CIE IGCSE Mathematics (0580) Money Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Money Study Notes
Key Concepts:
Core
1 Calculate with money.
2 Convert from one currency to another.
Supplement
1 Calculate with money.
2 Convert from one currency to another.
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