GCSE MATHS • HIGHER TIER

Compound Interest and Depreciation Made Simple

Use percentage multipliers and repeated percentage change to solve financial mathematics problems.

Clear method

Exam practice

Worked proofs

Compound Interest and Depreciation in Four Moves

1 Identify

Decide whether the amount is increasing or decreasing .

2 Convert

Convert the percentage change into the correct multiplier .

3 Power

Raise the multiplier to the number of years .

4 Calculate

Multiply by the original amount and interpret the final value .

What You’ll Learn

Understand Compound Interest

Know why interest is calculated on the growing balance.

Use Percentage Multipliers

Create increase and decrease multipliers .

Calculate Depreciation

Find the reduced value of an asset after repeated percentage decreases.

Compare Interest Types

Understand the difference between compound and simple interest .

Solve Financial Problems

Understand the difference between compound and simple interest .

Key Rules

Final Amount = Original Amount × (Multiplier)^Number of Years

This formula allows students to calculate compound growth quickly.

Worked Proof : Compound Interest and Depreciation

Step-by-Step Method

1. Identify whether the value is increasing or decreasing.
2. Convert the percentage change into a multiplier.
3. Raise the multiplier to the number of years.
4. Multiply by the original amount.
5. Round the final answer to the nearest penny.

More Worked Examples

1

Question : £1,200 is invested at 6% compound interest for 3 years .

Multiplier = 1.06

Final amount = £1,200 × (1.06)³
Final amount = £1,429.22

Answer: The investment is worth £1,429.22 after 3 years .

2

£1,000 is invested at 5% compound interest for 4 years .

£1,000 × (1.05)^4

≈ £1,215.51

3

A car worth £20,000 depreciates by 15% each year for 2 years .

Multiplier = 0.85

£20,000 × (0.85)^2

= £14,450

4

A laptop worth £800 depreciates by 10% each year for 3 years .

£800 × (0.90)^3

= £583.20

Multiplier: Do not use the percentage itself instead of the multiplier.
Power: Remember to raise the multiplier to the number of years.
Interest type: Do not confuse compound interest with simple interest.
Depreciation: Use a decrease multiplier below 1, not an increase multiplier.

Convert the percentage change to a multiplier before using the formula.
For an increase, the multiplier is greater than 1.
For depreciation, the multiplier is less than 1.
Use the number of years as the power.
Keep full calculator accuracy until the final money answer.
Check whether the final amount should be larger or smaller than the original value.