Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate simple and compound interest.
• Compare different loan options.
• Calculate loan repayments and interpret the results.
• Explain the difference between simple and compound interest.
• Create basic personal loan repayment schedules.

Lesson summary

This week, we're diving deeper into personal and household finance, a crucial skill for every South African. Understanding how to manage your money effectively, budget wisely, and make informed financial decisions is essential for achieving financial stability and security in the long run. With rising living costs and the complexities of the modern financial landscape, being financially literate is no longer a luxury, but a necessity. This week builds on last week's foundations, particularly focusing on understanding and applying different methods of calculating simple and compound interest, and applying this knowledge to loan repayments.

Lesson notes

Simple Interest Simple interest is calculated only on the principal amount (the initial amount of money). This means the interest earned or paid remains the same each year.

Formula: Simple Interest (SI) = P x r x t Where: P = Principal amount (the initial amount) r = Interest rate (as a decimal) t = Time (in years)

Example: Sipho invests R5,000 in a fixed deposit account that pays simple interest at a rate of 8% per annum for 3 years. How much interest will he earn? P = R5,000 r = 8% = 0.08 t = 3 years SI = R5,000 x 0.08 x 3 = R1,200 Therefore, Sipho will earn R1,200 in simple interest. His total amount after 3 years will be R5,000 + R1,200 = R6,

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0. Explanation: Simple interest is straightforward. You earn the same amount of interest each year based solely on your initial investment. It’s less common in long-term investments or loans, but understanding it is fundamental. Compound Interest Compound interest is calculated on the principal amount and the accumulated interest from previous periods. This means you earn interest on your interest, leading to faster growth (or larger debt) over time.

Formula: A = P(1 + r/n)^(nt)

Where: A = Future value of the investment/loan, including interest P = Principal investment amount (the initial 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: Thandi invests R5,000 in an account that pays compound interest at a rate of 8% per annum, compounded annually, for 3 years. How much will she have at the end of the 3 years? P = R5,000 r = 8% = 0.08 n = 1 (compounded annually) t = 3 years A = R5,000 (1 + 0.08/1)^(1*3) = R5,000 (1.08)^3 = R5,000 x 1.259712 = R6,298.56 Therefore, Thandi will have R6,298.56 at the end of 3 years. The interest earned is R6,298.56 - R5,000 = R1,298.56 Explanation: Compound interest is powerful. The more frequently interest is compounded (e.g., monthly, daily), the faster your money grows because you are earning interest on a larger base each period. Think of it as "interest earning interest." Conversely, with loans, compound interest can make the total amount you pay back significantly higher.

Compounding Period Frequency: Annually: n = 1 Semi-annually: n = 2 Quarterly: n = 4 Monthly: n = 12 Example with Monthly Compounding: If the same R5000 investment as above was compounded monthly (n=12), the future value after 3 years would be: A = R5,000 (1 + 0.08/12)^(12*3) = R5,000 (1.00666667)^36 = R5,000 x 1.270237 = R6,351.19 Therefore, Thandi will have R6,351.19 at the end of 3 years. The interest earned is R6,351.19 - R5,000 = R1,351.

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9. Notice how compounding more frequently (monthly instead of annually) resulted in a higher final amount. Loan Repayments and Comparing Loan Options When taking out a loan, understanding the repayment terms is crucial. The interest rate, the term (length of the loan), and any fees all affect the total amount you will repay. Loan repayments are usually calculated using a more complex formula than simple or compound interest accumulation, but often banks will provide you with the monthly installment amount. For our purposes, and as per CAPS requirements, we will focus on understanding and comparing loan options given the repayment amounts and interest rates.

Example: Lerato wants to buy a used car.

She has two loan options: Option 1: Loan amount: R50,000, Interest rate: 12% per annum, Repayment period: 5 years, Monthly Repayment: R1,112.

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2. Option 2: Loan amount: R50,000, Interest rate: 14% per annum, Repayment period: 4 years, Monthly Repayment: R1,291.67 Which option is better? To compare, we calculate the total amount repaid for each option: Option 1: Total Repaid = R1,112.22/month 12 months/year * 5 years = R66,733.20 Option 2: Total Repaid = R1,291.67/month 12 months/year * 4 years = R61,900.16 Analysis: Although Option 2 has a higher interest rate and a higher monthly repayment, the total amount repaid is lower because the repayment period is shorter.

Therefore, Option 2 is the better choice in terms of minimizing the total cost of the loan.

However, Lerato needs to consider whether she can afford the higher monthly repayments of Option

2. Important Considerations: Fees: Some loans have initiation fees or other charges that can add to the total cost. Always ask about these.

Affordability: Choose a loan with repayments you can comfortably afford each month, even if it means paying more interest in the long run. Missing repayments can damage your credit score and lead to further financial difficulties.

Credit Score: A good credit score can help you secure a lower interest rate on a loan. Guided Practice (With Solutions)

Question 1: Zola invests R8,000 in an account that pays simple interest at 9% per annum for 4 years. Calculate the simple interest earned and the total amount Zola will have at the end of the 4 years.