Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate simple and compound interest.
• Compare different loan options.
• Analyze the impact of inflation on investments.
• Evaluate investment options based on risk and return.
• Calculate total loan repayments and monthly instalments.

Lesson summary

This week, we delve deeper into the vital area of finance, specifically revisiting loan and investment scenarios. Understanding loans and investments is crucial for making informed financial decisions, whether it's securing a car loan, planning for higher education, or saving for retirement. In South Africa, many people face financial challenges due to a lack of financial literacy. By mastering these concepts, you will be empowered to manage your money effectively, avoid debt traps, and build a secure future for yourself and your family.

Lesson notes

2. 1.

Simple Interest: Simple interest is calculated only on the principal amount (the initial amount of money). It's a straightforward way to calculate interest, but it doesn't take into account the effect of compounding.

Formula: I = P r t Where: I = Simple Interest P = Principal Amount (the initial amount) r = Interest Rate (expressed as a decimal) t = Time (in years)

Example: Suppose you invest R5,000 in a savings account that offers a simple interest rate of 8% per year for 3 years.

Calculation: I = R5,000 0.08 3 = R1,200 Total Amount After 3 Years: R5,000 + R1,200 = R6,200 2.

2. Compound Interest: Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. This means you earn interest on your interest, leading to faster growth of your investment.

Formula: A = P (1 + r/n)^(nt)

Where: A = Amount after t years P = Principal Amount r = Interest Rate (expressed as a decimal) n = Number of times that interest is compounded per year t = Time (in years)

Example: Suppose you invest R5,000 in a fixed deposit account that offers a compound interest rate of 8% per year compounded annually for 3 years.

Calculation: A = R5,000 (1 + 0.08/1)^(1*3) A = R5,000 (1.08)^3 A = R5,000 * 1.259712 A = R6,298.56 Therefore, the total amount after 3 years will be R6,298.

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6. Important

Note: The more frequently interest is compounded (e.g., monthly, daily), the higher the final amount will be. 2.

3. Loans: A loan is an amount of money borrowed from a lender (e.g., a bank) that must be repaid over time, usually with interest. Common types of loans in South Africa include personal loans, home loans (mortgages), car loans, and student loans.

Key Factors Affecting Loan Repayments: Principal Amount: The original amount borrowed.

Interest Rate: The percentage charged by the lender for borrowing the money.

Repayment Period: The length of time you have to repay the loan.

Fees: Additional charges associated with the loan (e.g., application fees, service fees). 2.

4. Loan Calculations: Loan repayments are typically calculated using an amortization formula, which determines the monthly instalment required to repay the loan over a specific period. A simplified version of this concept can be calculated using compound interest principles.

However, the actual calculations used by banks are more complex. Estimating Monthly Repayments (Simplified): While the exact calculation is complex, understanding the principle can be achieved by using the compound interest formula in reverse and then dividing the total amount (A) by the number of months in the repayment period. This gives an estimated monthly repayment. This approach is valid for gaining a fundamental understanding.

Example: You want to take out a personal loan of R20,000 at an interest rate of 15% per year over 5 years. Calculate the total amount to be repaid (A): A = P(1 + r)^t A = R20,000(1 + 0.15)^5 A = R20,000(1.15)^5 A = R20,000 * 2.011357 A = R40,227.14 (This is the total amount to be paid back over the 5 years) Calculate the number of months in the repayment period: 5 years * 12 months/year = 60 months Calculate the estimated monthly repayment: R40,227.14 / 60 months = R670.45 (approximately) Therefore, your estimated monthly repayment would be R670.

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5. Important note: This is a simplified estimation. Banks use more complex amortization formulas for precise calculation. 2.

5. Inflation and Real Return: Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. In South Africa, the inflation rate is a key economic indicator. Inflation erodes the value of your money over time. Real Return = Nominal Return - Inflation Rate The nominal return is the stated interest rate or investment return. The real return is the return after accounting for inflation. It represents the actual increase in your purchasing power.

Example: You invest in an investment that yields a nominal return of 10% per year. The inflation rate is 6% per year. Real Return = 10% - 6% = 4% This means your investment is actually growing by only 4% in terms of purchasing power. 2.

6. Risk and Return: All investments involve some level of risk. Higher-risk investments typically offer the potential for higher returns, but also carry a greater chance of losing money. Lower-risk investments typically offer lower returns but are more stable. Examples of Investment Options in South Africa: Savings Accounts: Low risk, low return.

Fixed Deposits: Low to moderate risk, moderate return.

Unit Trusts (Mutual Funds): Moderate risk, moderate to high return. These are collections of shares managed by professionals.

Shares (Stocks): High risk, potentially high return. You are buying ownership in a company listed on the Johannesburg Stock Exchange (JSE).

Property: Moderate to high risk, potential for capital appreciation and rental income. 2.7.