Foreign Exchange Rates (Grade 10 NSC Matric Mathematics): Revision Notes
Foreign Exchange Rates
What are foreign exchange rates?
Foreign exchange rates show how much of one currency you can buy with another currency. Different countries use different currencies, so when you want to buy something from another country or travel abroad, you need to exchange your South African rand for their currency.
An exchange rate tells you how many rand you need to buy one unit of a foreign currency. For example, if £1 = R14, this means you need R14 to buy one British pound.
Understanding exchange rates is essential for international trade, travel, and comparing prices across different countries. The exchange rate acts as a bridge between different monetary systems.
How exchange rates affect prices
Exchange rates have a big impact on the prices of goods and services. When you buy the same product in different countries, it may cost different amounts in their local currencies, but the exchange rate determines how much you actually pay in rand.
Example: Comparing Meal Costs Across Countries
The same meal might cost £4 in England, R20 in South Africa, and 48 kr in Norway. Even though it's the same meal, the cost in rand depends on the exchange rates.
Given exchange rates: £1 = R12.41 and 1 kr = R1.37
Step 1: Calculate the English meal cost in rand
- £4 × R12.41 = R49.64
Step 2: Calculate the Norwegian meal cost in rand
- 48 kr × R1.37 = R65.76
Result: The same meal costs R20 in SA, R49.64 in England, and R65.76 in Norway.
Why exchange rates change
Exchange rates are not fixed - they change constantly based on economic conditions. Here are the key factors:
Currency strength and investment:
- When people invest money in South Africa, they need to buy rand, which makes the rand stronger
- When South Africans buy products made locally, we keep money in the country, supporting the rand
- When we buy imported products, we send money to other countries, which can weaken the rand
Supply and demand:
- If many people want to buy rand, its value goes up
- If fewer people want rand, its value goes down
- This affects how much foreign currency we can buy with our rand
Key Economic Principle: When you buy local products, you help strengthen the rand by keeping money within South Africa's economy. Buying imported goods sends money overseas, which can weaken our currency.
Common currencies you should know
The three most important currencies for South African students are:
- British pound (£) - used in the United Kingdom
- US dollar ($) - used in the United States
- Euro (€) - used in many European countries
These three currencies dominate international trade and are the most commonly encountered when dealing with foreign exchange in South Africa.
Converting between currencies
To convert from rand to a foreign currency, use this formula:
To convert from a foreign currency to rand, use:
Remember the Direction: Always check whether you're converting FROM rand TO foreign currency (divide) or FROM foreign currency TO rand (multiply). Getting this wrong is a common mistake!
Worked examples
Worked Example 1: Converting Rand to Euros
Question: Saba has R10,000 to spend on her trip to Spain. If the exchange rate is €1 = R10.68, how many euros can she buy?
Solution:
Step 1: Write down the equation
Let x = the amount in euros
Step 2: Calculate
Step 3: Write the final answer
Saba can buy €936.33 with R10,000.
Worked Example 2: Comparing Costs in Different Currencies
Question: An iPad costs £100 in London. If the exchange rate is £1 = R14, how much does the iPad cost in rand?
Solution:
Cost in rand = £100 × R14 = R1,400
Worked Example 3: Finding the Best Deal
Question: A book costs £7.19 in London or $8.49 in New York (plus $2 shipping). If £1 = R17.36 and $1 = R11.48, which option is cheaper?
Solution:
London option: £7.19 × R17.36 = R124.78
New York option: ($8.49 + $2) × R11.48 = $10.49 × R11.48 = R120.43
Result: The New York option is cheaper by R124.78 - R120.43 = R4.35.
Exam tips
Essential Exam Tips:
- Always check which direction you're converting (rand to foreign currency or foreign currency to rand)
- Remember to include any additional costs like shipping or fees
- Round your final answer appropriately (usually to 2 decimal places for money)
- Show all your working steps clearly
- Double-check your calculation by working backwards
Key Points to Remember:
- Exchange rates tell you how many rand you need to buy one unit of foreign currency
- Strong rand means you can buy more foreign currency with the same amount of rand
- Weak rand means you get less foreign currency for your rand
- The three main currencies to know are: British pound (£), US dollar ($), and Euro (€)
- Buying local products helps strengthen the rand by keeping money in South Africa
- Always show your working step-by-step in exchange rate calculations