Simple and Compound Interest Revision Notes for Grade 12 NSC Matric Business Studies

Simple and Compound Interest

Understanding interest as an investment return

When you invest money, you expect to earn a return on your investment. One of the most common ways this happens is through interest - the extra money you receive for allowing someone else (like a bank) to use your funds. Understanding how interest works is crucial for making smart investment decisions.

Capital gain refers to the increase in value of an investment over time compared to what you originally paid for it. This growth becomes taxable income that must be reported to SARS when you sell the investment.

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Interest represents the cost of borrowing money or the reward for lending it. When you invest, you're essentially lending your money to earn this reward.

What is simple interest?

Simple interest is the most straightforward way to calculate investment returns. With simple interest, you only earn money on your original investment amount (called the principal). No matter how long you leave your money invested, the interest calculation always uses the same starting amount.

Key characteristics of simple interest:

Interest is calculated only on the original principal amount
The principal value stays the same throughout the investment period
Returns are generally lower compared to compound interest
Each year's interest payment is exactly the same amount

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With simple interest, your earnings remain constant each period because the calculation never includes previously earned interest.

What is compound interest?

Compound interest is often called "interest on interest" because it's calculated on both your original investment and any interest you've already earned. This creates a snowball effect where your money grows faster over time.

Key characteristics of compound interest:

Interest is calculated on the original principal plus accumulated interest
The investment value increases each period as interest is added
Returns are generally higher than simple interest over time
Each period's interest payment grows larger than the previous period

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The "compounding effect" means that as your investment grows, each subsequent interest calculation is based on a larger amount, leading to exponential growth over time.

The key differences explained

Simple Interest	Compound Interest
Calculated only on original principal	Calculated on principal plus accumulated interest
Principal amount stays constant	Investment value grows with each interest payment
Lower total returns	Higher total returns over time
Interest earned separately from principal	Interest becomes part of the growing principal

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The key difference is that compound interest earns interest on previously earned interest, while simple interest does not. This difference becomes more significant over longer time periods.

Calculating simple interest

The formula for simple interest is straightforward:

$\text{Interest} = P \times r \times t$

Where:

P = Principal (original investment amount)
r = Interest rate (as a decimal - divide percentage by 100)
t = Time period (usually in years)

Simple interest calculation steps:

Identify the principal amount you're investing
Convert the interest rate percentage to a decimal
Determine the time period in years
Multiply all three values together

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Remember to convert percentages to decimals by dividing by 100. For example, 12% becomes 0.12.

Calculating compound interest

The formula for compound interest is more complex:

$\text{Interest} = P \times (1 + r)^n - P$

Where:

P = Principal (original investment amount)
r = Interest rate (as a decimal)
n = Number of compounding periods

Compound interest calculation steps:

Convert the interest rate to a decimal
Add 1 to the interest rate
Raise this result to the power of the number of periods
Multiply by the principal amount
Subtract the original principal to get just the interest earned

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The exponent n represents the number of compounding periods, which creates the exponential growth effect that makes compound interest so powerful.

Worked example: Kaley's investment decision

Let's compare both methods using a practical scenario to see how these calculations work in practice:

Scenario: Kaley wants to invest R50,000 for two years. Standford Bank offers 12% simple interest per year, while Capital Bank offers 12% compound interest per year.

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Worked Example: Comparing Simple vs Compound Interest

Simple interest calculation (Standford Bank):

P = R50,000
r = 12% = 0.12
t = 2 years

$\text{Interest} = \text{R50,000} \times 0.12 \times 2 = \text{R12,000}$

Total amount after 2 years: R50,000 + R12,000 = R62,000

Compound interest calculation (Capital Bank):

P = R50,000
r = 12% = 0.12
n = 2 years

$\text{Interest} = \text{R50,000} \times (1 + 0.12)^2 - \text{R50,000}$ $\text{Interest} = \text{R50,000} \times (1.12)^2 - \text{R50,000}$ $\text{Interest} = \text{R50,000} \times 1.2544 - \text{R50,000}$ $\text{Interest} = \text{R62,720} - \text{R50,000} = \text{R12,720}$

Total amount after 2 years: R62,720

The better choice:

Kaley should choose Capital Bank's compound interest option because:

She earns R720 more (R12,720 vs R12,000)
Compound interest allows her to earn interest on her interest
The longer the investment period, the greater the advantage of compound interest

Investment tips for students

Here are some practical tips to help you make better investment decisions and maximise your returns:

Start early: The power of compound interest becomes more dramatic over longer periods
Compare options: Always calculate both simple and compound interest when given a choice
Understand the terms: Make sure you know whether an investment offers simple or compound interest
Consider the frequency: Some investments compound monthly, quarterly, or annually - more frequent compounding means faster growth

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Time is your greatest ally when it comes to compound interest. Even small amounts invested early can grow substantially over decades due to the compounding effect.

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Key Points to Remember:

Simple interest is calculated only on the original amount you invested - it stays the same each year
Compound interest is calculated on your original investment plus any interest you've already earned - it grows each year
Compound interest always produces higher returns than simple interest over the same time period with the same interest rate
Use the correct formula: Simple interest = $P \times r \times t$ , while compound interest = $P \times (1 + r)^n - P$
The longer you invest, the bigger the difference between simple and compound interest becomes

Simple and Compound Interest (Grade 12 NSC Matric Business Studies): Revision Notes