Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate future and present value using compound interest.
• Calculate depreciation using reducing balance and straight-line methods.
• Solve problems with nominal and effective interest rates.
• Apply growth and decay models to real-world scenarios.
• Interpret and analyze financial information.

Lesson summary

This week, we delve into the fascinating and crucially important topic of finance, growth, and decay. Understanding these concepts is essential for making informed decisions about your future financial well-being. In South Africa, where economic inequalities are prevalent, a strong grasp of these principles is vital for managing personal finances, understanding investments, and making sound decisions about loans and savings. From managing your student loan to planning for retirement, these mathematical models will be your lifelong companions. We will be focusing on compound interest, depreciation (reducing balance and straight-line), and inflation.

Lesson notes

2.1 Compound Interest: Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods. It's often called "interest on interest," and it can make a significant difference in your investments over time.

The formula for compound interest is: A = P(1 + i) n 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 multiplied by the number of years the money is invested or borrowed for. (total number of compounding periods) Why does it work? Each time interest is calculated, it's added to the principal. The next time interest is calculated, it's based on the new, larger principal. This compounding effect leads to exponential growth.