Financial Maths – Percentages, Interest & Money

Core skills for Unit 1: percentage change, simple & compound interest, profit/loss and money problems.

Financial mathematics is a major part of the new Double Award GCSE. You will be expected to work confidently with money in real-life contexts – wages, shopping, interest, profit and loss.

Percentage of an amount

To find a percentage of an amount: **Method 1 – Decimal multiplier** 10% of £80 = 0.10 × 80 = £8 25% of £80 = 0.25 × 80 = £20 17.5% of £80 = 0.175 × 80 = £14 **Method 2 – Build from 10% and 1%** 10% of £80 = £8 1% of £80 = £0.80 So 17% = 10% + 7×1% = £8 + £5.60 = £13.60

Worked example

A jacket costs £64. In a sale it is reduced by 35%. What is the sale price?

Solution

35% of £64 = 0.35 × 64 = £22.40 Sale price = £64 − £22.40 = **£41.60** Alternatively: multiplier for 65% remaining = 0.65 0.65 × 64 = **£41.60**

Percentage increase and decrease

**Increase by a percentage** New amount = original × (1 + percentage/100) **Decrease by a percentage** New amount = original × (1 − percentage/100) Example multipliers: • Increase by 20% → × 1.20 • Decrease by 15% → × 0.85 • Increase by 7.5% → × 1.075

Worked example

A salary of £28,500 is increased by 4.5%. What is the new salary?

Solution

Multiplier = 1 + 0.045 = 1.045 New salary = 28500 × 1.045 = **£29,782.50**

Simple Interest

Simple Interest is calculated only on the original amount (the principal). **Formula:** Interest = Principal × Rate × Time I = P × r × t Where r is the rate as a decimal (e.g. 3% = 0.03) and t is time in years. Total amount = Principal + Interest

Worked example

£2,400 is invested for 3 years at 2.5% simple interest per year. How much interest is earned and what is the final amount?

Solution

I = 2400 × 0.025 × 3 = **£180** Final amount = 2400 + 180 = **£2,580**

Compound Interest

Compound interest is calculated on the principal plus any previous interest. **Formula:** Final amount = P × (1 + r)ⁿ Interest earned = Final amount − Principal

Worked example

£3,000 is invested for 4 years at 3% compound interest per year. What is the final amount (to the nearest penny)?

Solution

Final = 3000 × (1.03)⁴ 1.03² = 1.0609 1.03⁴ = 1.0609² = 1.12550881 3000 × 1.12550881 ≈ **£3,376.53**

Practice questions

Try these without looking at the answers first.

Q1.A phone costs £480. In a sale it is reduced by 22%. What is the sale price?

Hint: Use multiplier 0.78

Show answer

£374.40

Q2.£1,500 is invested at 4% simple interest for 5 years. How much interest is earned?

Show answer

£300

Q3.£2,000 is invested at 2.5% compound interest for 3 years. Final amount (nearest penny)?

Show answer

£2,153.78

Q4.A shop buys a coat for £35 and sells it for £56. What is the percentage profit?

Hint: Profit = £21. (21/35)×100

Show answer

60%

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