Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate simple interest on loans or investments.
• Explain and calculate the impact of inflation.
• Develop a personal budget.
• Analyse the relationship between interest, inflation, and money's value.
• Compare different budgeting methods.

Lesson summary

This week, we delve into the crucial aspects of finance that directly impact your life: simple interest, inflation, and budgeting. Understanding these concepts is essential for making informed financial decisions, whether you're saving for further education, planning your future career, or managing your personal finances. In South Africa, where economic inequalities persist, a solid grasp of these financial principles empowers you to navigate the challenges and opportunities of the financial landscape. You will learn how interest works, how inflation erodes your money's value, and how to create a budget that aligns with your financial goals.

Lesson notes

2.1 Simple Interest Simple interest is a straightforward way of calculating interest earned or paid on a principal amount.

The formula for simple interest is: Simple Interest (SI) = P × r × t Where: P = Principal amount (the initial amount of money) r = Interest rate (expressed as a decimal, e.g., 5% = 0.05) t = Time (usually in years) The total amount to be repaid (or the total value of the investment) is: Total Amount (A) = P + SI Example 1: Sipho invests R2,000 in a fixed deposit account that pays a simple interest rate of 8% per annum. He leaves the money in the account for 3 years. Calculate the simple interest earned and the total amount Sipho will have at the end of 3 years. P = R2,000 r = 8% = 0.08 t = 3 years SI = R2,000 × 0.08 × 3 = R480 A = R2,000 + R480 = R2,480 Sipho will earn R480 in simple interest and will have a total of R2,480 after 3 years.

Example 2: Thandi borrows R5,000 from a micro-lender at a simple interest rate of 20% per annum. She needs to repay the loan in 18 months (1.5 years). Calculate the total amount Thandi needs to repay. P = R5,000 r = 20% = 0.20 t = 1.5 years SI = R5,000 × 0.20 × 1.5 = R1,500 A = R5,000 + R1,500 = R6,500 Thandi needs to repay a total of R6,

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0. Note the high interest rate; micro-lenders often charge high rates due to the risk involved. It's important to compare different loan options before borrowing. 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 simple terms, it means that your money buys less than it did before. Inflation is usually expressed as a percentage. The South African Reserve Bank (SARB) targets an inflation rate between 3% and 6%. To calculate the future price of an item due to inflation, we can use a similar formula to simple interest: Future Price (FP) = Current Price (CP) × (1 + Inflation Rate)^t Where: CP = Current Price Inflation Rate = Inflation Rate (expressed as a decimal) t = Number of years Example 3: A loaf of bread currently costs R

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5. If the inflation rate is 6% per annum, what will be the approximate price of the loaf of bread in 2 years' time? CP = R15 Inflation Rate = 6% = 0.06 t = 2 years FP = R15 × (1 + 0.06)^2 = R15 × (1.06)^2 = R15 × 1.1236 = R16.85 (approximately) The loaf of bread will cost approximately R16.85 in 2 years' time.

Real Value of Money after Inflation: To determine the real value (purchasing power) of money after inflation, we can use the following formula: Real Value = Nominal Value / (1 + Inflation Rate)^t Where: Nominal Value = The face value of the money Inflation Rate = The inflation rate (as a decimal) t = Number of years Example 4: You receive R1,000 as a gift. If the inflation rate is 5% per annum, what will be the real value of that R1,000 in 3 years' time? Nominal Value = R1,000 Inflation Rate = 5% = 0.05 t = 3 years Real Value = R1,000 / (1 + 0.05)^3 = R1,000 / (1.05)^3 = R1,000 / 1.157625 = R863.84 (approximately) The real value of R1,000 in 3 years' time will be approximately R863.

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4. This means that due to inflation, the R1,000 will only be able to buy what R863.84 can buy today. 2.3 Budgeting A budget is a plan of how you will spend your money over a period of time (e.g., a month). It helps you to track your income and expenses, make informed spending decisions, and achieve your financial goals.

Steps to creating a budget: Calculate your income: List all sources of income (e.g., wages, allowances, grants).

Track your expenses: Monitor where your money goes. Categorize your expenses into fixed (e.g., rent, transport) and variable (e.g., entertainment, food).

Create your budget: Allocate your income to different expense categories.

Compare income and expenses: Determine if you have a surplus (more income than expenses) or a deficit (more expenses than income).

Adjust your budget: If you have a deficit, identify areas where you can reduce your spending.

Review and revise regularly: Your budget should be a living document that you update as your circumstances change.

Example 5: Zanele earns R2,500 per month from a part-time job.

Her monthly expenses are: Transport: R500 Food: R800 Airtime: R200 Entertainment: R400 Savings: R600 Let's create a budget for Zanele: Income: R2,500 Expenses: Transport: R500 Food: R800 Airtime: R200 Entertainment: R400 Savings: R600 Total Expenses: R2,500 Zanele's income equals her expenses, resulting in a balanced budget. If Zanele wanted to save more, she would need to reduce her spending in other categories like entertainment or food. Guided Practice (With Solutions)

Question 1: John invests R8,000 in a savings account that pays a simple interest rate of 7.5% per annum. How much interest will he earn after 5 years?

Solution: P = R8,000 r = 7.5% = 0.075 t = 5 years SI = R8,000 × 0.075 × 5 = R3,000 John will earn R3,000 in simple interest.

Question 2: A pair of jeans currently costs R450.