Maths Literacy Matric Revision: Exchange rates

CAPS Grade 12 Mathematical Literacy: Measurement and Exchange Rates


Introduction

Understanding exchange rates is crucial in Mathematical Literacy as it links the concepts of measurement and financial mathematics. Exchange rates allow for the conversion of one country’s currency into another, impacting global trade, travel, and personal finance.

Learning Objectives:
– Understanding the concept of exchange rates.
– Calculating conversions between different currencies.
– Applying these concepts in real-world scenarios.


1. Key Points

  1. Definition:
  2. Exchange Rate: The price of one country’s currency expressed in another country’s currency.
  3. Example: If $1 = €0.83, then one US dollar is equivalent to 0.83 Euros.

  4. Conversion:

  5. To convert from one currency to another, use the given exchange rate.
  6. Formula: ( \text{Amount in new currency} = \frac{\text{Amount in original currency}}{\text{Exchange rate}} ).

  7. Handling Fees:

  8. Often a percentage fee is subtracted when exchanging money.
  9. Formula: ( \text{Effective Amount} = \text{Converted Amount} \times (1 – \text{Fee Percentage}) ).

2. Real-World Applications

Example 1:

Convert R500 to US dollars (USD), Euros (EUR), and British pounds (GBP) given the exchange rates:
– $1 = R13.74
– €1 = R15.67
– £1 = R17.70

Solution:
USD: ( \text{Amount in USD} = \frac{R500}{R13.74} = \$36.39 )
EUR: ( \text{Amount in EUR} = \frac{R500}{R15.67} = €31.91 )
GBP: ( \text{Amount in GBP} = \frac{R500}{R17.70} = £28.25 )

Example 2:

Calculating euros for a given amount in rands with a handling fee of 0.75%:
– Bonny has R4000, and the exchange rate is R15.67 to the euro.
– Converted amount before fee: ( \frac{R4000}{R15.67} = €255.26 )
– Effective amount after fee: ( 255.26 \times (1 – 0.0075) = €253.35 )


3. Common Misconceptions and Errors

  1. Ignoring Fees:
  2. Overlooking handling fees can lead to incorrect conversions. Always adjust for these fees if applicable.

  3. Incorrect Division:

  4. Switching the numerator and denominator in conversions can lead to wrong answers. Remember: ( \text{Amount in new currency} = \frac{\text{Amount in original currency}}{\text{Exchange rate}} ).

  5. Static Exchange Rates:

  6. Exchange rates can fluctuate; use the latest rates for accuracy.

4. Practice and Review

Practice Questions:

  1. Convert R750 to USD, EUR, and GBP given the following rates:
  2. $1 = R13.80
  3. €1 = R16.00
  4. £1 = R18.50

  5. Handling Fee Calculation:

  6. If you exchange R5000 to USD and the handling fee is 1%, how much USD will you receive if $1 = R13.74?

Solutions:
– ( \frac{R5000}{R13.74} = \$364.05 )
– After fee: ( 364.05 \times (1 – 0.01) = \$360.41 )

5. Connections and Extensions

  • Foreign Trips:
  • Understanding exchange rates is vital for budgeting during international travel.
  • Economics:
  • Exchange rates impact trade, affecting how countries price their exports and imports.

6. Summary and Quick Review

  • Exchange rates convert one currency to another using the formula ( \frac{\text{Amount in original currency}}{\text{Exchange rate}} ).
  • Always consider handling fees.
  • Stay updated with current rates as they fluctuate.

7. Additional Resources


For more in-depth explanation and practice problems, refer to the CAPS Grade 12 Mathematical Literacy textbooks and guides provided by your educational institution【4:0†source】【4:7†source】【4:8†source】【4:11†source】【4:18†source】.

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