22 questions on percentage change, reverse percentages, simple and compound interest, and depreciation.

💷 Percentages and compound interest

Maths · GCSE Foundation · 22 questions · ~40 min

MathsUKwww.geekhero.co.uk

Percentages appear on all three papers and in more contexts than any other single topic — prices, wages, interest, VAT, population, depreciation. This sheet covers the whole of it in order. It begins with percentage of an amount and percentage change, including finding the percentage rather than applying it; moves to multipliers, which make everything after this easier; then to reverse percentages, where you are given the value after the change and asked for the original, and where subtracting instead of dividing is the commonest error in the topic; then to simple interest, compound interest and depreciation, where the multiplier is raised to a power rather than multiplied by the number of years. The last few questions mix the types without labelling them, because on the paper they are not labelled either.

1.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.
(a)£334.80
(b)£338.68
(c)£338.69
(d)£302.40
2.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
(a)no change
(b)an increase of 25%
(c)a decrease of 25%
(d)a decrease of 50%
3.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
(a)3
(b)30
(c)25
(d)24
4.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.
(a)£340.00
(b)£326.40
(c)£384.00
(d)£64.00
5.Work out 1/2 of 1/4 of 80.
(a)20
(b)10
(c)60
(d)40
6.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.
(a)18
(b)4
(c)24
(d)36
7.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
8.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
9.A machine is bought for £8500. Its value depreciates by 6% each year. Work out the value of the machine after 3 years, to the nearest pound.
(a)£6970
(b)£7511
(c)£7990
(d)£7060
10.2/3 of an amount of money is £30. Work out the amount.
(a)£15
(b)£45
(c)£20
(d)£90
11.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
12.Write 0.25 as a percentage.
(a)2.5%
(b)0.25%
(c)250%
(d)25%
13.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.
(a)£7560.00
(b)£10497.60
(c)£7617.60
(d)£8280.00
14.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.
(a)£3528
(b)£3392
(c)£136
(d)£128
15.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.
(a)£2620.00
(b)£2740.00
(c)£2743.60
(d)£4243.60
16.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.
(a)15
(b)6
(c)30
(d)60
17.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
(a)£15,400
(b)£13,860
(c)£13,650
(d)£15,750
18.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.
(a)90%
(b)80%
(c)20%
(d)125%
19.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.
(a)£120.00
(b)£580.00
(c)£480.00
(d)£720.00
20.Work out 8% of £250.
(a)£25
(b)£2
(c)£200
(d)£20
21.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
(a)£48
(b)£72
(c)£75
(d)£12
22.A sponsored walk raised £350 for charity. 20% of the money raised is spent on equipment. Work out how much is spent on equipment.
(a)£35
(b)£280
(c)£70
(d)£17.50

What is on this worksheet?

The sheet holds 22 questions drawn from the MathsUK bank — the content areas covered: Ratio, proportion and rates of change, Number (statements R9, R16, N12). It is pitched at GCSE Foundation and takes about 40 minutes to work through in full. It is built for independent practice, with full answers at the end for self-marking.

How to use the sheet well

Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
Do all 22 questions before checking — about 40 minutes is the guide, but there is no time pressure.
Check the answers — press “Show answers” or print the answer page separately.
Redo the questions you got wrong — twice as effective as doing 22 fresh ones.
“New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.

Why this sheet helps

MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.

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