Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate compound interest on investments and loans.
• Compare different loan and investment options.
• Analyse the impact of inflation on money.
• Calculate the total cost of a loan.

Lesson summary

In Week 5, we delve deeper into the crucial topic of Finance, specifically focusing on compound interest, loans, and investments. This is an area that directly impacts your future financial well-being. Understanding these concepts will empower you to make informed decisions about saving, borrowing, and investing money, crucial skills for navigating the South African economy. From understanding stokvels and loan sharks to planning for higher education and retirement, these mathematical literacy skills provide a foundation for financial stability. It is not enough to simply perform calculations; you must understand the implications of these calculations for real life.

Lesson notes

2.1 Compound Interest: The Power of Growth (or Debt) What is Compound Interest? Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. In simpler terms, it's "interest on interest." This makes your money grow faster than simple interest, because you earn interest not only on the original amount but also on the interest itself.

However, it can also make loans grow faster!

The Compound Interest Formula: 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 period (as a decimal; e.g., 10% = 0.10) n = the number of periods the money is invested or borrowed for Example 1: Investing in a Fixed Deposit Thando invests R5,000 in a fixed deposit account that pays 8% interest per year, compounded annually. How much will she have after 5 years?

Solution: P = R5,000 i = 8% = 0.08 n = 5 years A = R5,000 (1 + 0.08) 5 A = R5,000 (1.08) 5 A = R5,000 * 1.469328 A = R7,346.64 Therefore, Thando will have R7,346.64 after 5 years.

Example 2: Compounding Frequency Now, let's say the interest in Example 1 is compounded quarterly. This means the interest is calculated and added to the principal 4 times a year. P = R5,000 i = 8% per year / 4 = 2% per quarter = 0.02 n = 5 years 4 quarters/year = 20 quarters A = R5,000 (1 + 0.02) 20 A = R5,000 (1.02) 20 A = R5,000 * 1.485947 A = R7,429.74 Therefore, compounding quarterly resulted in a higher return (R7,429.74) than compounding annually (R7,346.64). This highlights the importance of compounding frequency.

Example 3: Loan Repayments Sipho takes out a loan of R20,000 to start a small business. The interest rate is 15% per year, compounded monthly. He plans to repay the loan over 3 years. Calculate the total amount he will have to repay (ignoring monthly payments for now, focusing on the compounding amount owed). P = R20,000 i = 15% per year / 12 = 1.25% per month = 0.0125 n = 3 years 12 months/year = 36 months A = R20,000 (1 + 0.0125) 36 A = R20,000 (1.0125) 36 A = R20,000 * 1.563757 A = R31,275.14 Therefore, Sipho will owe R31,275.14 after 3 years, before considering his monthly payments. This illustrates how interest accumulates on loans. The calculation of monthly repayment amount is more complex and involves another formula (loan amortization), but this calculation gives us a basic understanding of how compound interest impacts loans. 2.2 Comparing Loan Options When considering a loan, it's crucial to compare different options.

Key factors include: Interest Rate: The percentage charged for borrowing money. Lower is generally better.

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

Fees and Charges: Look out for initiation fees, service fees, insurance costs, and penalties for late payments. These add to the overall cost of the loan.

Security/Collateral: Some loans require you to provide collateral (e.g., your car or house). If you can't repay the loan, the lender can seize the collateral. It's important to remember the implications of borrowing from informal lenders ("loan sharks") that charge exorbitant interest rates. 2.3 Evaluating Investment Options Different investments carry different levels of risk and potential return: Savings Accounts/Fixed Deposits: Low risk, low return. Good for short-term savings.

Unit Trusts: Moderate risk, moderate return. Involve investing in a portfolio of shares or bonds.

Shares (Stocks): Higher risk, potentially higher return. You own a small piece of a company. Share prices can fluctuate significantly.

Property: Can be a good long-term investment, but requires significant capital and involves risks such as fluctuating property values and tenant issues.

Bonds: Debt instruments issued by governments or corporations. Generally considered less risky than shares.

Consider the following factors: Risk Tolerance: How comfortable are you with the possibility of losing money?

Time Horizon: How long do you plan to invest the money? Longer time horizons allow for higher-risk investments.

Investment Goals: What are you saving for? (e.g., retirement, education, a down payment on a house) Remember that "high risk, high reward" often comes with "high risk, high loss". Always research thoroughly and consider seeking professional financial advice. 2.4 The Impact of Inflation Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. Inflation erodes the value of your money over time.

Example: Let's say you have R100 today. If inflation is 6% per year, in one year, you'll need R106 to buy the same goods and services that R100 buys today.