Money & Finance — Level 2 — Functional Skills Maths

Compound interest

Unlike simple interest, compound interest is calculated on the amount including previously earned interest — interest on interest. This makes savings grow faster (and debts grow too).

A = P × (1 + r/100)ⁿ
A = final amount | P = principal | r = rate % | n = number of years

💡 Example: £1,000 at 5% for 3 years: A = 1000 × 1.05³ = 1000 × 1.157625 = £1,157.63

Reverse percentages

A reverse percentage question gives you a value after a percentage change and asks you to find the original. You must divide by the multiplier, not subtract the percentage.

After 20% increase: value = original × 1.20
So original = value ÷ 1.20

After 15% decrease: value = original × 0.85
So original = value ÷ 0.85

💡 Common mistake: Do NOT just subtract the percentage. If a price is £90 after a 10% discount, the original is NOT £90 + £9 = £99. It is £90 ÷ 0.90 = £100.

Income tax and tax bands

In the UK, income tax is charged at different rates on different portions of your income. You only pay tax above the Personal Allowance (tax-free amount).

Band	Taxable income	Rate
Personal Allowance	Up to £12,570	0%
Basic rate	£12,571 – £50,270	20%
Higher rate	£50,271 – £125,140	40%

💡 How it works: Only the income within each band is taxed at that rate. Earning £60,000 does NOT mean all of it is taxed at 40%.

Currency conversion

Exchange rates tell you how much one currency is worth in another. To convert, multiply or divide by the exchange rate, depending on direction.

Pounds → Foreign currency: multiply by exchange rate
Foreign currency → Pounds: divide by exchange rate

💡 Always check direction: If £1 = €1.17, then £200 = 200 × 1.17 = €234. To convert back: €234 ÷ 1.17 = £200.

1Compound interest calculation

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£2,500 is invested at 4% compound interest per year. What is the total after 3 years?

1Formula: A = P × (1 + r/100)ⁿ = 2500 × 1.04³
2Calculate 1.04³ = 1.04 × 1.04 × 1.04 = 1.124864
32500 × 1.124864 = £2,812.16

✅ Total after 3 years = £2,812.16

2Compound interest — depreciation

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A car worth £18,000 depreciates by 15% per year. What is its value after 4 years?

1Depreciation: each year worth 85% of previous. Multiplier = 0.85
2A = 18000 × 0.85⁴
30.85⁴ = 0.85 × 0.85 × 0.85 × 0.85 = 0.52200625
418000 × 0.52200625 = £9,396.11

✅ Value after 4 years ≈ £9,396

3Reverse percentage

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A laptop costs £612 after a 15% discount. What was the original price?

1After 15% off: price = 85% of original. Multiplier = 0.85
2Original = £612 ÷ 0.85 = £720
3Check: £720 × 0.85 = £612 ✓

✅ Original price = £720

4Calculating income tax

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Callum earns £38,000 per year. Using the tax bands above, how much income tax does he pay?

1Personal allowance (tax-free): £12,570
2Taxable income: £38,000 − £12,570 = £25,430
3All £25,430 is within the basic rate band (up to £50,270).
4Tax at 20%: £25,430 × 0.20 = £5,086

✅ Income tax = £5,086 per year

5Currency conversion

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The exchange rate is £1 = $1.26. (a) Convert £350 to dollars. (b) Convert $567 to pounds.

1(a) Pounds → dollars: £350 × 1.26 = $441
2(b) Dollars → pounds: $567 ÷ 1.26 = £450

✅ (a) $441 | (b) £450

6Comparing simple vs compound interest

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£5,000 invested at 6% for 4 years. How much more does compound interest earn than simple interest?

1Simple interest: (5000 × 6 × 4) ÷ 100 = £1,200
2Compound: 5000 × 1.06⁴ = 5000 × 1.26247696 = £6,312.38
3Compound interest earned: £6,312.38 − £5,000 = £1,312.38
4Difference: £1,312.38 − £1,200 = £112.38

✅ Compound earns £112.38 more than simple interest.

Question 1

£3,000 is invested at 5% compound interest per year for 2 years. What is the total amount?

Question 2

A phone costs £459 after a 15% VAT increase. What was the pre-VAT price?

Question 3

£1 = €1.15. How many euros do you get for £420?

Question 4

Priya earns £55,000. Using the tax bands above, how much income tax does she pay?

Question 5

A car costing £20,000 depreciates by 20% per year. What is it worth after 3 years?

Question 6

A jacket costs £94.50 after a 30% increase. What was the original price?

Question 7

£1 = 1.32 AUD. Convert 660 AUD to pounds.

Question 8

£4,000 at 3.5% compound interest for 3 years. How much interest is earned?

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