CIE IGCSE Mathematics (0580) Money Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Money Study Notes
LEARNING OBJECTIVE
- Calculating with Money
Key Concepts:
- Money
- Currency Conversion
Calculating with Money
Calculating with Money
Money calculations are essential in daily life, such as budgeting, shopping, banking, paying bills, and calculating wages or change.
Key Concepts:
- Use the correct units: dollars ($), cents (¢), pounds (£), euros (€), etc.
- 1 dollar = 100 cents, 1 pound = 100 pence
- Always align decimal points carefully in calculations.
- Round final answers to 2 decimal places (to the nearest cent or penny).
Common Tasks in Money Calculations:
- Adding/Subtracting: Total cost of items, calculating change.
- Multiplying: Total cost for multiple items, wages for hours worked.
- Dividing: Splitting bills, unit price comparisons.
- Converting: Currency conversions using exchange rates.
Real-Life Applications:
- Shopping receipts, calculating discounts and total bills
- Bank interest or loan payments (see compound and simple interest)
- Mobile bills, electricity bills, or shared restaurant bills
Tips:
- When using a calculator, ensure amounts are entered with two decimal places when necessary.
- If dealing with cents only (e.g. 235¢), consider converting to dollars: $2.35.
- Check final answers in context — e.g. people cannot be paid in fractions of a cent.
Example:
Amir buys 2 pens for $\$1.25$ each and a notebook for $\$3.60$. How much does he spend in total?
▶️ Answer/Explanation
Cost of 2 pens = \( 2 \times 1.25 = 2.50 \)
Total cost = \( 2.50 + 3.60 = 6.10 \)
Answer: $6.10
Example:
Sarah has $\$20$. She buys a lunch for $\$7.85$ and a drink for $\$2.60$. How much change does she receive?
▶️ Answer/Explanation
Total spent = \( 7.85 + 2.60 = 10.45 \)
Change = \( 20.00 – 10.45 = 9.55 \)
Answer: $9.55
Example:
A bill of $\$72$ is to be shared equally among 4 friends. How much does each person pay?
▶️ Answer/Explanation
Each pays = \( \frac{72}{4} = 18 \)
Answer: $18.00
Currency Conversion
Currency Conversion
Currency conversion is the process of changing money from one currency to another using a given exchange rate.
\(\text{Currency exchange }=\text{Amount} \times \frac{\text{New Rate}}{\text{Old Rate}}\)
An exchange rate tells you how much of one currency equals a unit of another currency. You either:
- Multiply if converting from a base currency to a foreign currency
- Divide if converting from a foreign currency to a base currency
For example, if the exchange rate is:
- 1 USD = ₹83.2
- 1 GBP = $1.26
- 1 EUR = ₹91.5
Then you can use the following methods:
- To convert $100 to INR: \( 100 \times 83.2 = \)₹\(8320 \)
- To convert ₹9150 to EUR: \( \frac{9150}{91.5} = \)€\(100 \)
- To convert £50 to USD: \( 50 \times 1.26 = \$63 \)
- To convert USD to GBP: \( \frac{\text{Amount in USD}}{1.26} \)
Note: Make sure to:
- Use the most updated exchange rate available
- Apply rounding appropriately to match currency decimal rules (e.g. $2.47, not $2.473)
- Be careful with inverse conversions (if going from currency A to B and vice versa)
Example:
Anita travels from India to the UK. She exchanges ₹74,880 into British pounds (£). The exchange rate is:
- 1 GBP = ₹93.6
While in the UK, she spends £300. On returning to India, she converts the remaining pounds back into rupees at the new rate:
- 1 GBP = ₹92
How much money (in ₹) does she have after returning to India?
▶️ Answer/Explanation
Step 1: Convert ₹74,880 to GBP at ₹93.6 per pound:
\( \frac{74880}{93.6} = 800 \, \text{GBP} \)
Step 2: She spends £300, so remaining = \( 800 – 300 = 500 \, \text{GBP} \)
Step 3: Convert remaining 500 GBP back to ₹ at ₹92 per pound:
\( 500 \times 92 =\) ₹\(46000 \)
Answer: Anita has ₹46,000 after returning to India.
Example:
Convert $150 into rupees if the exchange rate is 1 USD = ₹82.5.
▶️ Answer/Explanation
Amount in ₹ = \( 150 \times 82.5 = 12375 \)
Answer: ₹12,375
Example:
Convert ₹16,500 into dollars if the exchange rate is 1 USD = ₹82.5.
▶️ Answer/Explanation
Amount in $ = \( \frac{16500}{82.5} = 200 \)
Answer: $200