Interest (Grade 12 NSC Matric Mathematical Literacy): Revision Notes
Interest
Interest is a fundamental concept in finance that affects many purchasing decisions and loan agreements. Understanding how interest works helps you make informed financial choices and calculate the true cost of borrowing money.
What is interest?
Key Financial Terms:
Interest rate is the percentage amount charged when you borrow money over a specific period of time. Think of it as the "rental fee" for using someone else's money.
Interest is the actual rand amount you pay for borrowing money. This is calculated using the interest rate and represents the extra cost above the original amount borrowed.
For example, if you borrow R1000 at 10% interest rate, you will pay R100 in interest: .
Simple interest
Simple interest is calculated only on the original amount borrowed (called the principal). The interest amount stays the same for each payment period throughout the loan term.
Key characteristics of simple interest:
- Calculated on the original principal amount only
- Interest amount remains constant each period
- Total interest = Principal × Rate × Time
Calculating simple interest amounts
When you know the interest rate, calculating the interest is straightforward:
For example: 10% interest on R3500 = Total amount to repay =
Finding the interest rate
When you're given the final amount and need to find the interest rate:
- Find the interest amount: Final Amount - Original Amount = Interest
- Calculate the percentage:
Worked Example: Simple Interest in Hire Purchase
Problem: A wall unit costs R6499.99 cash, or you can pay a R650 deposit plus 36 monthly instalments of R449 each.
Step-by-step solution:
Step 1: Calculate total cost of instalments
Step 2: Calculate total interest paid
Step 3: Calculate interest rate
Amount owed after deposit =
This is over 3 years, so annual rate = per annum
Exam Tip: Remember to calculate the interest rate on the amount owed after paying the deposit, not on the full cash price.
Compound interest
Compound interest works differently from simple interest. Instead of calculating interest only on the original amount, compound interest is calculated on the current balance, which includes both the original amount and any interest already earned or owed.
Key characteristics of compound interest:
- Calculated on the current balance (principal + accumulated interest)
- Interest amount increases each period
- Results in higher total interest than simple interest over time
Worked Example: Comparing Simple vs Compound Interest
Let's compare two loan options for borrowing R16000 over 5 years:
Option A - Simple Interest (18% per annum):
- Annual interest =
- Total interest over 5 years =
- Total amount to repay =
Option B - Compound Interest (16% per annum):
- Year 1: interest → New balance:
- Year 2: interest → New balance:
- Year 3: interest → New balance:
- Year 4: interest → New balance:
- Year 5: interest → Final balance:
Total interest with compound interest =
Conclusion: Even though the compound interest rate (16%) is lower than the simple interest rate (18%), compound interest results in higher total interest ( vs ) because interest compounds annually.
Formula for compound interest:
Where the interest rate is expressed as a decimal (e.g., 16% = 0.16).
Exam Tips for Interest Calculations
- Always identify whether you're dealing with simple or compound interest
- For hire purchase problems, calculate interest on the balance after deposit
- Show all working steps clearly
- Double-check your calculations, especially when converting percentages
- Remember that compound interest always results in higher costs than simple interest over time
Key Points to Remember:
- Interest rate is the percentage charged for borrowing money over a specific time period
- Simple interest is calculated only on the original amount and stays constant each period
- Compound interest is calculated on the current balance and increases over time
- For hire purchase calculations, work out interest on the amount owed after paying the deposit
- Compound interest always costs more than simple interest over the same period, even at lower rates