Currency — Core Maths Compendium

Build it up, step by step

Understanding currency

Click each step below to reveal it — work through them in order the first time round.

Step 1 · What an exchange rate means

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An exchange rate tells you how much of one currency you get for one unit of another, e.g. £1 = €1.15 means every pound buys 1.15 euros at that rate. Exchange rates constantly change based on global markets.

Step 2 · Converting between currencies

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To convert pounds to euros, multiply by the exchange rate (£ → €: amount × 1.15). To convert euros back to pounds, divide by the same rate (€ → £: amount ÷ 1.15). Always check which direction you're converting — multiplying when you should divide is a common exam mistake.

Step 3 · Buy and sell rates

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Bureaux de change and banks don't use one single rate — they have a ‘buy’ rate and a ‘sell’ rate, and the rate they give you is always slightly worse than the ‘true’ market rate (this gap is how they make a profit). Exchanging currency and then immediately exchanging it back will always lose you money.

Step 4 · Commission and total cost

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Some providers also charge a flat commission fee or a percentage commission on top of the exchange rate. To find the true cost of a currency exchange, you need to apply the exchange rate and subtract any commission — exam questions often ask you to compare which of two providers gives better overall value.

Worked example

A bureau de change offers £1 = $1.28, with no commission. Sarah exchanges £350 for dollars. How many dollars does she receive?

350 × 1.28 = $448.00.

Test yourself

Past-paper style question

A bank offers an exchange rate of £1 = €1.16 with a flat £5 commission charge. A different bureau offers £1 = €1.14 with no commission. Ahmed wants to exchange £400 for euros.

(a) Calculate how many euros he would receive from each provider.
(b) State which provider gives Ahmed more euros, and by how much. [4 marks]

Show the answer

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(a) Bank: commission is taken first, so amount exchanged = 400−5 = 395. Euros = 395×1.16 = €458.20. Bureau: 400×1.14 = €456.00.

(b) The bank gives more euros, by 458.20 − 456.00 = €2.20.

Practice

Currency worksheet

Five short questions on currency. Work through them, then reveal the mark scheme to check.

£1 = $1.30. Convert £250 to dollars.
£1 = €1.17. Convert €585 back to pounds.
A bureau exchanges £1 for €1.10 when you buy euros, but only gives you £1 for every €1.15 when you sell euros back to them. If you exchange £200 for euros then immediately exchange all the euros back to pounds, how many pounds do you end up with, and how much have you lost overall?
Provider A: £1 = $1.32, no commission. Provider B: £1 = $1.35, but with a flat £8 commission. For an exchange of £600, which provider gives more dollars?
Explain, in your own words, why the exchange rate a bureau de change offers you is usually worse than the ‘real’ market exchange rate quoted online.

Mark scheme

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250 × 1.30 = $325.
585 ÷ 1.17 = £500.
Buy: 200×1.10 = €220. Sell back: 220÷1.15 = £191.30 (2dp). Loss = 200 − 191.30 = £8.70.
Provider A: 600×1.32 = $792. Provider B: (600−8)×1.35 = 592×1.35 = $799.20. Provider B gives more dollars ($799.20 vs $792).
Bureaux de change need to make a profit from the transaction, so they set their exchange rate slightly less favourably than the true market rate (giving you less foreign currency per pound than the ‘real’ rate) — the difference between their rate and the market rate is effectively their fee/profit margin.

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