Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Differentiate between simple and compound interest.
• Apply formulas to solve interest problems.
• Calculate the future value of an investment or loan.
• Calculate the present value needed for a future goal.
• Analyze real-world financial scenarios.

Lesson summary

This week, we delve into the crucial topic of Finance and Growth, specifically focusing on simple and compound interest calculations and their applications. Understanding these concepts is fundamental for managing personal finances, making informed investment decisions, and appreciating how money grows (or diminishes!) over time. In South Africa, with its unique socio-economic challenges and opportunities, financial literacy is a vital life skill. This topic directly impacts decisions about saving, borrowing, investing, and planning for the future.

Lesson notes

2.1 Simple Interest Simple interest is calculated only on the principal amount (the initial amount of money). The interest earned each year remains constant.

The formula for simple interest is: I = Prt Where: I = Simple Interest earned P = Principal amount (initial investment or loan) r = Interest rate (expressed as a decimal) t = Time period (in years) The total amount (A) after t years is given by: A = P + I or A = P(1 + rt)

Example 1: Sipho invests R5,000 in a fixed deposit account that pays a simple interest rate of 8% per annum. Calculate the interest earned and the total amount after 3 years.

Solution: P = R5,000 r = 8% = 0.08 t = 3 years I = Prt = 5000 0.08 * 3 = R1200 A = P + I = 5000 + 1200 = R6200 Therefore, Sipho earns R1200 in interest, and the total amount after 3 years is R6200. 2.2 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 faster growth.

The formula for compound interest is: A = P(1 + i)^n Where: A = Final amount (principal + accumulated interest) P = Principal amount (initial investment or loan) i = Interest rate per compounding period (expressed as a decimal) n = Number of compounding periods Important Considerations: Compounding Period: This is how often the interest is calculated and added to the principal.

Common compounding periods include: Annually (once per year) Semi-annually (twice per year) Quarterly (four times per year) Monthly (twelve times per year) Daily (365 times per year) If interest is compounded semi-annually, the annual interest rate is divided by 2 to get i, and the number of years is multiplied by 2 to get n. Similarly, for quarterly compounding, divide the annual rate by 4 and multiply the number of years by 4, and so on.

Example 2: Zanele invests R8,000 in an account that pays a compound interest rate of 10% per annum, compounded annually. Calculate the amount she will have after 5 years.

Solution: P = R8,000 i = 10% = 0.10 n = 5 years A = P(1 + i)^n = 8000 (1 + 0.10)^5 = 8000 * (1.10)^5 = R12,884.08 Therefore, Zanele will have R12,884.08 after 5 years.

Example 3: David borrows R12,000 from a bank at an interest rate of 15% per annum, compounded monthly. How much will he owe after 2 years?

Solution: P = R12,000 i = 15% / 12 = 0.15 / 12 = 0.0125 (monthly interest rate) n = 2 years 12 months/year = 24 months A = P(1 + i)^n = 12000 (1 + 0.0125)^24 = 12000 * (1.0125)^24 = R16,146.48 Therefore, David will owe R16,146.48 after 2 years. 2.3 Present Value Present value (P) is the current worth of a future sum of money or stream of cash flows, given a specified rate of return.

It answers the question: "How much money do I need to invest today at a certain interest rate to have a specific amount in the future?" The formula for present value with compound interest is derived from the future value formula: P = A / (1 + i)^n Where: P = Present Value A = Future Value i = Interest rate per compounding period n = Number of compounding periods Example 4: Thandi wants to have R20,000 in 4 years to pay for a short course. If she can invest her money in an account that pays 9% per annum, compounded quarterly, how much must she invest today?

Solution: A = R20,000 i = 9% / 4 = 0.09 / 4 = 0.0225 (quarterly interest rate) n = 4 years 4 quarters/year = 16 quarters P = A / (1 + i)^n = 20000 / (1 + 0.0225)^16 = 20000 / (1.0225)^16 = R13,964.04 Therefore, Thandi must invest R13,964.04 today. Guided Practice (With Solutions)

Question 1: Lebo invests R3,000 in a savings account that pays simple interest at a rate of 6% per annum. How much interest will she earn after 5 years?

Solution: P = R3,000 r = 6% = 0.06 t = 5 years I = Prt = 3000 0.06 * 5 = R900 Lebo will earn R900 in interest.

Commentary: This question uses the simple interest formula directly. Ensure the interest rate is converted to a decimal.

Question 2: John takes out a loan of R10,000 at an interest rate of 12% per annum, compounded monthly. What will be the total amount he owes after 3 years?

Solution: P = R10,000 i = 12% / 12 = 0.12 / 12 = 0.01 (monthly interest rate) n = 3 years 12 months/year = 36 months A = P(1 + i)^n = 10000 (1 + 0.01)^36 = 10000 * (1.01)^36 = R14,307.69 John will owe R14,307.69 after 3 years.

Commentary: This requires understanding the impact of monthly compounding on the interest rate and the number of periods.

Question 3: Aisha wants to buy a car in 2 years that is expected to cost R80,

0

0

0. How much should she invest today in an account that offers an interest rate of 8% per annum compounded quarterly to reach her goal?

Solution: A = R80,000 i = 8% / 4 = 0.08 / 4 = 0.02 (quarterly interest rate) n = 2 years 4 quarters/year = 8 quarters P = A / (1 + i)^n = 80000 / (1 + 0.02)^8 = 80000 / (1.02)^8 = R68,282.72 Aisha should invest R68,282.72 today.

Commentary: This problem demonstrates calculating present value with quarterly compounding.