Lesson Notes By Weeks and Term v5 - Grade 11
Finance: compound interest, loans and investments – Week 2 focus
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Finance: compound interest, loans and investments – Week 2 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 11
Term: 2nd Term
Week: 2
Theme: General lesson support
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This week, we delve deeper into the world of finance, specifically focusing on compound interest, loans, and investments. Understanding these concepts is crucial for making informed financial decisions throughout your life. In South Africa, many people struggle with debt and financial insecurity, often due to a lack of understanding of how interest works. Learning about compound interest, loans, and investments will equip you with the knowledge to plan for your future, avoid unnecessary debt, and potentially grow your wealth. This isn't just about numbers; it's about empowering you to control your financial future.
Compound Interest Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods. It's like earning interest on your interest! This is different from simple interest, which is calculated only on the principal. The power of compounding makes your money grow much faster over time.
Formula: A = P(1 + i/n)^(nt)
Where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) i = the annual interest rate (as a decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for Example 1: Savings Account Sipho invests R5,000 in a savings account that pays an annual interest rate of 8% compounded quarterly. How much will Sipho have in the account after 5 years? P = R5,000 i = 0.08 n = 4 (quarterly means 4 times per year) t = 5 A = 5000(1 + 0.08/4)^(4*5) A = 5000(1 + 0.02)^(20) A = 5000(1.02)^(20) A = 5000 * 1.485947 A = R7,429.74 Therefore, Sipho will have R7,429.74 in the account after 5 years.
Example 2: Comparing Simple vs. Compound Interest Nomusa invests R10,000 for 3 years. Option A offers simple interest at 10% per year. Option B offers compound interest at 9% per year, compounded monthly. Which option is better?
Option A (Simple Interest): Simple Interest = P r t = 10000 0.10 3 = R3,000 Total Amount = P + Simple Interest = 10000 + 3000 = R13,000 Option B (Compound Interest): A = P(1 + i/n)^(nt) A = 10000(1 + 0.09/12)^(12*3) A = 10000(1 + 0.0075)^(36) A = 10000(1.0075)^(36) A = 10000 * 1.308645 A = R13,086.45 Option B (compound interest) is better, as Nomusa will have R13,086.45, compared to R13,000 with simple interest. This demonstrates the power of compound interest, even with a slightly lower interest rate. Loans Loans involve borrowing money from a lender (e.g., a bank) and repaying it over a set period, usually with interest. Understanding loan agreements is vital to avoid getting into debt that you cannot manage. Key aspects include the principal amount, interest rate, loan term (duration), and repayment schedule.
Key Concepts: Principal: The original amount of the loan.
Interest Rate: The percentage charged by the lender for borrowing the money. Can be fixed or variable.
Loan Term: The length of time you have to repay the loan.
Repayment Schedule: How often you make payments (e.g., monthly, weekly).
Total Cost of the Loan: The sum of all repayments, including the principal and all interest paid. Calculating Monthly Loan Repayments (Using a Simplified Method): While banks use more complex formulas, we can use a simplified approach to estimate monthly repayments.
Note: this approximation can differ from actual bank calculations due to additional fees and variations in interest calculation methods. Approximate Monthly Repayment = (Principal + Total Interest) / Number of Months Example 3: Car Loan Zola wants to buy a car for R150,
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0. She takes out a loan with an interest rate of 12% per year over 5 years. What is her approximate monthly repayment?
Calculate the total interest: Simple Interest = P r t = 150000 0.12 5 = R90,000 Calculate the total amount to be repaid: Principal + Total Interest = 150000 + 90000 = R240,000 Calculate the number of months: 5 years * 12 months/year = 60 months Approximate Monthly Repayment = 240000 / 60 = R4,000 Therefore, Zola's approximate monthly repayment will be R4,
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Note: This is a simplified calculation. Banks use amortisation schedules which account for interest accruing differently each month. Investments Investments involve putting money into something (e.g., savings account, fixed deposit, unit trust, shares) with the expectation of earning a return in the future. Different investments carry different levels of risk and potential return.
Key Concepts: Risk: The possibility of losing money on an investment.
Return: The profit or income generated by an investment.
Liquidity: How easily an investment can be converted into cash.
Savings Account: A safe place to store money and earn a small amount of interest.
Fixed Deposit: An investment where you deposit a fixed amount of money for a fixed period at a fixed interest rate. Usually offers higher interest than a savings account but has less liquidity.
Unit Trust (Mutual Fund): A pooled investment where money from many investors is used to buy a portfolio of assets (e.g., shares, bonds). Offers diversification but involves management fees.
Shares (Stocks): Ownership in a company. Share prices can fluctuate significantly, offering the potential for high returns but also high risk.
Example 4: Comparing Investment Options Thabo has R20,000 to invest.
He considers two options: Option A: A fixed deposit paying 7% per year compounded annually for 3 years.
Option B: A unit trust that historically returns an average of 10% per year, but with higher risk.