Lesson Notes By Weeks and Term v5 - Grade 11

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 compound interest on investments and loans.
• Compare different loan options.
• Analyze the impact of inflation on investments.
• Explain basic investment options in South Africa.
• Make informed decisions about borrowing and investing.

Lesson summary

This week, we delve deeper into the world of finance, focusing specifically on compound interest, loans, and investments. Understanding these concepts is crucial for making informed financial decisions throughout your life. Whether you're saving for tertiary education, buying a car, or planning for retirement, a solid grasp of compound interest, loans, and investments is essential for financial success and security. In the South African context, where economic inequalities exist and financial literacy is vital for upward mobility, mastering these skills is even more critical.

Lesson notes

Compound Interest Compound interest is often described as "interest on interest." Unlike simple interest, where interest is calculated only on the principal amount, compound interest is calculated on the principal amount plus any accumulated interest from previous periods. This means your money grows faster over time.

Formula: A = P(1 + i)^n Where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) i = the annual interest rate (as a decimal) n = the number of times that interest is compounded per year the number of years the money is invested or borrowed for. If interest is calculated monthly for 5 years, n = 12 * 5 =

6

0. Example 1: Savings Account Thando invests R5,000 in a savings account that pays an annual interest rate of 8% compounded annually. How much will Thando have in the account after 5 years? P = R5,000 i = 8% = 0.08 n = 5 A = 5000(1 + 0.08)^5 A = 5000(1.08)^5 A = 5000(1.469328) A = R7,346.64 Therefore, Thando will have R7,346.64 in the account after 5 years.

Example 2: Loan Repayments Sipho takes out a loan of R20,000 to buy a used car. The loan has an annual interest rate of 12% compounded monthly, and Sipho will repay the loan over 3 years. What is the total amount Sipho will repay? P = R20,000 i = 12%/12 = 0.01 (monthly interest rate) n = 3 years 12 months/year = 36 A = 20000(1 + 0.01)^36 A = 20000(1.01)^36 A = 20000(1.430768) A = R28,615.36 Therefore, Sipho will repay a total of R28,615.36 over 3 years.

Note: We haven't calculated the monthly repayments here - just the total amount paid back. Understanding Loans A loan is an amount of money borrowed from a lender (like a bank or financial institution) that must be repaid over time, usually with interest. Different types of loans include personal loans, car loans, home loans (mortgages), and student loans. Factors to consider when evaluating a loan include: Interest Rate: The percentage charged by the lender for borrowing the money. Lower interest rates mean lower overall costs.

Repayment Term: The length of time you have to repay the loan. Shorter terms mean higher monthly payments but lower overall interest paid. Longer terms mean lower monthly payments but higher overall interest paid.

Fees: Additional charges associated with the loan, such as origination fees, late payment fees, etc.

Total Cost: The total amount you will pay back, including principal and interest. This is the most important factor to consider.

Example 3: Comparing Loan Options Lerato wants to borrow R50,

0

0

0. Bank A offers a loan at 10% interest compounded annually over 5 years. Bank B offers a loan at 9% interest compounded annually over 6 years. Which loan is cheaper overall?

Bank A: P = R50,000 i = 0.10 n = 5 A = 50000(1 + 0.10)^5 A = 50000(1.10)^5 A = 50000(1.61051) A = R80,525.50 Bank B: P = R50,000 i = 0.09 n = 6 A = 50000(1 + 0.09)^6 A = 50000(1.09)^6 A = 50000(1.67710) A = R83,855.00 Although Bank B has a lower interest rate, the longer repayment term results in a higher total cost. Bank A is the cheaper option. Investments An investment is an asset or item acquired with the goal of generating income or appreciation. Common investment options in South Africa include: Savings Accounts: Low-risk, low-return options ideal for short-term savings.

Fixed Deposits: Offer higher interest rates than savings accounts but require you to lock in your money for a specific period.

Unit Trusts (Mutual Funds): Pools of money from multiple investors managed by professionals. Offer diversification and potential for higher returns but also carry more risk.

Shares (Stocks): Represent ownership in a company. Offer the potential for high returns but also carry significant risk.

Property: Investing in real estate can generate income through rental or appreciation in value. Inflation Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. It is crucial to consider inflation when evaluating the real return on investments. The real return is the return on an investment after accounting for inflation. Real Return ≈ Nominal Return - Inflation Rate Example 4: An investment yields a nominal return of 10% per year. The inflation rate is 6%. What is the real return? Real Return ≈ 10% - 6% = 4% This means that although the investment grew by 10%, the purchasing power of the money only increased by 4% due to inflation. Guided Practice (With Solutions)

Question 1: Zola invests R10,000 in a fixed deposit account that pays 7% interest compounded annually. How much will she have after 3 years?

Solution: P = R10,000 i = 0.07 n = 3 A = 10000(1 + 0.07)^3 A = 10000(1.07)^3 A = 10000(1.225043) A = R12,250.43 Zola will have R12,250.43 after 3 years.

Question 2: Peter borrows R25,000 for renovations at an interest rate of 15% compounded monthly. He plans to repay the loan over 4 years. Calculate the total repayment amount.