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.
• Evaluate different investment options.
• Calculate the total cost of a loan.
• Make informed decisions about borrowing and investing.

Lesson summary

This week, we revisit fundamental concepts in finance, specifically loan and investment scenarios. This is crucial because understanding how loans work and how to make informed investment decisions directly impacts your financial well-being, enabling you to achieve your future goals. Whether it's buying a car, purchasing a home, or saving for retirement, sound financial literacy is an indispensable life skill. In the South African context, where many face financial challenges and are vulnerable to predatory lending practices, mastering these skills is even more critical.

Lesson notes

2.1 Simple Interest: Simple interest is calculated only on the principal amount of a loan or investment.

The formula for simple interest is: Simple Interest (SI) = P × R × T Where: P = Principal amount (the initial amount borrowed or invested) R = Interest rate (expressed as a decimal) T = Time period (in years)

Example 1: Nomusa invests R5,000 in a savings account that offers a simple interest rate of 6% per annum. How much interest will she earn after 3 years? What will be the total amount in the account after 3 years? P = R5,000 R = 6% = 0.06 T = 3 years SI = R5,000 × 0.06 × 3 = R900 Total amount after 3 years = Principal + Interest = R5,000 + R900 = R5,900 2.2 Compound Interest: Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. This means that you earn interest on your interest, leading to faster growth over time.

The formula for compound interest is: A = P (1 + R/n)^(nT)

Where: A = Future value of the investment/loan, including interest P = Principal investment amount (the initial deposit or loan amount) R = Annual interest rate (as a decimal) n = Number of times that interest is compounded per year T = Number of years the money is invested or borrowed for Example 2: Sipho invests R8,000 in a fixed deposit account that offers a compound interest rate of 8% per annum, compounded quarterly. How much will he have after 5 years? P = R8,000 R = 8% = 0.08 n = 4 (compounded quarterly) T = 5 years A = R8,000 (1 + 0.08/4)^(4*5) A = R8,000 (1 + 0.02)^(20) A = R8,000 (1.02)^(20) A = R8,000 × 1.485947 A = R11,887.58 Therefore, Sipho will have R11,887.58 after 5 years. 2.3 Understanding Loan Options: Different loan options have varying interest rates, repayment terms, and fees. Understanding these differences is crucial for making informed borrowing decisions.

Key aspects to consider include: Interest Rate: The percentage charged on the loan amount. Can be fixed (remains constant throughout the loan term) or variable (fluctuates with market conditions).

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

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

Annual Percentage Rate (APR): The total cost of the loan, including the interest rate and all fees, expressed as an annual percentage. APR provides a standardized way to compare different loan offers.

Example 3: Comparing Loan Options Zandile wants to borrow R20,000 for a small business.

She has two loan options: Loan A: Interest rate of 12% per annum, compounded monthly, with a repayment term of 3 years.

Loan B: Interest rate of 11% per annum, compounded annually, with a repayment term of 4 years. Which loan is the better option? We need to calculate the total cost of each loan.

Loan A: First, calculate the monthly interest rate: 12%/12 = 1% = 0.01 Then, calculate the number of months: 3 years * 12 months/year = 36 months. We will use a loan amortization formula (this is beyond basic compound interest, but important for loans): M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1] Where: M = Monthly Payment P = Principal Loan Amount i = Monthly Interest Rate n = Number of months M = 20000 [0.01(1 + 0.01)^36] / [(1 + 0.01)^36 - 1] M = 20000 [0.01 * 1.43076878] / [1.43076878 - 1] M = 20000 [0.0143076878] / [0.43076878] M = 20000 * 0.033214 M = R664.28 Total cost = R664.28 * 36 months = R23,914.08 Total interest paid = R23,914.08 - R20,000 = R3,914.08 Loan B: We use the same loan amortization formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1] Where: M = Annual Payment P = Principal Loan Amount i = Annual Interest Rate n = Number of years M = 20000 [0.11(1 + 0.11)^4] / [(1 + 0.11)^4 - 1] M = 20000 [0.11 * 1.51807041] / [1.51807041 - 1] M = 20000 [0.1669877451] / [0.51807041] M = 20000 * 0.322323 M = R6,446.46 Total cost = R6,446.46 * 4 years = R25,785.84 Total interest paid = R25,785.84 - R20,000 = R5,785.84 Conclusion: Loan A is the better option because the total interest paid (R3,914.08) is less than the total interest paid for Loan B (R5,785.84). 2.4 Understanding Investment Options: Similar to loans, different investment options offer varying levels of risk and return.

Key aspects to consider include: Risk: The possibility of losing some or all of your investment. Higher-risk investments typically offer the potential for higher returns, but also carry a greater risk of loss.

Return: The profit you earn on your investment. Expressed as a percentage of the initial investment amount.

Liquidity: How easily you can access your money when you need it. Some investments, like savings accounts, are highly liquid, while others, like fixed deposits, may have restrictions on withdrawals.

Common Investment Options: Savings Accounts: Low-risk, low-return option. Highly liquid.