Lesson Notes By Weeks and Term v5 - Grade 12

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 monthly repayments on a loan.
• Calculate the future value of an investment using simple and compound interest.
• Compare different loan and investment options.
• Determine the impact of inflation on your money.

Lesson summary

This week, we're diving back into the world of loans and investments, which are crucial financial tools that affect everyone, from students managing bursaries to families buying homes. Understanding these concepts is vital for making informed financial decisions, planning for the future, and achieving financial security in South Africa's diverse economic landscape. We'll be building upon your Grade 11 knowledge, focusing on calculating and comparing loan repayments, understanding the power of compound interest in investments, and analyzing different investment options available in the South African market.

Lesson notes

2.1 Loans: Understanding the Basics A loan is a sum of money borrowed from a lender (e.g., a bank, credit union) that must be repaid over a specified period, usually with interest. Understanding loans involves several key components: Principal: The original amount of money borrowed.

Interest Rate: The percentage charged by the lender for the use of their money. This can be fixed (stays the same throughout the loan term) or variable (can change based on market conditions).

Loan Term: The length of time you have to repay the loan, usually expressed in months or years.

Repayment Schedule: The plan for repaying the loan, usually involving regular (e.g., monthly) payments.

Total Repayment: The total amount paid back to the lender, including the principal and all interest charges. Simple Interest vs.

Compound Interest (in Loans): While investments commonly use compound interest, loans typically calculate interest on a reducing balance. This means that interest is calculated on the outstanding principal amount after each payment. This is fairer to the borrower than calculating simple interest over the entire loan term on the initial principal.

Loan Repayment Formulas: The actual formula for calculating loan repayments is complex and often uses financial calculators or software.

However, understanding the principle is key. The higher the interest rate and the longer the loan term, the higher the total repayment will be.

Example 1: Understanding Interest on a Loan Zanele takes out a personal loan of R20,000 from a bank. The interest rate is 15% per annum, compounded monthly, and the loan term is 3 years.

Principal (P): R20,000 Interest Rate (i): 15% per annum = 0.15 per year = 0.15/12 = 0.0125 per month Loan Term (n): 3 years = 3 12 = 36 months While we won't calculate the precise monthly repayment using the formula here (as that's beyond the scope of a textbook-replacement explanation focusing on understanding), we can illustrate how interest accumulates. In the first month, interest is calculated on R20,

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0. The interest for the first month would be: R20,000 0.0125 = R

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0. Zanele's first monthly payment would need to cover this R250 interest plus a portion of the R20,000 principal. As she makes payments, the principal balance decreases, and therefore the interest charged each month also decreases. 2.2 Investments: Growing Your Money An investment is the act of allocating money with the expectation of receiving a future benefit or profit.

Understanding investments involves: Principal: The initial amount of money invested.

Interest Rate (or Rate of Return): The percentage earned on the investment, expressed as an annual rate.

Investment Term: The length of time the money is invested.

Simple Interest: Interest calculated only on the principal amount.

Compound Interest: Interest calculated on the principal amount plus any accumulated interest. This is the "interest on interest" effect and is key to long-term wealth accumulation.

Regular Deposits: Contributing additional money to the investment at regular intervals (e.g., monthly).

Simple Interest Formula: A = P(1 + rt)

Where: A = Amount (future value) P = Principal (initial investment) r = Interest rate (as a decimal) t = Time (in years)

Compound Interest Formula: A = P(1 + i)^n Where: A = Amount (future value) P = Principal (initial investment) i = Interest rate per compounding period (as a decimal) n = Number of compounding periods Compound Interest with Regular Deposits (Future Value of an Annuity): This formula is more complex and is generally not tested directly, but understanding the concept is important. Many investments involve regular contributions (e.g., monthly savings plans). Each deposit earns interest, compounding over time. The formula for the future value of an ordinary annuity (deposits made at the end of each period) is: FV = P * (((1 + i)^n - 1) / i)

Where: FV = Future Value of the annuity P = Periodic payment (deposit amount) i = Interest rate per period n = Number of periods Example 2: Simple Interest Calculation Sipho invests R5,000 in a fixed deposit account that pays simple interest at a rate of 8% per annum for 5 years. Calculate the future value of his investment. P = R5,000 r = 8% = 0.08 t = 5 years A = P(1 + rt) A = 5000(1 + 0.08 * 5) A = 5000(1 + 0.4) A = 5000(1.4) A = R7,000 Therefore, the future value of Sipho's investment after 5 years will be R7,

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0. Example 3: Compound Interest Calculation Thandi invests R2,000 in a savings account that pays compound interest at a rate of 6% per annum, compounded annually, for 4 years. Calculate the future value of her investment. P = R2,000 i = 6% = 0.06 n = 4 years A = P(1 + i)^n A = 2000(1 + 0.06)^4 A = 2000(1.06)^4 A = 2000 * 1.26247696 A = R2,524.95 (rounded to two decimal places) Therefore, the future value of Thandi's investment after 4 years will be approximately R2,524.95.