Compound Interest

Master the power of "interest on interest" growth

CAPS Grade 10 Mathematics

This topic forms part of the CAPS-aligned Grade 10 Mathematics curriculum and focuses on financial mathematics, particularly the concept of "interest on interest" growth. Each section includes interactive games and quizzes to test your understanding.

Learning Outcomes

  • Define compound interest and differentiate it from simple interest
  • Apply the compound interest formula to calculate future value
  • Calculate principal, interest rate, or time period when other values are known
  • Understand different compounding periods (annually, monthly, etc.)
  • Solve real-world financial problems involving compound interest
  • Compare different investment options based on compound interest rates
  • Understand the exponential growth nature of compound interest

The Compound Interest Formula

Compound Interest Formula
A = P(1 + i)n
where:
A = Future value (including interest)
P = Principal amount (initial investment)
i = Interest rate per period (as decimal)
n = Number of compounding periods

Basic Example

Example

Invest R1000 at 8% annual interest compounded annually for 5 years.

Solution
P = 1000, i = 0.08, n = 5
A = 1000(1.08)5
A = 1000 × 1.46933 = R1469.33

Quiz 1 - Compound Interest Formula

What does 'i' represent in the formula A = P(1 + i)n?

A) Principal amount
B) Interest rate per period (as decimal)
C) Number of years
D) Future value

Finding Different Variables

A

Find A (Future Value)

A = P(1 + i)n

Example: P=1000, i=0.05, n=3

A = 1000(1.05)3 = R1157.63
P

Find P (Principal)

P = A/(1 + i)n

Example: Want A=5000, i=0.06, n=10

P = 5000/(1.06)10 ≈ R2791.97
i,n

Find i or n

Grade 10: Usually given or find by estimation

n = log(A/P) ÷ log(1 + i)

Compounding Periods

A

Annually

i = annual rate, n = years

8% p.a. for 5 years: i=0.08, n=5

S

Semi-annually

i = rate/2, n = years×2

8% for 5 years: i=0.04, n=10

Q

Quarterly

i = rate/4, n = years×4

8% for 5 years: i=0.02, n=20

M

Monthly

i = rate/12, n = years×12

12% for 3 years: i=0.01, n=36

Monthly Compounding

Problem

Invest R5000 at 12% annual compounded monthly for 3 years.

i = 0.12/12 = 0.01, n = 3×12 = 36
A = 5000(1.01)36 = 5000 × 1.43077 = R7153.85

Quiz 2 - Compounding Periods

For monthly compounding, how do you find n?

A) n = years
B) n = years × 2
C) n = years × 4
D) n = years × 12

Compound vs Simple Interest

Simple Interest

A = P(1 + i×n)
  • Interest only on principal
  • Linear growth
Example: R1000 at 10% for 3 years = R1300

Compound Interest

A = P(1 + i)n
  • Interest on principal + accumulated interest
  • Exponential growth
Example: R1000 at 10% for 3 years = R1331

Comparison (10 years)

R1000 at 10% for 10 years:

Simple: R2000
Compound: R2593.74

Quiz 3 - Simple vs Compound

Which grows faster over time?

A) Simple interest
B) Compound interest
C) They grow at the same rate
D) Depends on the amount

Effective Annual Rate (EAR)

What is EAR?

The actual annual rate when compounding is considered.

EAR = (1 + i/m)m - 1

i = nominal annual rate, m = compounding periods per year

Example Calculation

12% nominal rate compounded monthly:

EAR = (1 + 0.12/12)12 - 1
EAR = 1.12683 - 1 = 0.12683 = 12.68%

Practice & Assess

Test your knowledge with these interactive games.

Match - Compounding Periods

Annually
i = rate, n = years
Semi-annually
i = rate/2, n = years×2
Quarterly
i = rate/4, n = years×4
Monthly
i = rate/12, n = years×12

Fill - EAR Formula

EAR = (1 + i/__)m - 1

Practice Questions

Q1

R8000 at 7% compounded annually for 6 years. Find A.

Q2

Want R15000 in 4 years. Bank offers 5.5% compounded quarterly. Find P.

Q3

R12000 at 9% compounded monthly for 3 years. Calculate interest earned.

Q4

Calculate EAR for 6% compounded monthly.

Answers

Q1: R12006.10 | Q2: R12064.77 | Q3: R3957.96 | Q4: 6.17%

Common Errors to Avoid

Error 1

Wrong i/n: Not adjusting for compounding period

Solution: i and n must match frequency

Error 2

Forgetting decimal: Using 8 instead of 0.08

Solution: Always convert % to decimal

Error 3

Confusing A and P: Mixing up principal and future value

Summary of Key Concepts

Compound Interest Formula: A = P(1 + i)n
Principal Formula: P = A/(1 + i)n
EAR: EAR = (1 + i/m)m - 1
Compounding Adjustments: More frequent compounding = higher returns

Key Terms

Principal Interest Rate Future Value Compounding Period Annual Monthly Quarterly EAR Simple Interest Exponential Growth
Simple Interest Hire Purchase