Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate and compare simple and compound interest.
• Compare different loan options.
• Understand the impact of inflation on investments.
• Analyse investment scenarios.
• Use Time Value of Money principles.

Lesson summary

This week, we delve deeper into the critical world of personal finance, specifically revisiting loan and investment scenarios. Understanding how loans and investments work is absolutely essential for making informed financial decisions that will impact your life significantly. As South African citizens, navigating the complexities of loans (like student loans, vehicle financing, or home mortgages) and investments (such as fixed deposits, unit trusts, or even informal savings clubs known as stokvels) is vital for financial security and growth.

Lesson notes

Simple Interest vs.

Compound Interest 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 (in years)

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 over time.

Formula: Amount (A) = P (1 + R)^T Where: A = Total amount (principal + interest) P = Principal amount R = Interest rate (expressed as a decimal) T = Time (in years)

Example 1 (Simple Interest): Thando invests 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 she earn?

Solution: SI = P × R × T = R5,000 × 0.08 × 3 = R1,200 Thando will earn R1,200 in interest. Her total amount after 3 years will be R5,000 + R1,200 = R6,

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0. Example 2 (Compound Interest): Sipho invests R5,000 in a unit trust that pays compound interest at a rate of 8% per year for 3 years. How much will his investment be worth?

Solution: A = P (1 + R)^T = R5,000 (1 + 0.08)^3 = R5,000 (1.08)^3 = R5,000 × 1.259712 = R6,298.56 Sipho's investment will be worth R6,298.56 after 3 years. The compound interest earned is R6,298.56 - R5,000 = R1,298.56, which is more than the simple interest in the previous example.

Explanation: Compound interest is almost always more beneficial when investing or more costly when borrowing, especially over longer periods. The difference becomes significantly greater as the interest rate and time period increase. Comparing Loan Options When considering a loan, it’s important to compare different options beyond just the headline interest rate.

Key factors include: Interest Rate: The percentage charged on the loan amount. This can be fixed (remains the same throughout the loan) or variable (can change over time).

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

Fees: Look out for initiation fees, service fees, and early repayment penalties.

Total Cost of Credit: This is the total amount you will repay, including principal and interest. It’s the best way to compare different loan options.

Example 3: Zanele wants to buy a car.

She has two options: Option A: A personal loan from the bank at 12% interest per year, repayable over 5 years.

Option B: Hire purchase agreement from the dealership at 14% interest per year, repayable over 5 years. Let's assume the car costs R100,

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0. We need to calculate the monthly repayments and total cost of credit for both options. (This calculation often requires financial calculators or spreadsheet software to provide accurate monthly repayments). Assuming we had those tools, we could find: Option A (Personal Loan): Monthly repayment ~ R2,224.

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4. Total cost of credit ~ R133,466.40 Option B (Hire Purchase): Monthly repayment ~ R2,326.

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8. Total cost of credit ~ R139,600.80 Explanation: Even though the difference in interest rates might seem small (2%), the total cost of credit is significantly higher with the hire purchase agreement (Option B) due to the specific way HP agreements are structured. Inflation and Real Rate of Return Inflation: 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 Reserve Bank targets an inflation rate between 3% and 6%.

Real Rate of Return: The real rate of return is the return on an investment after adjusting for inflation. It shows the actual increase in purchasing power.

Formula: Real Rate of Return ≈ Nominal Rate of Return – Inflation Rate Example 4: You invest in a fixed deposit that offers a nominal interest rate of 7% per year. The inflation rate is 5%. What is the real rate of return?

Solution: Real Rate of Return ≈ 7% - 5% = 2% Explanation: While your investment appears to be earning 7%, your actual increase in purchasing power is only 2% after accounting for inflation. This is critical to understand because if your investment's nominal return is lower than the inflation rate, you are actually losing purchasing power. Time Value of Money (TVM) The Time Value of Money (TVM) is the concept that money available at the present time is worth more than the same amount in the future due to its potential earning capacity.

Key TVM concepts include: Present Value (PV): The current worth of a future sum of money or stream of cash flows, given a specified rate of return.

Future Value (FV): The value of an asset or investment at a specified date in the future, based on an assumed rate of growth.