Inflation & Population Growth
Applying compound interest to real-world scenarios
This document explores the application of the compound interest formula in real-world scenarios, specifically focusing on inflation and population growth. Both concepts illustrate how values increase over time, compounding on previous growth, in contrast to simple interest calculations like those used in hire purchase agreements.
Learning Outcomes
- Apply compound interest formula to inflation calculations
- Apply compound interest formula to population growth
- Understand the concept of "loss of purchasing power"
- Calculate future prices given current price and inflation rate
- Calculate future population given current size and growth rate
- Differentiate between simple and compound growth applications
The Unified Formula
Future Value = Present Value × (1 + rate)n
where:
rate = annual inflation/growth rate (as decimal)
n = number of years
| Variable | For Inflation | For Population Growth |
|---|---|---|
| Present Value | The original price of an item (past) | The initial population size |
| Rate | The annual inflation rate (as decimal) | The annual growth rate (as decimal) |
| n | Number of years | Number of years |
| Future Value | The future price of the item | The future population size |
Quiz 1 - Formula Variables
In the inflation formula, what does the present value represent?
1. Inflation (Price Growth)
Inflation Example
- Current Price of a Loaf of Bread: R15.00
- Annual Inflation Rate: 6% (0.06)
- Number of Years: 3
After 3 years, the loaf of bread will cost approximately R17.87.
Quiz 2 - Inflation
If a R20 item has 5% inflation for 2 years, what is the future price?
2. Population Growth
Population Growth Example
- Current Population: 50,000
- Annual Growth Rate: 2% (0.02)
- Number of Years: 10
After 10 years, the population will be approximately 60,949.
Quiz 3 - Population Growth
A town of 10,000 grows at 3% per year. What is the population after 5 years?
Simple vs Compound in Finance
| Topic | Formula Type | CAPS Formula |
|---|---|---|
| Hire Purchase | Simple Growth | A = P(1 + i × n) |
| Inflation | Compound Growth | A = P(1 + i)n |
| Population Growth | Compound Growth | A = P(1 + i)n |
Quiz 4 - Simple vs Compound
Which type of growth does inflation use?
Practice & Assess
Test your knowledge with these interactive games.
Match - Scenario to Type
Fill - Compound Formula
Future Value = Present × (1 + ___)n
Practice Questions
Current price R25, inflation 4% for 3 years. Find future price.
Population 120,000, growth rate 2.5% for 8 years. Find future population.
A house costs R500,000 now. With 7% inflation, what will it cost in 5 years?
Q1: R28.12 | Q2: 146,208 | Q3: R701,275.58
Common Errors to Avoid
Using simple interest formula: Inflation uses compound, not simple.
Use A = P(1 + i)n, not A = P(1 + i×n)
Forgetting decimal conversion: Using 5 instead of 0.05 for 5%.
Confusing present and future values: Know which is which in the problem.
