Lesson Notes By Weeks and Term v5 - Grade 12
Finance: revisiting loan and investment scenarios – Week 4 focus
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Finance: revisiting loan and investment scenarios – Week 4 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 12
Term: 1st Term
Week: 4
Theme: General lesson support
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This week, we delve back into the essential world of loans and investments, building upon your existing knowledge and skills. Finance is not just about numbers; it's about making informed decisions that directly impact your future financial well-being. Understanding loans and investments empowers you to navigate the complexities of personal finance, whether it's securing funding for further education, buying a car, investing for retirement, or starting a business. In a South African context, where economic inequalities persist, financial literacy is crucial for breaking cycles of poverty and creating opportunities for wealth building.
Loans: Borrowing Money Wisely A loan is an amount of money borrowed from a lender (like a bank or credit union) that must be repaid over a specified period, usually with interest. Understanding loan terms is crucial to making informed decisions.
Principal: The original amount of money borrowed.
Interest Rate: The percentage charged by the lender for the use of their money. This can be fixed (stays the same throughout the loan term) or variable (changes based on market conditions).
Loan Term: The length of time you have to repay the loan.
Fees: Additional charges associated with the loan, such as application fees, origination fees, or late payment fees.
Simple Interest: Calculated only on the principal amount.
The formula is: `Simple Interest = Principal x Rate x Time` (where Time is in years).
Compound Interest: Calculated on the principal amount plus accumulated interest. This means you earn interest on your interest.
The formula is: `A = P(1 + r/n)^(nt)` where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.
Amortization Schedule: A table showing the breakdown of each loan payment, including the amount going towards principal and interest. It's crucial for understanding how your loan is being repaid.
Example 1: Comparing Simple vs. Compound Interest on a Loan Sipho borrows R10,000 to buy a used bakkie.
He has two loan options: Option A: Simple interest at 12% per year for 3 years.
Option B: Compound interest at 11% per year, compounded annually for 3 years. Which loan option is cheaper?
Option A (Simple Interest): Interest = R10,000 x 0.12 x 3 = R3,600 Total Repayment = R10,000 + R3,600 = R13,600 Option B (Compound Interest): A = R10,000(1 + 0.11/1)^(13) = R10,000(1.11)^3 = R10,000 x 1.367631 = R13,676.31 Total Repayment = R13,676.31 Conclusion: Option A (simple interest) is cheaper (R13,600) than Option B (compound interest) (R13,676.31).
Investments: Growing Your Money An investment is an asset purchased with the expectation that it will generate income or appreciate in value over time. Understanding investment options is essential for building wealth.
Principal: The initial amount of money invested.
Interest Rate/Rate of Return: The percentage earned on the investment.
Investment Term: The length of time the money is invested.
Risk: The possibility of losing some or all of the investment. Higher-risk investments typically have the potential for higher returns, but also a greater chance of loss.
Savings Account: A safe, low-yield investment offered by banks.
Fixed Deposit: An investment held for a fixed period, with a guaranteed interest rate. Usually offers a higher interest rate than a savings account, but you cannot access the money until the end of the term without penalty.
Unit Trusts: Collective investment schemes that pool money from many investors to invest in a diversified portfolio of assets (e.g., stocks, bonds). Carry more risk but potentially higher returns than savings accounts or fixed deposits.
Inflation: The rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. It is crucial to consider inflation when evaluating investment returns.
Example 2: Calculating Investment Returns and the Impact of Inflation Zinhle invests R5,000 in a fixed deposit account that pays 8% interest per year, compounded annually for 5 years. The average inflation rate over the 5 years is 6% per year. What is the real rate of return on her investment?
Future Value of Investment: A = R5,000(1 + 0.08/1)^(15) = R5,000(1.08)^5 = R5,000 x 1.469328 = R7,346.64 Understanding Inflation: Inflation erodes the purchasing power of money. To find the real return, we need to adjust for inflation. A simplified approximation of real return is: `Real Return ≈ Nominal Return - Inflation Rate` Approximate Real Return: 8% - 6% = 2% per year.
Note: This is an approximation. A more accurate calculation requires a slightly more complex formula, but for Mathematical Literacy purposes, this approximation is often sufficient. The implication is that although Zinhle appears to be getting an 8% return, the actual increase in her purchasing power is only about 2% per year due to the effect of inflation.
Example 3: Analysing Loan Amortization Thabo takes out a R20,000 loan with a 15% interest rate to start a small business selling vetkoek. The loan is to be paid back over 2 years, with monthly payments. A portion of the amortization schedule is shown below: | Payment Number | Starting Balance | Payment Amount | Interest Paid | Principal Paid | Ending Balance | |---|---|---|---|---|---| | 1 | R20,000.00 | R967.46 | R250.00 | R717.46 | R19,282.54 | | 2 | R19,282.54 | R967.46 | R241.03 | R726.43 | R18,556.11 | | 3 | R18,556.11 | R967.46 | R231.95 | R735.51 | R17,820.60 | Analysis: The payment amount is the same each month.