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.
• Calculate future value of investments and present value of loans.
• Understand the impact of inflation.
• Analyze loan repayment schedules.

Lesson summary

This week, we delve back into the crucial world of loans and investments. Understanding these concepts is vital for your financial well-being, both now and in the future. South Africa has a complex financial landscape, and making informed decisions about borrowing money (loans) and growing your money (investments) can significantly impact your ability to achieve your financial goals, whether it's buying a car, paying for tertiary education, or securing your retirement. Poor financial decisions can lead to debt traps and hinder your long-term financial stability. We will revisit and reinforce concepts learned previously, applying them to more complex scenarios.

Lesson notes

2.1 Simple Interest: Simple interest is calculated only on the principal amount (the initial amount borrowed or invested).

Formula: Simple Interest (SI) = P × r × t Where: P = Principal amount r = Interest rate (expressed as a decimal) t = Time period (in years) Total Amount (A) = P + SI Example 1: You invest R5,000 in a fixed deposit account that pays simple interest at a rate of 8% per year for 3 years. How much interest will you earn, and what will be the total amount in your account after 3 years? SI = R5,000 × 0.08 × 3 = R1,200 A = R5,000 + R1,200 = R6,200 Therefore, you will earn R1,200 in interest, and the total amount in your account will be 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.

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 period (in years)

Example 2: You invest R10,000 in an investment account that pays compound interest at a rate of 10% per year, compounded annually, for 5 years. What will be the value of your investment after 5 years? A = R10,000 (1 + 0.10/1)^(1*5) A = R10,000 (1.10)^5 A = R10,000 × 1.61051 A = R16,105.10 Therefore, the value of your investment after 5 years will be R16,105.

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0. Example 3: You take out a loan of R20,000 to start a small business. The interest rate is 15% per year, compounded monthly. You plan to repay the loan over 2 years. What is the total amount you will repay? A = R20,000 (1 + 0.15/12)^(12*2) A = R20,000 (1 + 0.0125)^(24) A = R20,000 (1.0125)^24 A = R20,000 × 1.3490 A = R26,980 Therefore, the total amount you will repay is R26,980. 2.3 Loan Repayment Schedules: Loan repayment schedules show the breakdown of each payment towards the principal and interest. This helps you understand how much of each payment is actually reducing the amount you owe. South African banks and lenders are required to provide these schedules.

Factors affecting loan repayments: Principal Amount: The larger the principal, the higher the repayments.

Interest Rate: Higher interest rates increase repayments.

Repayment Period: Longer repayment periods lower individual payments but increase the total interest paid.

Compounding Frequency: The more frequently interest is compounded, the higher the overall cost of the loan. 2.4 Inflation: Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. Understanding inflation is crucial when evaluating the real return on your investments. The "real return" is the return adjusted for inflation. Real Return = Nominal Return - Inflation Rate Example 4: You have an investment that earns a nominal return of 12% per year. The inflation rate is 6%. What is your real return? Real Return = 12% - 6% = 6% Even though your investment earned 12%, your purchasing power only increased by 6% after accounting for inflation. 2.5 Comparing Loan Options: Effective Interest Rate: When comparing loan options, it's important to consider the effective interest rate. This rate takes into account all fees and charges associated with the loan, providing a more accurate comparison than just looking at the nominal interest rate. Banks are legally required to show the Annual Percentage Rate (APR), which serves as the effective interest rate. Guided Practice (With Solutions)

Question 1: Sarah invests R8,000 in a savings account that pays simple interest at a rate of 7.5% per year. After 4 years, how much interest will she have earned?

Solution: SI = P × r × t SI = R8,000 × 0.075 × 4 SI = R2,400 Sarah will have earned R2,400 in interest.

Question 2: John borrows R15,000 to buy a motorcycle. The loan has an interest rate of 14% per year, compounded annually. He agrees to repay the loan in 3 years. What is the total amount he will repay?

Solution: A = P (1 + r/n)^(nt) A = R15,000 (1 + 0.14/1)^(1*3) A = R15,000 (1.14)^3 A = R15,000 × 1.481544 A = R22,223.16 John will repay a total of R22,223.

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6. Question 3: Thandi invests R25,000 in a unit trust that earns a nominal return of 15% per year. The inflation rate is 5%. What is her real rate of return?

Solution: Real Return = Nominal Return - Inflation Rate Real Return = 15% - 5% = 10% Thandi's real rate of return is 10%. Independent Practice (Questions Only) Calculate the simple interest earned on an investment of R12,000 at an interest rate of 9% per year for 5 years. Also, calculate the total amount at the end of the term. A loan of R30,000 is taken out at an interest rate of 16% per year, compounded monthly. If the loan is to be repaid over 4 years, what is the total amount that will be repaid? You invest R5,000 in an account that pays 11% interest compounded quarterly for 7 years. How much will you have at the end of the 7 years?