What is Currency in Money?

Currency: The system of money used in a particular country (e.g., Dollars $, Euros €, Pounds £).

What is Exchange Rate in Money?

Exchange Rate: The value of one currency expressed in terms of another currency.

What is Profit in Money?

Profit: The amount gained when a selling price is higher than the cost price.

What is Loss in Money?

Loss: The amount lost when a selling price is lower than the cost price.

What is Unit Price in Money?

Unit Price: The cost of a single item or a specific unit of weight/volume (e.g., price per kg).

Money — Cambridge IGCSE Mathematics Revision Notes

1. Overview

Money calculations are a practical application of mathematical skills, crucial for both the IGCSE Mathematics exam and everyday financial literacy. This topic focuses on performing calculations involving money, converting between currencies using exchange rates, and determining profit or loss. Accuracy and clear presentation of working are essential. Always give your answer to two decimal places unless instructed otherwise.

Key Definitions

Currency: The system of money used in a particular country (e.g., Dollars $, Euros €, Pounds £).
Exchange Rate: The value of one currency expressed in terms of another currency.
Profit: The amount gained when a selling price is higher than the cost price.
Loss: The amount lost when a selling price is lower than the cost price.
Unit Price: The cost of a single item or a specific unit of weight/volume (e.g., price per kg).

Core Content

3.1 Basic Calculations with Money

In money calculations, you must always give your answer to two decimal places (e.g., $5.70, not $5.7), unless the question asks for a whole number.

Worked Example 1 — Calculating Total Cost

A customer buys 5 apples at $0.65 each and 3 bananas at $0.45 each. They pay with a $10 note. How much change do they receive?

Step 1: Calculate the cost of the apples: $5 \times 0.65 = 3.25$
- Multiply the quantity of apples by the price per apple.
Step 2: Calculate the cost of the bananas: $3 \times 0.45 = 1.35$
- Multiply the quantity of bananas by the price per banana.
Step 3: Calculate the total cost: $3.25 + 1.35 = 4.60$
- Add the cost of the apples and bananas.
Step 4: Calculate the change: $10.00 - 4.60 = 5.40$
- Subtract the total cost from the amount paid.
Answer: $5.40

3.2 Currency Conversion

To convert between currencies, we use the exchange rate.

To change from the "home" currency (the one represented as '1') to the foreign currency: Multiply.
To change from the foreign currency back to the "home" currency: Divide.

Worked Example 2 — Currency Conversion

The exchange rate is £1 = $1.25. (a) Convert £320 into Dollars ($). (b) Convert $950 into Pounds (£).

(a) Working:

Step 1: Identify the correct operation: $320 \times 1.25$
- Converting from Pounds to Dollars, so multiply.
Step 2: Calculate: $320 \times 1.25 = 400$
- Perform the multiplication.
Answer: $400

(b) Working:

Step 1: Identify the correct operation: $950 \div 1.25$
- Converting from Dollars to Pounds, so divide.
Step 2: Calculate: $950 \div 1.25 = 760$
- Perform the division.
Answer: £760

📊A flowchart showing 'Currency A' with an arrow pointing to 'Currency B' labeled 'Multiply by Rate', and a return arrow labeled 'Divide by Rate'

Extended Content (Extended Only)

4.1 Percentage Profit and Loss

In the extended curriculum, you are often required to find the percentage profit or loss based on the original cost price.

Formula:

$\qquad \text{Percentage Profit/Loss} = \frac{\text{Actual Profit or Loss}}{\text{Original Cost Price}} \times 100$

Worked Example 3 — Calculating Percentage Profit

A shop buys a bicycle for $180 and sells it for $225. Calculate the percentage profit.

Step 1: Find the actual profit: $225 - 180 = 45$
- Subtract the cost price from the selling price.
Step 2: Use the formula: $\frac{45}{180} \times 100$
- Divide the profit by the original cost price and multiply by 100.
Step 3: Simplify: $0.25 \times 100 = 25$
- Perform the calculation.
Answer: 25%

4.2 Multi-step Currency Conversions

Sometimes you must convert through a "base" currency or handle commission charges. These questions require careful reading to understand the sequence of operations.

