Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate and compare the total cost of different loans.
• Determine the future value of investments with varying interest rates and periods.
• Analyze and compare different investment opportunities.
• Interpret the effects of interest rate changes on loans and investments.

Lesson summary

Welcome back to Finance! This week, we're diving deeper into the world of loans and investments. Understanding these concepts is absolutely crucial for making smart financial decisions throughout your life. Whether you're thinking about buying a car, furthering your education, or saving for a future goal, the principles we'll cover will empower you to make informed choices. Many South Africans struggle with debt due to a lack of financial literacy, or miss out on opportunities to grow their wealth because they don't understand investments. This week, we aim to combat that.

Lesson notes

Loans: A loan is a sum of money borrowed from a lender (e.g., a bank, credit union) that must be repaid over a set period, usually with interest. The principal is the original amount borrowed. The interest is the cost of borrowing the money. The term is the length of time you have to repay the loan.

Simple Interest: Interest calculated only on the principal amount.

The formula is: `Simple Interest = Principal x Interest Rate x Time (in years)`

Example:* Sipho borrows R5,000 at a simple interest rate of 10% per year for 3 years. The simple interest is R5,000 x 0.10 x 3 = R1,

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0. He'll repay a total of R5,000 + R1,500 = R6,

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0. Simple interest is generally used for very short-term loans.

Compound Interest: Interest calculated on the principal and any accumulated interest. This means you earn interest on your interest!

The formula is: `Future Value (FV) = Principal x (1 + Interest Rate/n)^(n x Time)` where n is the number of times interest is compounded per year.

Example:* Zinhle invests R10,000 at a compound interest rate of 8% per year, compounded annually, for 5 years. FV = R10,000 x (1 + 0.08/1)^(1 x 5) = R10,000 x (1.08)^5 = R10,000 x 1.4693 = R14,693.

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8. She earns R4,693.28 in interest. Now, let's say it was compounded quarterly. Then n =

4. FV = R10,000 x (1 + 0.08/4)^(4 x 5) = R10,000 x (1.02)^20 = R10,000 x 1.4859 = R14,859.

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7. Compounding more frequently results in a higher return.

Loan Repayments: Most loans are repaid in regular installments (e.g., monthly). Calculating these repayments can be complex, but often involves using online loan calculators.

Factors affecting repayments include: the loan amount, the interest rate, and the repayment period. A longer repayment period means lower monthly payments, but higher overall interest paid.

Example:* Ayanda wants to buy a car for R150,

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0. Bank A offers a loan at 12% interest over 5 years. Bank B offers a loan at 11.5% interest over 6 years. She should use an online loan calculator to determine the monthly payments and total interest paid for each option to make an informed decision. Bank B might have lower monthly repayments, but the total interest paid over 6 years might be higher than with Bank

A. Investments: Putting money into something (e.g., stocks, bonds, property, unit trusts) with the expectation of generating income or profit. Simple vs.

Compound Interest: As explained above, compound interest is generally more beneficial for investments because it allows your money to grow exponentially over time.

Inflation: The rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. It's crucial to consider inflation when evaluating investments. A return of 5% might sound good, but if inflation is 4%, your real return is only 1%. The real rate of return can be approximated by `Real interest rate = Nominal interest rate – Inflation rate`. Risk vs.

Return: Generally, higher potential returns come with higher risk. Low-risk investments like government bonds usually have lower returns than higher-risk investments like stocks. Diversification (spreading your investments across different asset classes) is a key strategy to manage risk.

Example:* Thabo invests R20,000 in a unit trust that promises an average annual return of 15%.

However, this return is not guaranteed, and the value of the investment could fluctuate. He needs to consider his risk tolerance and investment time horizon (how long he plans to invest the money) before making this investment.

Another example: Precious invests R5000 in a fixed deposit account with a 7% annual interest rate. She needs to consider the inflation rate to determine the real rate of return on her investment. If inflation is 5%, the real rate of return is only 2%. Guided Practice (With Solutions)

Question 1: Lebo wants to borrow R80,000 to start a small business. Bank A offers a loan at 14% simple interest per year for 4 years. Bank B offers a loan at 12% compound interest per year, compounded annually, for 4 years. Calculate the total amount Lebo would need to repay for each loan. Which loan is cheaper?

Solution: Bank A (Simple Interest):* Interest = R80,000 x 0.14 x 4 = R44,800 Total Repayment = R80,000 + R44,800 = R124,800 Bank B (Compound Interest):* FV = R80,000 x (1 + 0.12/1)^(1 x 4) = R80,000 x (1.12)^4 = R80,000 x 1.5735 = R125,884.80 Comparison:* Bank A is cheaper (R124,800 < R125,884.80).

Commentary:* In this case, the simple interest loan is cheaper despite the higher interest rate because it's calculated only on the original principal. The power of compounding makes Bank B more expensive.

Question 2: Nandi invests R15,000 in a savings account that pays 6% interest per year, compounded monthly. How much will she have in the account after 6 years?