Simple & Compound Interest
Master the logic of how money grows — simple vs compound interest, hire purchase, inflation, and exchange rates — with full worked examples.
Finance and Growth
Table of Contents
Finance: Simple Interest, Compound Interest & Real-World Applications#
In Grade 10, you learn how money grows over time (investment) and how costs increase over time (inflation, hire purchase). There are two growth models — and understanding the difference is crucial.
Simple Interest vs Compound Interest#
| Simple Interest | Compound Interest | |
|---|---|---|
| Formula | $A = P(1 + in)$ | $A = P(1 + i)^n$ |
| Interest calculated on | Original amount only | New total each period |
| Growth | Linear (constant) | Exponential (accelerating) |
| Graph shape | Straight line | Curve (gets steeper) |
| Symbol | Meaning |
|---|---|
| $A$ | Final amount (what you end up with) |
| $P$ | Principal (starting amount) |
| $i$ | Interest rate as a decimal (e.g., 8% = 0.08) |
| $n$ | Number of years |
Worked Example#
R5 000 invested for 3 years at 10% per annum:
Simple: $A = 5000(1 + 0.10 \times 3) = 5000(1.3) = \text{R}6\,500$
Compound: $A = 5000(1 + 0.10)^3 = 5000(1.331) = \text{R}6\,655$
💡 Compound interest earns R155 more because you earn “interest on interest”. The longer the time, the bigger the gap.
Hire Purchase (HP)#
Hire purchase is a way to buy expensive items (cars, appliances) by paying monthly instalments. HP always uses simple interest on the full cash price.
Key formula: $A = P(1 + in)$, then divide by the number of months.
The catch: You also pay a deposit upfront, so the loan amount = cash price − deposit.
Inflation#
Inflation measures how the cost of living increases over time. It uses the compound interest formula:
$$A = P(1 + i)^n$$Example: A loaf of bread costs R15 today. If inflation is 6% per year, in 5 years it will cost:
$A = 15(1.06)^5 = 15 \times 1.338 = \text{R}20.07$
Exchange Rates#
To convert between currencies:
- Buying foreign currency: Use the higher rate (you pay more rands)
- Selling foreign currency: Use the lower rate (you receive fewer rands)
⚠️ Read the question carefully — “buying” and “selling” are from the bank’s perspective, not yours.
Deep Dive#
- Simple & Compound Interest, HP & Inflation — full worked examples for all calculation types, comparison tables, and real-world scenarios
🚨 Common Mistakes#
- Interest rate not converted: 8% must be written as 0.08 in the formula, not 8.
- Confusing simple and compound: Simple → multiply by $n$. Compound → power of $n$. Mixing them up changes the answer significantly.
- Hire purchase deposit: Subtract the deposit FIRST, then calculate interest on the remaining balance.
- Exchange rates — wrong direction: Buying dollars? Multiply rands by the bank’s selling rate. Read carefully.
🔗 Related Grade 10 topics:
- Exponents — compound interest uses exponential growth ($P(1+i)^n$)
- Functions — simple interest = linear graph, compound interest = exponential graph
📌 Where this leads in Grade 11: Finance, Growth & Decay — nominal vs effective rates, depreciation, and timeline problems
⏮️ Functions | 🏠 Back to Grade 10 | ⏭️ Probability