Worked Example 4 — Multi-step Conversion

A traveler wants to change 500 Singapore Dollars (SGD) into British Pounds (£). The exchange rates are: $1 USD = 1.35 SGD$ $1 USD = 0.80 GBP$ How many British Pounds will the traveler receive?

Step 1: Convert SGD to USD: $500 \div 1.35 = 370.37$ (USD)
- Divide the SGD amount by the SGD/USD exchange rate.
Step 2: Convert USD to GBP: $370.37 \times 0.80 = 296.30$ (GBP)
- Multiply the USD amount by the USD/GBP exchange rate.
Answer: £296.30

Worked Example 5 — Currency Conversion with Commission

A bank charges a 2% commission on all currency exchanges. A customer wants to exchange €800 into US dollars ($). The exchange rate is €1 = $1.15. Calculate how many dollars the customer will receive after the commission is deducted.

Step 1: Calculate the equivalent amount in USD before commission: $800 \times 1.15 = 920$
- Multiply the Euro amount by the exchange rate.
Step 2: Calculate the commission amount: $920 \times 0.02 = 18.40$
- Multiply the USD amount by the commission rate (2% = 0.02).
Step 3: Subtract the commission from the USD amount: $920 - 18.40 = 901.60$
- Subtract the commission amount from the initial USD amount.
Answer: $901.60

Key Equations

Equation	Symbols	Units
$\text{Total Cost} = \text{Quantity} \times \text{Unit Price}$	-	Currency (e.g., $)
$\text{New Amount} = \text{Original Amount} \times \text{Exchange Rate}$	-	Target Currency
$\text{Profit} = \text{Selling Price} - \text{Cost Price}$	-	Currency (e.g., $)
$\text{Loss} = \text{Cost Price} - \text{Selling Price}$	-	Currency (e.g., $)
$% \text{ Profit} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$	-	Percentage (%)
$% \text{ Loss} = \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100$	-	Percentage (%)

Note: These formulas are not provided on the IGCSE formula sheet; they must be memorised.

Common Mistakes to Avoid

❌ Wrong: Forgetting to include the currency symbol. Writing '25.50' instead of '$25.50'.
- ✓ Right: Always include the correct currency symbol in your final answer.
❌ Wrong: Rounding to fewer than 2 decimal places. Writing $12.5 instead of $12.50.
- ✓ Right: Always use two decimal places for money unless the question specifies otherwise.
❌ Wrong: Dividing instead of multiplying during conversion (or vice versa).
- ✓ Right: Before calculating, ask yourself: "Should the answer be a bigger or smaller number?" If converting £ to $, and £1 is worth more than $1, then the $ amount should be larger than the £ amount.
❌ Wrong: Using the Selling Price as the denominator in percentage profit/loss calculations.
- ✓ Right: Always divide by the Original Cost Price.
❌ Wrong: Rounding intermediate values during a multi-step calculation.
- ✓ Right: Keep the full number in your calculator and only round the final answer to 2 decimal places to avoid accuracy errors.

Exam Tips

Calculator Tip: Use the fraction button ($ \frac{\Box}{\Box} $) for percentage profit/loss calculations to ensure the order of operations is correct.
Command Words: "Calculate" means you must show the arithmetic steps; "Convert" means you must apply an exchange rate.
Real-world contexts: Expect questions involving utility bills (electricity/water), bank interest, discounts, or travel costs.
Show Working: Marks are often awarded for the method (e.g., showing the multiplication by the exchange rate) even if you make a typing error on your calculator.
Units: Always write the currency symbol ($, £, €) in your final answer. If the question provides a symbol, make sure your answer matches it.
Read Carefully: Pay close attention to the wording of the question, especially when dealing with buying and selling rates or commission charges. Determine which rate applies to the specific transaction.