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 price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.
(a)0%
(b)−1%
(c)−2%
(d)+1%
2.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.
(a)288 km
(b)4.5 km
(c)12 km
(d)24 km
3.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.
(a)2978
(b)3156
(c)2809
(d)2950
4.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.
(a)£2200.00
(b)£2205.00
(c)£205.00
(d)£2100.00
5.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.
(a)3200 × 0.64
(b)3200 × 0.12³
(c)3200 × 0.88 × 3
(d)3200 × 0.88³
6.Work out 35% of 180.
(a)45
(b)63
(c)145
(d)126
7.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
8.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.
(a)£18
(b)£8
(c)£138
(d)£12
9.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
10.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
11.2/3 of an amount of money is £30. Work out the amount.
(a)£15
(b)£45
(c)£20
(d)£90
12.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
13.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
(a)200 m
(b)1050 m
(c)150 m
(d)50 m
14.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.
(a)1/4
(b)1/3
(c)3/4
(d)1/5
15.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.
(a)£72
(b)£640
(c)£80
(d)£6480
16.A savings account pays 3.5% compound interest each year. Bilal invests £1200. Work out how much interest, in total, he earns after 2 years, to the nearest penny.
(a)£85.47
(b)£1285.47
(c)£84.00
(d)£42.00
17.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
18.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
19.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
20.The population of a village is 1200. It is predicted to grow by 5% next year. Work out the predicted population after 1 year, to the nearest whole number.
(a)1260
(b)1800
(c)1205
(d)60
21.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
22.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

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.

Similar worksheets worth a look

✏️ Paper 1 non-calculator warm-up — Foundation · 20 questions · ~25 min
🎯 Grade 4 pass booster · 25 questions · ~40 min
⚖️ Foundation to Higher crossover check · 20 questions · ~35 min
⚗️ Ratio and proportion mastery — Higher · 24 questions · ~45 min