by 100
The result of the calculation of percentage change should be multiplied by 100 to convert the decimal to a percentage.
Example:
The price of a product increased from $100 to $110. What is the percentage change in the price of the product?
Solution
The difference between the new price and the original price is $110-$100 = $10. To find the percentage change, divide the difference by the original price and multiply by 100 ($10/$100) x 100 = 10%. The price of the product has increased by 10%.
Not considering the time interval
Percentage change is usually calculated over a specific time interval, such as a year or a quarter. It is important to make sure the time interval is clear and consistent when calculating percentage change.
Example:
The number of customers increased from 100 to 120 in one year. What is the average annual percentage change in the number of customers?
Solution:
The difference between the new number and the original number is 120-100 = 20. To find the average annual percentage change, divide the difference by the original number and the time interval and multiply by 100
(20/100) x 100/1 = 20%.
The average annual percentage change in the number of customers is 20%.
Rounding errors
Rounding can introduce errors into the calculation of percentage change. It is important to carry out intermediate calculations to sufficient precision before rounding the final result.
Example:
The value of a stock increased from $100 to $110 and then decreased to $105. What is the percentage change in the value of the stock?
Solution:
- The stock increased from $100 to $110, resulting in a change of $10.
- The stock then decreased from $110 to $105, resulting in a change of -$5.
- To calculate the percentage change, divide the change by the original value and multiply by 100:
- For the first change: ($10/$100) x 100 = 10%. This means the stock increased by 10%.
- For the second change: ($5/$110) x 100 = -4.54%.
-: This means the stock decreased by 4.54%.
Percent Change Questions in Different Industries
Finance
Q1. What is the percentage change in the value of a bond over a year?
Example: A bond increased from $100 to $105 over a year.
The percentage change in the value of the bond is (105-100)/100 x 100 = 5%.
Q2. What is the percentage change in the value of a mutual fund over a year?
Example: A mutual fund increased from $50 to $55 over a year. The percentage change in the value of the mutual fund is (55-50)/50 x 100 = 10%.
Q3. What is the percentage change in the value of a real estate property over a year?
Example: A real estate property increased from $200,000 to $220,000 over a year. The percentage change in the value of the property is (220,000-200,000)/200,000 x 100 = 10%.
Economics
What is the percentage change in the Gross Domestic Product (GDP) over a year?
Example: The GDP increased from $20 trillion to $21 trillion over a year. The percentage change in the GDP is (21-20)/20 x 100 = 5%.
What is the percentage change in the unemployment rate over a year?
Example: The unemployment rate decreased from 8% to 7% over a year. The percentage change in the unemployment rate is (8-7)/8 x 100 = 12.5%.
What is the percentage change in the inflation rate over a year?
Example: The inflation rate increased from 2% to 3% over a year. The percentage change in the inflation rate is (3-2)/2 x 100 = 50%.
Business
What is the percentage change in the operating expenses of a company over a quarter?
Example: The operating expenses of a company decreased from $500,000 to $450,000 over a quarter. The percentage change in the operating expenses is (500,000-450,000)/500,000 x 100 = 10%.
What is the percentage change in the profit margin of a company over a quarter?
Example: The profit margin of a company increased from 8% to 9% over a quarter. The percentage change in the profit margin is (9-8)/8 x 100 = 12.5%.
What is the percentage change in the return on investment (ROI) of a company over a year?
Example: The ROI of a company increased from 10% to 12% over a year. The percentage change in the ROI is (12-10)/10 x 100 = 20%.
Accounting
What is the percentage change in the total assets of a company over a year?
Example: The total assets of a company increased from $100 million to $120 million over a year.
The percentage change in the total assets is (120-100)/100 x 100 = 20%.
What is the percentage change in the total liabilities of a company over a year?
Example: The total liabilities of a company decreased from $50 million to $45 million over a year.
The percentage change in the total liabilities is (50-45)/50 x 100 = 10%
What is the percentage change in the shareholders' equity of a company over a year?
Example: The shareholders' equity of a company increased from $60 million to $65 million over a year.
The percentage change in the shareholders' equity is (65-60)/60 x 100 = 8.33%.
