Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate simple interest and future value.
• Understand the impact of inflation on prices.
• Develop a basic personal budget.
• Analyse financial information and make informed decisions.

Lesson summary

This week, we delve into the crucial aspects of personal finance: simple interest, inflation, and budgeting. Understanding these concepts is vital for making informed financial decisions throughout your life. Whether it's saving for further education, buying a car, starting a small business, or simply managing your monthly expenses, a grasp of these principles is essential, particularly in the South African context, where socio-economic challenges demand careful financial planning. Many South African families rely on careful budgeting and understanding interest rates on loans and savings to navigate the economic landscape.

Lesson notes

Simple Interest Simple interest is a method of calculating interest where the interest earned only applies to the original principal amount. It's a straightforward way to understand how money grows over time, especially in short-term investments or loans.

Formula: I = P r t Where: I = Interest earned P = Principal (the initial amount of money) r = Interest rate (expressed as a decimal) t = Time (in years)

Future Value (A): The total amount (principal + interest) after a certain period. A = P + I or A = P(1 + rt)

Example 1: Saving for a Matric Dance Sarah wants to save R5000 for her Matric dance. Her father offers to give her an interest free loan, and she intends to deposit this R5000 into a simple interest savings account for 2 years with an interest rate of 7.5% per annum. a) What will be the simple interest earned? b) What is the total amount Sarah has after 2 years?

Solution: a) I = P r t I = 5000 0.075 2 I = R750 b) A = P + I A = 5000 + 750 A = R5750 Explanation: The formula is applied directly by substituting the values. Note that the interest rate is converted to a decimal by dividing by

1

0

0. The total amount is the original principal plus the interest earned.

Example 2: Taking out a Small Loan Thabo needs to borrow R2000 to buy a used bicycle to get to his part-time job. He borrows the money from a friend who charges him 10% simple interest per annum. Thabo agrees to repay the loan in 18 months (1.5 years). How much will Thabo have to repay in total?

Solution: A = P(1 + rt) A = 2000(1 + 0.10 * 1.5) A = 2000(1 + 0.15) A = 2000(1.15) A = R2300 Explanation: Here we directly calculated the total amount Thabo needs to repay, which included the original R2000 and the accumulated interest. The time is 18/12=1.5 since simple interest calculations are yearly. 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, it means that your money buys less over time. The South African Reserve Bank (SARB) targets inflation within a range of 3-6%.

Formula: New Price = Original 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 annual inflation rate is 6%, what will the approximate price of a loaf of bread be in 3 years?

Solution: New Price = 15 * (1 + 0.06)^3 New Price = 15 * (1.06)^3 New Price = 15 * 1.191016 New Price = R17.87 (approximately)

Explanation: The original price is multiplied by (1 + inflation rate) raised to the power of the number of years. This shows how the price escalates over time due to inflation.

Example 4: Salary and Inflation Zola earns R8000 per month. If the inflation rate is 5% per year, and Zola's salary stays the same, what is the equivalent purchasing power of her salary in 2 years? This question requires understanding that the R8000 salary will buy less in 2 years due to inflation. To find the equivalent purchasing power, we determine how much more something that originally cost R1 now costs in 2 years, and then divide the original salary by that amount. Price Factor = (1 + 0.05)^2 = (1.05)^2 = 1.1025 New Price = 8000/1.1025 = R7256.24 In 2 years, Zola's R8000 salary will only be able to purchase the equivalent of what R7256.24 can buy now. Budgeting A budget is a plan for how you will spend your money. It helps you track your income and expenses, identify areas where you can save, and achieve your financial goals. Budgeting is crucial for financial stability and planning for the future.

Key Components: Income: Money you receive (e.g., salary, allowance).

Expenses: Money you spend.

These can be: Fixed Expenses:* Consistent amounts each month (e.g., rent, loan repayments).

Variable Expenses:* Amounts that change each month (e.g., groceries, entertainment, transport).

Savings: Money you set aside for future goals (e.g., education, down payment on a house).

Example 5: Creating a Simple Budget Sipho earns R2500 per month from his part-time job.

His expenses are: Transport: R400 Food: R800 Entertainment: R300 Cellphone: R200 Clothes: R300 Create a budget for Sipho and determine how much he can save each month.

Solution: Income: R2500 Expenses: Transport: R400 Food: R800 Entertainment: R300 Cellphone: R200 Clothes: R300 Total Expenses: R400 + R800 + R300 + R200 + R300 = R2000 Savings: R2500 (Income) - R2000 (Expenses) = R500 Explanation: This is a basic budget, subtracting total expenses from total income to calculate savings. Sipho can save R500 each month if he sticks to his budget. Guided Practice (With Solutions)

Question 1: Calculate the simple interest earned on an investment of R8000 at an interest rate of 9% per annum for 4 years. What is the final amount of the investment?

Solution: I = P r t I = 8000 0.09 4 I = R2880 A = P + I A = 8000 + 2880 A = R10880

Commentary: We first calculate the simple interest using the formula.