Learning Objectives
- identify principal, rate and time;
- calculate simple interest;
- find the final amount;
- rearrange the simple-interest formula;
- solve borrowing and saving problems.
Introduction
This lesson develops Simple 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 Simple Interest Explorer
Move the sliders and watch the amount grow in a straight line. The graph is linear because the same interest is added each year.
Simple interest
Total amount
Simple-interest amount
Growth scale
Principal
Interest
Total amount
$0$2,000$4,000$6,000$8,000+
Formula: I = Prt/100. The graph helps you understand the relationship, but you still need to know and apply the formula.
🌍 Where Will You Use This?
Interest appears when money is saved, invested or borrowed. Simple interest is calculated only on the original amount.
The Meaning of Interest
Simple Interest Formula
I = Prt / 100
Amount = Principal + Interest
Simple interest is always calculated on the original principal.
Worked Example 1
Find simple interest on US$600 at 8% per year for 3 years.
1
P=600, r=8, t=3.
2
I=600×8×3÷100 = US$144.
3
Amount = 600+144 = US$744.
Matching Time Units
If the rate is per year, express time in years.
US$900 at 10% per year for 9 months.
1
9 months = 9/12 = 0.75 years.
2
I=900×10×0.75÷100 = US$67.50.
Finding a Missing Value
Interest is US$120 on US$500 for 4 years. Find the rate.
1
120=500×r×4÷100.
2
120=20r.
3
r=6% per year.
💼 Money Smart Tip
Always check whether the question asks for interest only or the total amount including the principal.
🧠 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.
Practice Questions
Foundation- Find simple interest on US$400 at 5% for 3 years.
- Find the total amount for US$750 at 6% for 2 years.
- Find interest on US$1,200 at 9% for 8 months.
- US$180 interest is earned on US$900 for 5 years. Find the rate.
- At 7% simple interest, how long will US$500 take to earn US$105?
- A loan grows to US$1,260 after 4 years at 6.5% simple interest. Find the principal.
- Two investments earn the same simple interest. The first is US$800 at 9% for 2 years. The second is invested at 6% for 4 years. Find the second principal.
✅ Check Your Work
Show practice answers
- US$60.
- Interest=90; amount=US$840.
- US$72.
- 4%.
- 3 years.
-
Amount=P(1+0.065×4)=1.26P.
P=1260÷1.26=US$1,000. -
First interest=800×9×2÷100=144.
144=P×6×4÷100, so P=US$600.
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
- Simple interest uses only the original principal.
- I=Prt/100.
- Amount = principal + interest.
- Time units must match the rate period.