Frequently Asked Questions in Exams
Q1. What is the percentage increase in the perimeter of a rectangle if one side is increased by 20% and the other side is decreased by 10%?
A. The original perimeter of the rectangle was 40 units. One side was increased from 20 units to 20 units + 20% of 20 units = 24 units. The other side was decreased from 20 units to 20 units - 10% of 20 units = 18 units. The new perimeter is 24 units + 18 units = 42 units. The percentage change in the perimeter is (42-40)/40 x 100 = 5%.
Q2, What is the percentage change in the price of a commodity if its supply decreases and demand increases?
A. The original price of a commodity was $100. Its supply decreased by 10% and its demand increased by 20%. The new price is $100 + 20% of $100 - 10% of $100 = $108. The percentage change in the price is (108-100)/100 x 100 = 8%.
Q3. What is the percentage increase in the revenue of a company if its expenses decrease and its sales increase?
A. The original revenue of a company was $1000. Its expenses decreased by 10% and its sales increased by 20%. The new revenue is $1000 + 20% of $1000 - 10% of $1000 = $1080. The percentage change in the revenue is (1080-1000)/1000 x 100 = 8%.
Q4. What is the percentage change in the profit of a company if its revenue decreases and its expenses increase?
A. The original profit of a company was $100. Its revenue decreased by 10% and its expenses increased by 20%. The new profit is $100 - 10% of $100 + 20% of $100 = $98. The percentage change in the profit is (98-100)/100 x 100 = -2%.
Q5. What is the percentage change in the mean of a set of data if one value is added and another value is removed?
A. The original mean of a set of data was 50. One value was added to the set, increasing the mean to 55, and another value was removed from the set, decreasing the mean to 45. The percentage change in the mean is (45-50)/50 x 100 = -10%.
Q6. What is the percentage change in the market share of a company if its competitors increase their market share and the company launches a new product?
A. The original market share of a company was 30%. Its competitors increased their market share by 10% and the company launched a new product. The new market share is 30% + 10% - 10% = 30%. The percentage change in the market share is (30-30)/30 x 100 = 0%.
Q7. What is the percentage change in the exam scores of a student if their scores increase in one subject and decrease in another subject?
A. The original exam scores of a student was 50. Their scores increased in one subject to 60 and decreased in another subject to 40. The new exam scores is (60+40)/2 = 50. The percentage change in the exam scores is (50-50)/50 x 100 = 0%.
Q8. What is the percentage increase in the height of a person who grows from 5 feet to 6 feet?
A. The percentage increase in height is (6-5)/5 x 100 = 20%.
Q9. What is the percentage decrease in the weight of a person who loses 20 pounds from a starting weight of 200 pounds?
A. The percentage decrease in weight is (200-180)/200 x 100 = 10%.
Q10. A store raises the price of a product from $20 to $22. What is the percentage increase in price?
A. The percentage increase in price is (22-20)/20 x 100 = 10%.
Q11. A stock price decreases from $100 to $90. What is the percentage decrease in price?
A. The percentage decrease in price is (100-90)/100 x 100 = 10%
Q12 A student scores 80 out of 100 in a test. What is the percentage score of the student?
A. The percentage score of the student is 80/100 x 100 = 80%.
Q13. A company's sales increase from $100,000 to $120,000. What is the percentage increase in sales?
A. The percentage increase in sales is (120,000-100,000)/100,000 x 100 = 20%.
Q14. A car's fuel efficiency decreases from 20 miles per gallon to 18 miles per gallon. What is the percentage decrease in fuel efficiency?
A. The percentage decrease in fuel efficiency is (20-18)/20 x 100 = 10%.
Q16. A stock's dividend yield decreases from 4% to 3%. What is the percentage decrease in dividend yield?
A. The percentage decrease in dividend yield is (4-3)/4 x 100 = 25%.
Q17. A person saves $1000 in a year. The next year, their savings increase to $1200. What is the percentage increase in savings?
A. The percentage increase in savings is (1200-1000)/1000 x 100 = 20%
Q18. A company's profits increase from $500,000 to $600,000. What is the percentage increase in profits?
A. The percentage increase in profits is (600,000-500,000)/500,000 x 100 = 20%.