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 options.
• Analyze the impact of interest rates and time.
• Apply calculations to real-world scenarios.
• Interpret financial documents related to loans and investments.

Lesson summary

This week, we delve into the crucial topic of compound interest, loans, and investments. Understanding these concepts is not just about passing an exam; it's about equipping yourselves with the knowledge to make informed financial decisions throughout your lives. Whether it's saving for university, buying a car, or planning for retirement, understanding compound interest, loans, and investments is vital for financial security in South Africa's dynamic economic landscape. Many South Africans struggle with debt or miss out on investment opportunities due to a lack of financial literacy. This week aims to address this gap.

Lesson notes

2. 1.

Compound Interest: The Power of Growth Compound interest is the interest earned not only on the principal amount but also on the accumulated interest from previous periods. In simpler terms, it's interest on interest. This makes it a powerful tool for wealth accumulation but also a potential burden when applied to loans.

Formula: A = P(1 + i)^n Where: A = Accumulated amount (principal + interest) P = Principal amount (initial investment or loan amount) i = Interest rate per compounding period (expressed as a decimal; e.g., 10% = 0.10). It's crucial to adjust the interest rate to match the compounding period (e.g., for an annual rate compounded monthly, divide the annual rate by 12) n = Number of compounding periods (total number of times interest is compounded during the investment or loan term). It's crucial to adjust the number of periods to match the compounding period (e.g., for an investment of 5 years compounded monthly, multiply the number of years by 12)

Example 1: Savings Account Sipho invests R5,000 in a savings account that pays 8% interest per year, compounded annually. How much will he have after 3 years? P = R5,000 i = 8% = 0.08 n = 3 years A = 5000(1 + 0.08)^3 A = 5000(1.08)^3 A = 5000 * 1.259712 A = R6,298.56 Sipho will have R6,298.56 after 3 years.

Example 2: Fixed Deposit (Compounded Monthly) Nomusa invests R10,000 in a fixed deposit account that pays 6% interest per year, compounded monthly. How much will she have after 5 years? P = R10,000 i = 6%/12 = 0.06/12 = 0.005 (monthly interest rate) n = 5 years 12 months/year = 60 months A = 10000(1 + 0.005)^60 A = 10000(1.005)^60 A = 10000 * 1.34885 A = R13,488.50 Nomusa will have R13,488.50 after 5 years. 2.

2. Loans: Understanding the Cost of Borrowing Loans involve borrowing money from a lender (e.g., a bank) and repaying it over a specified period, usually with interest. Compound interest often plays a significant role in calculating loan repayments. Understanding the interest rate, repayment period, and any associated fees is crucial when considering a loan. Amortization schedules can be generated to show each payment's distribution between interest and principal. While the formulas for calculating loan repayments are complex and often pre-calculated by financial institutions, we can use our compound interest knowledge to estimate the total interest paid and understand the overall cost.

Example 3: Car Loan Zanele takes out a car loan of R150,000 at an interest rate of 12% per year, compounded monthly, for a period of 5 years (60 months). A complex formula is used to calculate the monthly payment.

However, let's say the monthly payment is R3,336.

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4. What is the total amount Zanele will pay and the total interest?

Total Amount Paid: R3,336.74 * 60 = R200,204.40 Total Interest Paid: R200,204.40 - R150,000 = R50,204.40 Zanele will pay a total of R200,204.40, including R50,204.40 in interest. 2.

3. The Impact of Interest Rates and Time Periods The interest rate and the time period significantly impact both investments and loans. Higher interest rates lead to faster growth in investments but also higher costs for loans. Longer time periods can exponentially increase the accumulated amount in investments but also dramatically increase the total interest paid on loans.

Example 4: Comparing Loan Terms Two friends, Thabo and Aisha, each borrow R100,000 at 10% per year, compounded monthly. Thabo chooses a repayment period of 3 years (36 months), while Aisha chooses a repayment period of 5 years (60 months). Assume Thabo's monthly payment is R3,226.72 and Aisha's monthly payment is R2,124.

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0. Thabo's Total Repayment: R3,226.72 * 36 = R116,161.92 Thabo's Total Interest: R116,161.92 - R100,000 = R16,161.92 Aisha's Total Repayment: R2,124.70 * 60 = R127,482.00 Aisha's Total Interest: R127,482.00 - R100,000 = R27,482.00 Although Aisha's monthly payments are lower, she pays significantly more interest over the longer repayment period. This illustrates the importance of considering the total cost, not just the monthly payment. Guided Practice (With Solutions)

Question 1: Bongi invests R8,000 in a unit trust that earns 10% interest per year, compounded annually. How much will her investment be worth after 4 years?

Solution: P = R8,000 i = 10% = 0.10 n = 4 years A = 8000(1 + 0.10)^4 A = 8000(1.10)^4 A = 8000 * 1.4641 A = R11,712.80 Bongi's investment will be worth R11,712.80 after 4 years.

Question 2: David borrows R25,000 to start a small business. The bank charges 15% interest per year, compounded annually. If he repays the loan after 2 years, how much will he owe?

Solution: P = R25,000 i = 15% = 0.15 n = 2 years A = 25000(1 + 0.15)^2 A = 25000(1.15)^2 A = 25000 * 1.3225 A = R33,062.50 David will owe R33,062.50 after 2 years.

Question 3: Lerato invests R12,000 in a money market account that pays 7% interest per year, compounded quarterly. How much will she have after 2 years?