# 5.1 Percentage increases and decreases

You’ll often see percentage increases and decreases in sales and pay rises.

## Example: Anjali’s pay rise

Anjali earns £18,000 per year. She is given a 10% pay rise. How much does she now earn?

### Method

In order to identify Anjali’s new salary, you need to find out what 10% () of £18,000 is. To do this, first you need to find out of £18,000:

18,000 ÷ 100 = 180

So of £18,000 is:

10 × 180 = 1,800

Anjali’s pay rise is £1,800, so her new salary is:

£18,000 + £1,800 = £19,800

## Example: A sale at the furniture shop

A furniture shop reduces all of its prices by 20%. How much does a £300 double bed cost in the sale?

### Method

In order to identify the new price of the double bed, you need to find out what 20% () of £300 is. To do this, first you need to find out of £300:

300 ÷ 100 = 3

So of £300 is:

20 × 3 = 60

The discount is £60, so the sale price of the double bed is:

£300 – £60 = £240

Use the examples above to help you with the following activity. Remember to check your answers once you have completed the questions.

## Activity 16: Calculating percentage increases and decreases

- You buy a car for £9,000. Its value depreciates (decreases) by 25% annually. How much will the car be worth at the end of the first year?
- Since the start of the 21st century, the shares in the InstaBank have risen by 30%. If the price of one share was £10 in 2000, what is it worth now?

### Answer

- In order to identify how much the value of the car will decrease by, you need to find out what 25% () of £9,000 is. To do this, first you need to find out of £9,000:
- 9,000 ÷ 100 = 90

- So of £9,000 is:
- 25 × 90 = 2,250

- The car’s value depreciates by £2,250 in the first year, so the value of the car at the end of the first year will be:
- £9,000 – £2,250 = £6,750

- It might be easier in this example to convert £10 into pence (£10 = 1,000p). In order to identify the new value of the share, you need to find out what 30% () of 1,000p is. To do this, first you need to find out of 1,000p:
- 1,000 ÷ 100 = 10

- So of 1,000p is:
- 30 × 10 = 300

- The share’s value has increased by 300p, or £3, since 2000, so the current value of the share is:
- £10 + £3 = £13

In this section you have learned how to calculate percentage increases and decreases. This will be useful when working out the value of a pay increase or how much an item will cost in a sale. You have also seen, and successfully used, two methods of calculating a percentage. There is one method that you haven’t been shown (and it’s probably the easiest!): using the percentage button on your calculator. The percentage button looks like this:

To successfully use it when calculating percentages you would enter the sum into your calculator as follows.

If you were asked to find 20% of 80, on your calculator you would input:

- 80 × 20%

This would give you the following answer:

- 80 × 20% = 16

This is by far the easiest way of calculating percentages when you have a calculator handy.

## Summary

In this section you have learned how to solve problems using percentages, and how to calculate percentage increases and decreases.