8.3 Percentage change
If an amount has increased by a percentage: calculate the percentage amount, then add it to the original figure to find the new amount. Or you can add the percentage increase to the original percentage (100%) and then do the calculation.
If an amount has decreased by a percentage: calculate the percentage amount, then subtract it from the original figure to find the new amount. Or you can subtract the percentage decrease from the original percentage (100%) and then do the calculation.
Watch the video below on how to calculate percentage change, then complete Activity 23.
Transcript
You will already be familiar with the concept that if you buy a new car, when you come to sell it, its value is likely to have decreased. On the other hand, if you're lucky, when you buy a house and then wish to sell, you may be able to sell it for more than you bought it for.
The percentage difference between the original price and the sale price is called percentage change. This can be useful for working out the percentage profit, or loss, or finding out by what percentage an item has changed in value. It's important to recognise that percentage change can be either positive, if the price has increased, or negative, if the value of the item has gone down.
To calculate the percentage change, we need to use the simple formula: percentage change equals the difference, divided by the original, multiplied by 100. 'Difference' refers to the difference between the two values. That is, the cost before and after. 'Original' means the original value of the item.
Let's use this formula in an example. A train ticket used to cost £24. The price has gone up to £27.60. How do we find the percentage increase? First, you need to find the difference in cost. The difference = £27.60 - £24, which is £3.60.
Next, divide this difference by the original cost, and then multiply by 100. £3.60 divided by £24, x 100, = 15. The cost of the train ticket has increased by 15%.
Now try another example. You bought a car for £4,500 and you managed to sell it for £3,200. What is the percentage decrease? You should give your answer to two decimal places. The difference is £4,500 - £3,200, which = £1,300. Divide this by the original cost of £4,500. 1,300 divided by 4,500, x 100, equals a 28.89% per cent decrease. Now practise using the percentage change formula in the next activity.
Activity 23: Percentage change formula
Practise using the percentage change formula which you learned about in the video above on the four questions below. Where rounding is required, give your answer to two decimal places.
Last year your season ticket for the train cost £1300. This year the cost has risen to £1450. What is the percentage increase?
Answer
Difference: £1450 − £1300 = £150
Original: £1300
Percentage change = × 100
Percentage change = 0.11538... × 100 = 11.54% increase (rounded to two d.p.)
You bought your house 10 years ago for £155 000. You are able to sell your house for £180 000. What is the percentage increase the house has made?
Answer
Difference: £180 000 − £155 000 = £25 000
Original: £155 000
Percentage change = × 100
Percentage change = 0.16129... × 100 = 16.13% increase (rounded to two d.p.)
You purchased your car 3 years ago for £4200. You sell it to a buyer for £3600. What is the percentage decrease of the car?
Answer
Difference: £4200 − £3600 = £600
Original: £4200
Percentage change = × 100
Percentage change = 0.14285... × 100 = 14.29% decrease (rounded to two d.p.)
Stuart buys a new car for £24 650. He sells it 1 year later for £20 000. What is the percentage loss?
Answer
Difference: £24 650 − £20 000 = £4650
Original: £24 650
Percentage change = × 100
4650 ÷ 24 650 × 100 = 18.86% loss (rounded to two d.p.)
Congratulations, you now know everything you need to know about percentages! As you have seen, percentages come up frequently in many different areas of life and having completed this section, you now have the skills to deal with all kinds of situations that involve them.
You saw at the beginning of the section that percentages are really just fractions. Decimals are also closely linked to both fractions and percentages. In the next section you will see just how closely related these three concepts are and also learn how to convert between each of them.
Understanding VAT
VAT, or Value Added Tax, is a type of tax that is applied to the sale of goods and services. It is a common form of indirect tax used in many countries around the world. It is set by the government.
Stages of Production and Distribution: VAT is charged at each stage of production and distribution, from the manufacturer to the retailer, until the final sale to the consumer.
Tax on Added Value: At each stage, the tax is applied only to the value added to the product or service, not the entire price. This means that businesses can claim a credit for the VAT they pay on their purchases, reducing their overall tax liability.
If a shop sells a toy for £10 and the VAT rate is 20%, the total price the customer pays is £12. The shopkeeper keeps the original £10 and passes the £2 VAT to the government.
Activity 24: calculating the VAT amount
A customer buys a laptop that costs £500 before VAT. If the VAT rate is 20%, what is the total cost of the laptop including VAT?
Answer
1. Calculate the VAT amount:
VAT amount = Price before VAT ×
VAT amount = £500 × = £100
2. Calculate the total cost including VAT:
Total cost = Price before VAT + VAT amount
Total cost = £500 + £100 = £600
The total cost of the laptop including VAT is £600.
Summary
In this section you have:
found percentages of amounts
calculated percentage increase and decrease
calculated percentage change using a formula
expressed one number as a percentage of another.