Summary (Grade 10 NSC Matric Mathematics): Revision Notes
Summary
Interest rates and calculations
Interest is the additional money you earn when you invest money, or the extra amount you pay when you borrow money. There are two main types of interest calculations you need to understand.
The key difference between simple and compound interest lies in what the interest is calculated on - understanding this distinction is crucial for choosing the right formula for different financial scenarios.
Simple interest
Simple interest is calculated only on the original amount (principal) throughout the entire period. The money grows in a straight line pattern.
Formula:
Simple interest creates linear growth - the same amount of interest is added each period. This is commonly used for short-term loans and hire purchase agreements.
Compound interest
Compound interest is calculated on both the original amount and any interest already earned. This creates exponential growth because you earn "interest on interest".
Formula:
Compound interest creates exponential growth - the interest earned increases each period because you're earning interest on previously earned interest. This is the foundation of long-term investment growth and population modelling.
Key variables
Essential Variables for Interest Calculations:
- A = accumulated amount (final total after interest)
- P = principal amount (original money invested or borrowed)
- i = interest rate written as a decimal (e.g., 8% = 0.08)
- n = number of years
Financial applications
Understanding how to apply these interest formulas to real-world financial situations is essential for making informed decisions about loans, investments, and economic modelling.
Hire purchase loans
When you buy something on hire purchase, you typically pay a deposit first, then make monthly payments on the remaining amount. The calculations work as follows:
- Use the simple interest formula to calculate the total amount owed on the cash price minus the deposit
- Divide the total accumulated amount by the number of months to find your monthly payment
This method ensures you understand exactly how much extra you're paying in interest over the loan period.
Hire purchase agreements use simple interest because the loan amount remains fixed throughout the payment period, making it easier for consumers to understand their total payment obligations.
Population growth and inflation
Both population changes and inflation calculations use the compound interest formula because they involve exponential growth or decline over time.
- Population growth: The rate compounds each year as new births add to an already growing population
- Inflation: Prices increase on already increased prices from previous years
These scenarios use compound interest because each year's growth builds upon the previous year's total - creating the "snowball effect" of exponential change over time.
Foreign exchange
Foreign exchange rate is the price of one currency expressed in terms of another currency.
Currency conversion process
When converting between currencies, you need to:
- Identify the exchange rates between all currencies involved
- Convert step by step if going through multiple currencies
- Check your direction - are you converting from rand to foreign currency or vice versa?
Worked Example: Currency Conversion
If you have R5000 and the exchange rate is R1 = 39.46 MWK (Malawian kwacha):
Step 1: Set up the conversion
- You have: R5000
- Exchange rate: R1 = 39.46 MWK
Step 2: Calculate
- R5000 × 39.46 MWK/R1 = 197,300 MWK
Step 3: Check your answer makes sense
- Since 1 rand buys many kwacha, your kwacha amount should be much larger than your rand amount ✓
Common Exchange Rate Mistake: Always check the direction of your conversion. If 1 rand = many foreign units, your foreign currency amount should be larger than your rand amount, and vice versa.
Exam tips
Essential Exam Strategies:
- Always write down your formula before substituting values
- Check which interest type to use - simple for most loan calculations, compound for growth scenarios
- Convert percentages to decimals before calculating (divide by 100)
- Keep exchange rate directions clear - write out what 1 unit of each currency equals
- Show all working steps - partial marks are often available even if your final answer is incorrect
Key Points to Remember:
- Simple interest grows in a straight line:
- Compound interest grows exponentially:
- Hire purchase uses simple interest on the amount after deposit
- Population growth and inflation use compound interest formulas
- Foreign exchange rates tell you the price of one currency in terms of another
- Always double-check currency conversion directions and calculations