Simple Interest
Calculate interest earned only on the principal amount
This topic forms part of the CAPS-aligned Grade 10 Mathematics curriculum and focuses on calculating interest earned only on the principal amount. Each section includes interactive games and quizzes to test your understanding.
Learning Outcomes
- Define simple interest and understand its components
- Calculate simple interest using the formula
- Determine accumulated amount (principal + interest)
- Find principal, interest rate, or time when other values are known
- Solve real-world financial problems
- Compare different investment/loan options
- Understand the difference between simple and compound interest
Core Concepts
Principal (P)
- Initial amount invested/borrowed
- Starting capital
- Measured in Rands (R)
- Example: R1000 deposit
Interest Rate (r)
- Percentage charged/earned per year
- Must convert to decimal for calculations
- Example: 8% = 0.08
- Usually per annum (p.a.)
Time (t)
- Duration in years
- Can be months/weeks converted to years
- Example: 18 months = 1.5 years
- 6 months = 0.5 years
Simple Interest Formula
I = P × r × t
where:
I = Simple Interest
P = Principal amount
r = Interest rate (as decimal)
t = Time (in years)
Basic Calculation
Invest R1000 at 8% simple interest per annum for 3 years.
Quiz 1 - Simple Interest Formula
What is the formula for simple interest?
Accumulated Amount
Formula 1
Add interest to principal
Formula 2
Combined formula
Accumulated Amount
R1000 at 8% simple interest for 3 years. Find total amount.
Quiz 2 - Accumulated Amount
R2000 at 5% simple interest for 4 years gives total?
Finding Different Variables
Find P (Principal)
Example: I=R300, r=6%, t=5 years
Find r (Rate)
Example: I=R400, P=R2000, t=4 years
Find t (Time)
Example: I=R100, P=R500, r=10%
Time Conversions
Months to Years
6 months = 0.5 years
18 months = 1.5 years
Weeks to Years
26 weeks = 0.5 years
13 weeks = 0.25 years
Days to Years
90 days ≈ 0.2466 years
Time Conversion Example
R8000 at 9% simple interest for 9 months. Calculate interest.
Quiz 3 - Time Conversion
18 months = ? years
Real-World Applications
Loan Example
John borrows R5000 at 12% simple interest. How much after 2 years?
Savings Example
Save R3000 at 5.5% simple interest. Interest in 4 years?
Investment Comparison
Option A: R2000 at 7% for 3 years = R2420
Option B: R2000 at 6% for 4 years = R2480
Option B better!
Simple vs Compound Interest
Simple Interest
- Interest only on principal
- Same interest each year
- Linear growth
Compound Interest
- Interest on principal + accumulated interest
- Exponential growth
- R1000 at 10% for 3 years: R1331
Quiz 4 - Simple vs Compound
Which grows faster over 10 years?
Practice & Assess
Test your knowledge with these interactive games.
Match - Formula Parts
Fill - Simple Interest
I = P × ___ × t
Word Problem Strategies
Read Carefully
- Identify principal amount
- Note interest rate
- Extract time period
- Determine what to find
Convert Units
- % to decimal
- Months/days to years
Choose Formula
- I = Prt (interest only)
- A = P(1 + rt) (total amount)
Complex Word Problem
Maria invests R7500. After 2.5 years, she has R8625. What was the simple interest rate?
Practice Questions
R4000 at 6.5% simple interest for 4 years. Find interest.
Want R9000 total in 3 years at 8% simple interest. What principal needed?
R1500 earns R337.50 interest in 2.5 years. Find interest rate.
Q1: R1040 | Q2: R7258.06 | Q3: 9%
Common Errors to Avoid
Decimal conversion: Using 8 instead of 0.08
Solution: Always ÷ 100
Time units: Not converting months to years
Confusing I and A: Interest vs total amount
Formula Summary
Main Formulas
- I = P × r × t
- A = P(1 + rt)
- A = P + I
Rearranged Formulas
- P = I ÷ (r × t)
- r = I ÷ (P × t)
- t = I ÷ (P × r)
Key Points
- r must be decimal
- t must be in years
- Linear growth
