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 simple and compound interest.
• Analyse the impact of different interest rates and time periods.
• Understand compounding frequency (e.g., monthly vs. annually).
• Apply these concepts to realistic South African scenarios.

Lesson summary

This week, we delve into the crucial topic of finance, specifically focusing on compound interest, loans, and investments. Understanding these concepts is vital for making informed financial decisions throughout your life. Whether it's saving for tertiary education, buying a car, taking out a home loan, or simply planning for retirement, a strong grasp of compound interest and its implications is essential. In South Africa, where economic inequalities are prevalent, financial literacy empowers individuals to improve their circumstances and build a more secure future.

Lesson notes

What is Interest? Interest is essentially the "price" you pay for borrowing money (in the case of a loan) or the "reward" you receive for lending money (in the case of an investment). It's usually expressed as a percentage per year (per annum). Simple Interest vs.

Compound Interest Simple Interest: Simple interest is calculated only on the principal amount (the initial amount borrowed or invested). The interest earned each year remains constant.

Formula: `Simple Interest = Principal × Rate × Time` (I = PRT), where: P = Principal (initial amount) R = Interest Rate (as a decimal) T = Time (in years) `Final Amount = Principal + Simple Interest` Compound Interest: Compound interest is calculated on the principal amount and on the accumulated interest from previous periods. This means you earn interest on your interest, leading to exponential growth.

Formula: `A = P(1 + r/n)^(nt)`, where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = 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 The Power of Compounding The key difference between simple and compound interest is that compound interest allows your money to grow at an accelerating rate. The more frequently interest is compounded (e.g., daily, monthly, quarterly), the faster the growth. Compounding Frequency (n) The 'n' in the compound interest formula refers to how many times the interest is compounded within a year.

Common values include: Annually: n = 1 Semi-annually: n = 2 Quarterly: n = 4 Monthly: n = 12 Daily: n = 365

Worked example

Example 1: Simple Interest vs. Compound Interest

Thando invests R5,000 in a savings account. One account offers simple interest at 8% per annum, and another offers compound interest at 8% per annum compounded annually. Calculate the amount in each account after 5 years.

Simple Interest:

I = PRT = 5000 0.08 * 5 = R2,000

Final Amount = 5000 + 2000 = R7,000

Compound Interest:

A = P(1 + r/n)^(nt) = 5000(1 + 0.08/1)^(15) = 5000(1.08)^5 = R7,346.64 (rounded to two decimal places)

Analysis: After 5 years, the compound interest account has R346.64 more than the simple interest account. This illustrates the power of compounding.