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 for loans and investments.
• Compare different loan and investment options.
• Understand the power and danger of compounding.
• Apply these skills to make informed financial decisions.

Lesson summary

This week, we delve into the crucial world of finance, specifically focusing on compound interest, loans, and investments. Understanding these concepts is absolutely vital for your financial well-being, both now and in the future. In South Africa, where access to financial services and responsible financial planning are key to overcoming inequality, mastering these skills is even more important. From saving for tertiary education or a deposit on a house, to understanding the implications of taking out a loan or investing in a business, this knowledge empowers you to make informed financial decisions.

Lesson notes

2.1 Compound Interest: Compound interest is the interest earned not only on the principal amount but also on the accumulated interest from previous periods. In simpler terms, it's "interest on interest." This can work in your favor when saving or investing, but it can also be detrimental when taking out loans.

The formula for compound interest is: 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 interest rate per compounding period (expressed as a decimal; e.g., 10% = 0.10). This is crucial. If the annual interest is 12% compounded monthly, then 'i' is 0.12/12 = 0.01 n = the number of compounding periods (how many times the interest is compounded during the period)

Important Considerations for 'i' and 'n': Annually Compounded: Interest is calculated once per year. 'i' is the annual interest rate, and 'n' is the number of years.

Semi-Annually Compounded: Interest is calculated twice per year. 'i' is the annual interest rate divided by 2, and 'n' is the number of years multiplied by

2. Quarterly Compounded: Interest is calculated four times per year. 'i' is the annual interest rate divided by 4, and 'n' is the number of years multiplied by

4. Monthly Compounded: Interest is calculated twelve times per year. 'i' is the annual interest rate divided by 12, and 'n' is the number of years multiplied by

1

2. Example 1: Savings Account Thando invests R5,000 in a savings account that pays 8% interest per year, compounded annually. How much will she have after 5 years? P = R5,000 i = 0.08 n = 5 A = 5000(1 + 0.08)^5 A = 5000(1.08)^5 A = 5000 * 1.469328077 A = R7,346.64 (rounded to two decimal places) Thando will have R7,346.64 after 5 years.

Example 2: Loan Repayment Sipho takes out a personal loan of R10,000 at an interest rate of 18% per year, compounded monthly, to start a small spaza shop. How much will he owe after 1 year if he makes no repayments? P = R10,000 i = 0.18 / 12 = 0.015 (monthly interest rate) n = 1 12 = 12 (number of months) A = 10000(1 + 0.015)^12 A = 10000(1.015)^12 A = 10000 * 1.195618171 A = R11,956.18 (rounded to two decimal places) Sipho will owe R11,956.18 after 1 year. This highlights the rapid increase in debt due to compounding interest, especially at higher rates. 2.2 Loans: Loans are amounts of money borrowed from a lender (e.g., a bank, credit union, or microfinance institution) that must be repaid over a specified period, usually with interest. Understanding the interest rate, compounding period, and repayment terms is crucial for managing debt responsibly. Types of Loans (examples in the South African Context): Personal Loans: Used for various purposes, often with higher interest rates.

Student Loans (NSFAS): Government-sponsored loans for tertiary education, often with favorable interest rates and repayment terms.

Home Loans (Mortgages): Loans to purchase property, secured by the property itself.

Car Loans: Loans to purchase vehicles, secured by the vehicle.

Microloans: Small loans, often with higher interest rates, targeted at small businesses or individuals with limited access to traditional banking. 2.3 Investments: Investments are assets purchased with the intention of generating income or appreciation in value. Compound interest plays a significant role in the growth of investments over time. Types of Investments (examples in the South African Context): Savings Accounts: Low-risk accounts that offer interest on deposits.

Fixed Deposits: Deposits held for a fixed period, offering a higher interest rate than savings accounts.

Unit Trusts (Mutual Funds): Collections of stocks, bonds, or other assets managed by professionals.

Shares (Stocks): Ownership stakes in companies, offering the potential for high returns but also carrying higher risk. Consider companies listed on the JSE (Johannesburg Stock Exchange).

Bonds: Debt securities issued by governments or corporations, offering fixed interest payments.

Retirement Annuities (RAs): Tax-advantaged investments designed for retirement savings.

Property: Investment in real estate, offering potential rental income and appreciation in value. 2.4 The Power (and Danger) of Compounding: Compounding is a powerful tool, but its effects can be either positive or negative depending on whether you are saving or borrowing.

Saving/Investing: The earlier you start, the more time your money has to grow through compounding. Even small amounts invested regularly can accumulate significantly over long periods. This is the "power of compounding" working in your favor.

Borrowing: High interest rates and long repayment periods can lead to a significant increase in the total amount owed due to compounding. This is the "danger of compounding" working against you. Guided Practice (With Solutions)

Question 1: Zanele invests R2,000 in a fixed deposit account that earns 6% interest per year, compounded quarterly. How much will she have after 3 years?