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This lesson covers DfE content statement L2.13 — solving problems involving money, including calculating amounts of money, simple and compound interest, percentage changes applied to money, income tax, budgets, and best-buy comparisons.
Money calculations follow the same rules as decimal calculations. The key is to always work in the same unit (either all in pounds or all in pence) and round final answers to 2 decimal places (the nearest penny).
Scenario: An employee works 37.5 hours at £12.80 per hour, plus 5 hours overtime at time-and-a-half. What is the gross weekly pay?
| Component | Hours | Rate | Amount |
|---|---|---|---|
| Basic pay | 37.5 | £12.80 | £480.00 |
| Overtime | 5 | £12.80 × 1.5 = £19.20 | £96.00 |
| Gross pay | £576.00 |
In the UK, most workers receive a Personal Allowance — an amount of income that is tax-free. The rates for 2025/26 are:
| Band | Taxable income | Rate |
|---|---|---|
| Personal Allowance | First £12,570 | 0% |
| Basic rate | £12,571 to £50,270 | 20% |
| Higher rate | £50,271 to £125,140 | 40% |
| Additional rate | Over £125,140 | 45% |
Scenario: A worker earns £32,000 per year. Calculate their annual income tax.
Step 1: Taxable income = £32,000 − £12,570 = £19,430 Step 2: All taxable income falls within the basic rate band: £19,430 × 0.20 = £3,886
Scenario: A manager earns £58,000. What is their income tax?
| Band | Amount | Rate | Tax |
|---|---|---|---|
| Personal Allowance | £12,570 | 0% | £0 |
| Basic rate | £50,270 − £12,570 = £37,700 | 20% | £7,540 |
| Higher rate | £58,000 − £50,270 = £7,730 | 40% | £3,092 |
| Total | £10,632 |
Exam Tip: Income tax questions often appear in the exam. Remember: the Personal Allowance is tax-free, then each band only applies to the income within that band — it is NOT applied to the full salary.
Employees also pay National Insurance (NI) on earnings above a threshold:
| Earnings | NI Rate |
|---|---|
| Below £12,570/year | 0% |
| £12,570 to £50,270/year | 8% |
| Above £50,270/year | 2% |
Scenario: Calculate the annual NI for someone earning £30,000.
NI-liable income = £30,000 − £12,570 = £17,430 NI = £17,430 × 0.08 = £1,394.40
Formula: Interest = Principal × Rate × Time (I = PRT)
Where the rate is expressed as a decimal and time is in years.
Scenario: You invest £2,000 in a savings account that pays 3.5% simple interest per year. How much interest do you earn in 4 years?
I = £2,000 × 0.035 × 4 = £280
Total after 4 years = £2,000 + £280 = £2,280
With compound interest, the interest earned each period is added to the principal, so you earn interest on the interest.
Formula: Final amount = P × (1 + r)ⁿ
Where P = principal, r = rate (as a decimal), n = number of years/periods.
Scenario: You invest £5,000 at 4% compound interest per year. What is it worth after 3 years?
| Year | Start | Interest (4%) | End |
|---|---|---|---|
| 1 | £5,000.00 | £200.00 | £5,200.00 |
| 2 | £5,200.00 | £208.00 | £5,408.00 |
| 3 | £5,408.00 | £216.32 | £5,624.32 |
Using the formula: £5,000 × 1.04³ = £5,000 × 1.124864 = £5,624.32
Compare with simple interest: £5,000 + (£5,000 × 0.04 × 3) = £5,600.00 Compound interest earns £24.32 more over 3 years.
Exam Tip: In the exam, if a question says "compound interest" you MUST apply the interest to the new total each year, not to the original amount. This is different from simple interest.
The standard UK VAT rate is 20%.
Scenario: A builder quotes £3,200 + VAT. What is the total?
£3,200 × 1.20 = £3,840
Scenario: A printer costs £156 including VAT. What is the price before VAT?
£156 ÷ 1.20 = £130
A budget is a plan for income and expenditure over a period of time.
Scenario: Sarah earns £2,100 per month (after tax). Her expenses are:
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