Use a repeated multiplier to work out how savings grow or how a value falls year after year. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Compound interest is a multiplier used repeatedly: 1.04n for 4% up, n years. Depreciation is the same with a multiplier less than 1: 0.85n for 15% off each year. The formula is new=original×(multiplier)n. Do not add 4% of the original each year — that is simple interest, a different topic.
A typical 3-mark question is three years of growth or decay, maybe with a comparison against a simple-interest offer. Keep the unrounded value in the calculator until the last line, then round to the nearest penny. For 'after how many years does it first exceed…', you can step year by year or take logarithms later in Higher.
Compound interest (and depreciation) means the multiplier is used on the new amount each year: original ×(1.04)n. Simple interest would add the same pounds every year — that is a different, usually smaller, total. 'How much interest' is the final amount minus the start.
Objectives
An increase of 10% multiplies by 1.1. A decrease of 10% multiplies by 0.9.
£100 increased by 10% is £110. The next year, 10% of £110 is £11, so the total is £121.
Two years at 10% is × 1.1². Three years is × 1.1³.
Key points
Turn a percentage change into a single decimal multiplier (up 3% is ×1.03, down 12% is ×0.88).
Raise the multiplier to the power of the number of years.
Tell the difference between the final amount and the interest earned.
Compare compound interest with simple interest over the same time.
Worked examples
Example 1
£100 earns 10% compound interest for 2 years. What is the amount at the end?
3 marks
Each year the amount is multiplied by 1.1.
After year 1: 100 × 1.1 = 110.
After year 2: 110 × 1.1 = 121.
Answer: £121
Common slips
Slip: Add 10% of the original amount each year. That is simple interest. Compound interest uses a multiplier on the latest amount.
Slip: 10% of 100 is 10, so each year adds 10. In year two the interest is 10% of the new amount, not of the original.
Slip: After 2 years: 100 + 20 = 120. The compound amount is larger than this.
Example 2
A van worth £200 depreciates by 10% each year for 2 years. What is it worth at the end?
3 marks
Each year the value is multiplied by 0.9.
After year 1: 200 × 0.9 = 180.
After year 2: 180 × 0.9 = 162.
Answer: £162
Common slips
Slip: Multiply by 1.1 each year. A fall of 10% multiplies by 0.9, not 1.1.
Slip: After year 1: 200 × 1.1 = 220. That value has gone up, but the van loses value.
Slip: After year 2: 220 × 1.1 = 242. The van cannot be worth more than it started at.
Example 3
£300 earns 10% compound interest for 2 years. What is the amount at the end?
3 marks
Each year the amount is multiplied by 1.1.
After year 1: 300 × 1.1 = 330.
After year 2: 330 × 1.1 = 363.
Answer: £363
Common slips
Slip: Add 10% of the original amount each year. That is simple interest. Compound interest uses a multiplier on the latest amount.
Slip: 10% of 300 is 30, so each year adds 30. In year two the interest is 10% of the new amount, not of the original.
Slip: After 2 years: 300 + 60 = 360. The compound amount is larger than this.
Questions and answers
GCSE Maths compound interest & depreciation questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
£200 is invested at 20% compound interest for 2 years. What is the final amount?
Show answer
Answer: 288
Multiply by 6/5 twice.
The value is 288.
M1 — Multiply by 6/5 twice.
A1 — Answer 288
Question 2 Easy2 marks
£1000 earns 10% compound interest for 3 years. How much interest is earned?
Show answer
Answer: 331
The three-year multiplier is 1.331.
Subtract the original sum from the final amount.
M1 — The three-year multiplier is 1.331.
A1 — Answer 331
Question 3 Medium2 marks
What is the multiplier for a 25% compound increase?
Show answer
Answer: 1.25
Add the percentage to 100.
Divide by 100.
M1 — Add the percentage to 100.
A1 — Answer 1.25
Question 4 Medium2 marks
After 3 years at 10% compound interest an investment is worth £1331. How much was invested originally?
Show answer
Answer: 1000
Divide by 1.331.
That undoes three 10% increases.
M1 — Divide by 1.331.
A1 — Answer 1000
Question 5 Hard2 marks
£200 rises by 25% in the first year and by 20% in the second year. What is the final amount?
Show answer
Answer: 300
Multiply by 5/4, then by 6/5.
The value is 300.
M1 — Multiply by 5/4, then by 6/5.
A1 — Answer 300
Question 6 Hard2 marks
An item worth £800 falls by half and then by 20%. What is it worth?
Show answer
Answer: 320
Halve the value first.
Then take 80% of what remains.
M1 — Halve the value first.
A1 — Answer 320
Question 7 Exam-style3 marks
£300 rises by 25% in the first year and by 20% in the second year. What is the final amount?
Show answer
Answer: 450
Multiply by 5/4, then by 6/5.
The value is 450.
M1 — Multiply by 5/4, then by 6/5.
M1 — The value is 450.
A1 — Answer 450
Common mistakes
Most lost marks on this topic are one slip.
Adding 10% of the original again in year two.
The second year uses the new amount.
Using 1.1 for a 10% loss.
A loss of 10% multiplies by 0.9.
Multiplying the percentage by the years and adding once.
That is simple interest, not compound.
Spot the slip
10% interest for one year multiplies by
1.1
0.1
10
Show the slip
1.1 You keep the original amount and add 10% of it.
Exam tips
A calculator is useful here. Show the calculation you typed, not only the final line.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the multiplier down before you calculate; it usually earns a method mark even if you press a wrong button later.
Check the answer makes sense: growth should end above the start, depreciation should end below it.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.