Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Calculate simple interest and total amounts on loans.
• Calculate the effect of inflation on prices and purchasing power.
• Create a personal budget, analyzing income and expenses.
• Compare different budgeting methods.
• Interpret financial documents like bank statements and loan agreements.

Lesson summary

This week, we delve into the crucial aspects of personal finance: simple interest, inflation, and budgeting. These are not just abstract mathematical concepts; they are fundamental tools for navigating the South African economy and making informed financial decisions throughout your lives. Understanding simple interest allows you to calculate the earnings on savings or the cost of borrowing. Inflation awareness helps you understand the eroding effect of rising prices on your money. Budgeting provides a structured framework for managing income and expenses, essential for achieving financial stability and future goals.

Lesson notes

Simple Interest Simple interest is a straightforward way to calculate interest. It is calculated only on the principal amount (the initial amount of money invested or borrowed).

Formula: `Simple Interest (SI) = P r t` Where: `P` = Principal amount (the initial investment or loan amount) `r` = Interest rate (expressed as a decimal, e.g., 8% = 0.08) `t` = Time period (in years)

Total Amount (A) after t years: `A = P + SI = P + (P r t) = P(1 + rt)` Example 1: Saving for a Laptop Sipho invests R5,000 in a savings account that pays simple interest at a rate of 7% per year. How much interest will he earn after 3 years? What will be the total amount in his account?

Solution: P = R5,000 r = 7% = 0.07 t = 3 years SI = P r t = R5,000 0.07 3 = R1,050 The total amount in his account after 3 years is: A = P + SI = R5,000 + R1,050 = R6,050 Why it works: The interest is only calculated on the initial R5,

0

0

0. Each year, Sipho earns 7% of R5,000, which is R

3

5

0. Over three years, this totals R1,

0

5

0. Example 2: Taking out a Loan Thandi borrows R12,000 from a micro-lender to start a small business. The loan has a simple interest rate of 25% per year and must be repaid in 2 years. How much will she have to repay in total?

Solution: P = R12,000 r = 25% = 0.25 t = 2 years SI = P r t = R12,000 0.25 2 = R6,000 The total amount to repay is: A = P + SI = R12,000 + R6,000 = R18,000 Important

Note: Be wary of very high interest rates from micro-lenders, as these can lead to a cycle of debt. Always compare interest rates from different sources before taking out a loan. Always include any fees when calculating the total amount you will repay. Inflation Inflation refers to the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. It is usually expressed as a percentage per year. In South Africa, inflation is measured by the Consumer Price Index (CPI).

Formula: `Future Price = Present Price * (1 + Inflation Rate)^Number of Years` Example 3: The Rising Cost of Bread A loaf of bread currently costs R

1

5. If the inflation rate is 6% per year, how much will a loaf of bread cost in 5 years?

Solution: Present Price = R15 Inflation Rate = 6% = 0.06 Number of Years = 5 Future Price = R15 (1 + 0.06)^5 = R15 (1.06)^5 = R15 * 1.3382255776 = R20.07 (rounded to the nearest cent) Therefore, a loaf of bread will cost approximately R20.07 in 5 years.

Why it matters: Inflation erodes the value of your money. The same amount of money will buy fewer goods and services in the future. This is why it's important to invest your money so that it grows at a rate higher than inflation.

Example 4: Salary Increases and Inflation Zanele earns R8,000 per month. The inflation rate is 5% per year. To maintain her purchasing power, how much of a salary increase does she need to receive?

Solution: She needs a salary increase of 5% of R8,000: Increase = 0.05 * R8,000 = R400 Therefore, Zanele needs a salary increase of R400 per month to maintain her current purchasing power. Her new salary needs to be R8,400 per month. Budgeting A budget is a plan for managing your income and expenses. It helps you track where your money is going, identify areas where you can save, and achieve your financial goals.

Key Components of a Budget: Income: Money received (e.g., salary, wages, grants, investments).

Expenses: Money spent (e.g., rent, food, transport, entertainment).

Fixed Expenses: Expenses that are relatively constant each month (e.g., rent, loan repayments).

Variable Expenses: Expenses that fluctuate from month to month (e.g., food, entertainment, electricity).

Savings: Money set aside for future goals (e.g., education, emergencies, retirement).

Creating a Budget: Calculate your income: Determine your total income for the month.

Track your expenses: Record all your expenses for a month. Use a notebook, spreadsheet, or budgeting app.

Categorize your expenses: Group your expenses into categories (e.g., housing, food, transport).

Analyze your expenses: Identify areas where you are spending too much money.

Create a budget: Allocate your income to different categories based on your priorities.

Track your progress: Monitor your spending and adjust your budget as needed.

Example 5: Creating a Simple Budget Let's say Maria earns R4,000 per month.

Her expenses are as follows: Rent: R1,500 Food: R1,000 Transport: R500 Electricity: R300 Entertainment: R200 Savings: R500 Her budget would look like this: Income: R4,000 Expenses: Rent: R1,500 Food: R1,000 Transport: R500 Electricity: R300 Entertainment: R200 Savings: R500 Total Expenses: R4,000 Balance: R0 Why it's important: A balanced budget (where income equals expenses) is a starting point. Ideally, you want to have a surplus (income greater than expenses) so you can save more and achieve your financial goals faster. Guided Practice (With Solutions)

Question 1: John invests R8,000 in a fixed deposit account that pays simple interest at a rate of 9% per year.