Learning Objectives
- explain how compound interest differs from simple interest;
- calculate growth year by year;
- use the compound-interest formula;
- calculate depreciation;
- compare simple and compound growth.
Introduction
This lesson develops Compound Interest from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
📊 Interactive Growth and Depreciation Lab
Compare simple interest, compound interest and depreciation on the same graph.
Growth comparison scale
🌍 Where Will You Use This?
Compound growth appears in savings, investments, loans, inflation and population growth. Depreciation applies the same idea in reverse.
Why Compound Interest Grows Faster
Compound interest is calculated on the current balance, including interest already earned.
Year-by-Year Example
| Year | Opening balance | 10% interest | Closing balance |
|---|---|---|---|
| 1 | US$1,000 | US$100 | US$1,100 |
| 2 | US$1,100 | US$110 | US$1,210 |
| 3 | US$1,210 | US$121 | US$1,331 |
Compound Interest Formula
Invest US$2,000 at 6% per year for 4 years.
A=2000(1.06)⁴.
A≈US$2,524.95.
Interest≈US$524.95.
Depreciation
Depreciation is a repeated percentage decrease in value.
A car worth US$12,000 depreciates by 15% per year for 3 years.
Value = 12000(0.85)³ ≈ US$7,369.50.
Simple vs Compound Interest
| Simple Interest | Compound Interest |
|---|---|
| Interest based on original principal | Interest based on current balance |
| Same interest each period | Interest changes each period |
| Linear growth | Exponential growth |
💼 Money Smart Tip
The longer the time period, the greater the difference between simple and compound interest.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
Foundation- Find the amount on US$1,000 at 5% compound interest for 2 years.
- Find the compound interest on US$800 at 10% for 3 years.
- A machine worth US$5,000 depreciates by 8% per year for 2 years. Find its value.
- Find the amount on US$2,500 at 7.5% for 4 years.
- Compare simple and compound interest on US$1,200 at 6% for 5 years.
- A laptop depreciates to US$648 after 2 years at 10% per year. Find its original value.
- An investment grows from US$2,000 to US$2,662 after 3 years. Determine the annual compound rate.
✅ Check Your Work
Show practice answers
- 1000(1.05)² = US$1,102.50.
- Amount=800(1.10)³=1064.80; interest=US$264.80.
- 5000(0.92)² = US$4,232.
- 2500(1.075)⁴ ≈ US$3,338.67.
-
Simple interest=1200×6×5÷100=US$360.
Compound amount=1200(1.06)⁵≈US$1,605.87, so interest≈US$405.87.
Compound earns about US$45.87 more. - Original=648÷0.9²=US$800.
- 2662/2000=1.331=1.1³, so the annual rate is 10%.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Compound interest uses the current balance.
- A=P(1+r/100)ⁿ.
- Compound interest = amount − principal.
- Depreciation uses a multiplier below 1.