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 games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
(a)21%
(b)81%
(c)20%
(d)19%
2.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.
(a)12%
(b)4%
(c)112%
(d)0.04%
3.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%
4.Work out 15% of £40, using 10% and 5%.
(a)£6
(b)£4
(c)£600
(d)£2
5.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
(a)£598
(b)£494
(c)£478.40
(d)£416
6.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.
(a)£3244.80
(b)£3120.00
(c)£244.80
(d)£3240.00
7.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
8.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.
(a)£504
(b)£1,890
(c)£840
(d)£2,100
9.Work out 3/8 of 96.
(a)72
(b)12
(c)32
(d)36
10.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32
11.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
12.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
(a)60
(b)460
(c)340
(d)415
13.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
14.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
15.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
(a)£1,000
(b)£600
(c)£825
(d)£200
16.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.
(a)£65
(b)£67.50
(c)£60
(d)£70
17.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
(a)55
(b)75
(c)20
(d)60
18.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
19.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.
(a)£48.00
(b)£52.00
(c)£47.00
(d)£40.00
20.A box holds 140 pens. 25% of the pens are red. Work out how many of the pens are red.
(a)35
(b)105
(c)25
(d)70
21.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
22.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

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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