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# GCSE Maths | Compound Interest
- URL: https://www.a-level-maths-tutor.com/gcse-maths-compound-interest/
- Published: 2026-07-22T11:08:21.000Z
- Updated: 2026-07-22T11:08:21.000Z
- Author: Jaisul Naik
- Tags: GCSE Maths

Final value = original value $\\times$ multiplier$^{\\text{(number of years)}}$

**Worked Example**

£1000 is invested at 4% per year for 3 years.

Multiplier $= 1.04$

Final value $= 1000 \\times 1.04^3 = £1124.86$

## Question 1

Find the total value after the given number of years, to the nearest penny.

**a)** £500 is invested at 5% compound interest per year for 3 years.

**b)** £1200 is invested at 3% per year for 4 years.

**c)** £800 grows at 4.5% per year for 5 years.

**d)** £1000 is invested at 2.5% per year for 2 years.

**e)** £2000 increases by 6% each year for 3 years.

**f)** £1500 is invested at 1.2% per year for 6 years.

**g)** £600 grows at 7% compound interest for 4 years.

**h)** £1800 increases by 2% a year for 10 years.

**i)** £100 grows at 10% interest per year for 3 years.

**j)** £2500 is invested at 3.5% per year for 8 years.

Show Answers 

**a)** £578.81

**b)** £1350.61

**c)** £996.95

**d)** £1050.63

**e)** £2382.03

**f)** £1611.29

**g)** £786.48

**h)** £2194.19

**i)** £133.10

**j)** £3292.02

**Worked Example**

£900 depreciates at 20% per year for 3 years.

Multiplier $= 0.8$

Final value $= 900 \\times 0.8^3 = £460.80$

## Question 2

Find the value after the given number of years, to the nearest penny.

**a)** A car worth £12,000 depreciates at 10% per year for 3 years.

**b)** A laptop worth £800 loses 15% of its value each year for 2 years.

**c)** A phone bought for £1000 depreciates 20% annually for 4 years.

**d)** A machine costing £6000 depreciates at 5% per year for 5 years.

**e)** A sofa worth £1500 loses 12% of its value per year for 3 years.

**f)** A TV valued at £400 depreciates 25% a year for 2 years.

**g)** A bike costing £700 depreciates at 7% for 6 years.

**h)** A fridge bought for £300 depreciates 10% per year for 5 years.

**i)** A printer costing £500 loses 18% value annually for 3 years.

**j)** A used van worth £9000 depreciates by 8% a year for 4 years.

Show Answers 

**a)** £8748.00

**b)** £578.00

**c)** £409.60

**d)** £4642.69

**e)** £1022.21

**f)** £225.00

**g)** £452.89

**h)** £177.15

**i)** £275.68

**j)** £6447.54

**Worked Example**

Naoby invests £6000 for 5 years. The investment gets compound interest of $x\\%$ per annum. At the end of 5 years the investment is worth £8029.35\. Work out the value of $x$.

$6000 \\times x^5 = 8029.35$

Divide by 6000: $x^5 = 1.338225$

5th root both sides: $x = 1.06$

Convert the multiplier to a percentage: $x = 6$

## Question 3

Each of the following investments grows for 5 years at a fixed annual compound interest rate. Find the interest rate in each case, correct to 1 decimal place.

**a)** £4000 grows to £4416.32 after 5 years.

**b)** £5500 grows to £6376.01 after 5 years.

**c)** £3000 grows to £3649.96 after 5 years.

**d)** £7200 grows to £9189.23 after 5 years.

**e)** £2500 grows to £2828.52 after 5 years.

**f)** £6000 grows to £7126.12 after 5 years.

**g)** £8000 grows to £9969.46 after 5 years.

**h)** £1500 grows to £2007.34 after 5 years.

**i)** £9000 grows to £9695.56 after 5 years.

**j)** £4800 grows to £6732.25 after 5 years.

Show Answers 

**a)** $2.0\\%$

**b)** $3.0\\%$

**c)** $4.0\\%$

**d)** $5.0\\%$

**e)** $2.5\\%$

**f)** $3.5\\%$

**g)** $4.5\\%$

**h)** $6.0\\%$

**i)** $1.5\\%$

**j)** $7.0\\%$

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