**Percentage Change**

Examples

**L.O. - Use multipliers to calculate the result of percentage changes (Grades 4 to 7)**

The value of machinery in a factory

depreciates by 20% each year. The

machinery was bought for £74,500.

James says, "20% of £74500 is £14900, so after 2 years, the price of the machinery will have fallen by £29800."

Is James right? Justify your answer.

The polar ice cap in the Arctic is 4 metres

thick. If the ice is thinning at a rate of 6% per

year, how thick will the ice be in 5 years time?

£14,000 is invested at 9.25% per annum compound interest. Find the total amount at

the end of 3 years.

The value of machinery in a factory depreciates by 20% each year. The machinery was bought for £74,500.

James says, "20% of £74500 is £14900, so after 2 years, the price of the machinery will have fallen by £29800."

Is James right? Justify your answer.

No, because after the first year, 20% will no longer be £14900.

Starter

Teachers wages rise by 1% each year. The starting salary for a teacher is £22,244.

(a) How much will it be next year?

(b) Most teachers go up a point on the pay scales after 1 year. This represents a rise of 7.9% on the starting salary. Taking into account that this too will be subject to a 1% increase, work out pay for a second year teacher next year.

Teachers wages rise by 1% each year. The starting salary for a teacher is £22,244.

(a) How much will it be next year?

£22244 x 1.01 = £22,466

(b) Most teachers go up a point on the pay scales after 1 year. This represents a rise of 7.903% on the starting salary. Taking into account that this too will be subject to a 1% increase, work out pay for a second year teacher next year.

Either £22466 x 1.07903 or £22244 x 1.07903 x 1.01 = £24242

£14,000 is invested at 9.25% per annum compound interest. Find the total amount at

the end of 3 years.

£14000 x 1.0925 = £18255

The polar ice cap in the Arctic is 4 metres

thick. If the ice is thinning at a rate of 6% per

year, how thick will the ice be in 5 years time?

4 x 0.94 = 2.94 metres.

3

5

Examples

£308.70

£357.36

30565

6 years

Main Activity

Complete the percentage change

sheet.

Main Activity

£1375

(a) £1272

(b) £1348.32

(c) £1605.87

(a) £8144.47

(b) £7990.66

(c) £10021.16

C (£51.94)

£227.29

(a) £900

(b) £284.77

(c) £90.10

£4608

(a) 6 years

(b) (i) 5 years

(ii) 8 years

£94.50

£1.78

(a) 45,229,406

(b) 8 years

(a) (i) £3,132

(ii) 52.2%

(b) (i) £6,264

(ii) 52.2%

(c) Same % reduction

(a) £180

(b) £571.31

Plenary

An item undergoes successive percentage changes of 90%, then 80%, then 70%, and so on until a final change of 10%.

(a) If the changes are increases, calculate the total percentage increase.

(b) If the changes are decreases, calculate the total percentage decrease.

Plenary

An item undergoes successive percentage changes of 90%, then 80%, then 70%, and so on until a final change of 10%.

(a) If the changes are increases, calculate the total percentage increase.

3352%

(b) If the changes are decreases, calculate the total percentage decrease.

99.96%

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