Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate simple interest earned or paid.
• Calculate the impact of inflation on purchasing power.
• Develop a personal budget with income, expenses, and savings.
• Analyse the financial implications of spending choices.
• Explain the relationship between interest, inflation, and budgeting.

Lesson summary

This week, we delve into the critical aspects of personal finance, focusing on simple interest, inflation, and budgeting. These concepts are not just abstract mathematical ideas; they are fundamental tools that empower you to make informed financial decisions throughout your life. Understanding how interest works, how inflation erodes the value of money, and how to create a budget are vital for managing your finances effectively, whether you are saving for a car, planning for tertiary education, or simply managing your monthly expenses. In the South African context, where socio-economic disparities are prevalent, financial literacy is even more crucial for building a secure future.

Lesson notes

2.1 Simple Interest Simple interest is a method of calculating the interest earned on a principal amount. It's "simple" because the interest earned each period is based only on the original principal and not on any accumulated interest.

Formula: `Simple Interest (SI) = P × R × T` Where: `P` = Principal amount (the initial amount of money borrowed or invested) `R` = Interest rate (expressed as a decimal, e.g., 8% = 0.08) `T` = Time period (usually in years, but can be in months or days if the interest rate is given accordingly).

Total Amount (A) after T years: `A = P + SI` or `A = P (1 + RT)` Example 1: Thando invests R5,000 in a fixed deposit account that earns simple interest at a rate of 7% per year. How much interest will she earn after 3 years? What will be the total amount in her account? P = R5,000 R = 7% = 0.07 T = 3 years `SI = P × R × T = R5,000 × 0.07 × 3 = R1,050` Thando will earn R1,050 in interest. `A = P + SI = R5,000 + R1,050 = R6,050` The total amount in her account after 3 years will be R6,

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0. Example 2: Sipho borrows R12,000 from a loan shark at a simple interest rate of 25% per year. How much will he owe after 6 months? P = R12,000 R = 25% = 0.25 T = 6 months = 0.5 years (6/12) `SI = P × R × T = R12,000 × 0.25 × 0.5 = R1,500` Sipho will owe R1,500 in interest. `A = P + SI = R12,000 + R1,500 = R13,500` Sipho will owe a total of R13,500 after 6 months. This example highlights the danger of high-interest loans. 2.2 Inflation Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. In simpler terms, inflation means that your money buys less than it did before.

Formula: `Future Value (FV) = Present Value (PV) × (1 + Inflation Rate)^Number of Years` Example 1: A loaf of bread currently costs R

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5. If the inflation rate is 6% per year, how much will a loaf of bread cost in 5 years? PV = R15 Inflation Rate = 6% = 0.06 Number of Years = 5 `FV = R15 × (1 + 0.06)^5 = R15 × (1.06)^5 = R15 × 1.3382 = R20.07` A loaf of bread will cost approximately R20.07 in 5 years. This demonstrates the impact of inflation.

Example 2: Your parents gave you R1000 for your birthday five years ago. If the average inflation rate over those five years was 5%, what is the real value of that R1000 today in terms of purchasing power? (This is a backwards calculation – we're finding the Present Value given the Future Value and inflation rate) We need to rearrange the formula to solve for PV: `PV = FV / (1 + Inflation Rate)^Number of Years` FV = R1000 Inflation Rate = 5% = 0.05 Number of Years = 5 `PV = R1000 / (1 + 0.05)^5 = R1000 / (1.05)^5 = R1000 / 1.2763 = R783.53` The real value of that R1000 today is approximately R783.53 in terms of purchasing power. It can buy less than it could five years ago. 2.3 Budgeting A budget is a financial plan that helps you track your income and expenses over a specific period (e.g., a month). Budgeting is essential for managing your finances effectively, saving money, and achieving your financial goals.

Key Components of a Budget: Income: All the money you receive (e.g., allowance, part-time job earnings, grant money).

Expenses: All the money you spend.

Expenses can be categorized as: Fixed Expenses: Expenses that remain relatively constant each month (e.g., rent, loan repayments, insurance premiums).

Variable Expenses: Expenses that fluctuate each month (e.g., groceries, transportation, entertainment, clothing).

Savings: The portion of your income that you set aside for future goals (e.g., education, a car, emergencies).

Creating a Budget: Calculate your income: Determine your total income for the budget period (usually a month).

List your expenses: Identify all your fixed and variable expenses. Estimate the amount you spend on each category.

Calculate your total expenses: Add up all your fixed and variable expenses.

Calculate your savings/surplus/deficit: Subtract your total expenses from your total income.

Surplus: Income > Expenses (you have money left over)

Deficit: Income < Expenses (you are spending more than you earn)

Adjust your budget (if needed): If you have a deficit, you need to find ways to reduce your expenses or increase your income.

Example: Consider a Grade 10 learner, Zola, who receives a monthly allowance of R500 from her parents. She also earns R300 from a part-time job.

Her expenses include: Airtime: R100 (fixed)

Data: R50 (variable)

Transportation: R150 (variable)

Entertainment: R200 (variable)

Snacks: R100 (variable)

Let's create a budget for Zola: Income: Allowance: R500 Part-time Job: R300 Total Income: R800 Expenses: Fixed Expenses: Airtime: R100 Variable Expenses: Data: R50 Transportation: R150 Entertainment: R200 Snacks: R100 Total Expenses: R100 + R50 + R150 + R200 + R100 = R600 Savings/Surplus/Deficit: Total Income - Total Expenses = R800 - R600 = R200 Zola has a surplus of R

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0. She can choose to save this amount or allocate it to other expenses.