Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate percentages (discounts, VAT, etc.)
• Solve problems with simple and compound interest
• Work effectively with ratios and rates
• Interpret basic financial documents
• Use calculators proficiently

Lesson summary

This week, we're revisiting and expanding upon our understanding of numbers and calculations, a fundamental skill crucial for navigating everyday life in South Africa. From budgeting your monthly expenses to understanding loan repayments and interpreting statistics in news articles, a strong grasp of numbers empowers you to make informed decisions. Many South African households struggle with financial literacy; mastering these skills can help improve financial well-being and make informed choices about things like investments, loans and budgeting.

Lesson notes

This section details the core concepts we will be learning or revising. 2.1 Percentages A percentage is a way of expressing a number as a fraction of

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0. The word "percent" means "out of one hundred." Calculating a Percentage of a Number: To find x% of a number y, multiply y by x/

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0. Example: What is 15% of 800 ZAR?

Solution: (15/100) 800 = 120 ZAR Percentage Increase/Decrease: Increase: (New Value - Original Value) / Original Value 100% Decrease: (Original Value - New Value) / Original Value 100%

Example: The price of bread increased from R12 to R

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5. What is the percentage increase?

Solution: (15 - 12) / 12 100% = 25% VAT (Value Added Tax): VAT is a consumption tax added to the price of most goods and services. In South Africa, the standard VAT rate is currently 15%.

Calculating VAT amount: Price VAT Rate Price including VAT: Price + VAT amount or Price (1 + VAT Rate)

Example: A cellphone costs R2000 before VA

T. What is the price including VAT?

Solution: R2000 0.15 = R300 (VAT amount)

Price including VAT: R2000 + R300 = R2300 or R2000 (1 + 0.15) = R2300 2.2 Interest (Simple and Compound) Interest is the cost of borrowing money or the return on an investment.

Simple Interest: Interest is calculated only on the principal amount.

Formula: A = P(1 + rt)

Where: A = Amount after t years P = Principal amount (initial investment or loan amount) r = Interest rate (as a decimal) t = Time (in years)

Example: You invest R5000 in a savings account with a simple interest rate of 8% per year for 3 years. How much will you have after 3 years?

Solution: A = 5000(1 + 0.08 3) = 5000(1 + 0.24) = 5000 * 1.24 = R6200 Compound Interest: Interest is calculated on the principal amount and any accumulated interest from previous periods.

Formula: A = P(1 + r/n)^(nt)

Where: A = Amount after t years P = Principal amount r = Interest rate (as a decimal) n = Number of times interest is compounded per year t = Time (in years)

Example: You invest R5000 in a savings account with a compound interest rate of 8% per year, compounded quarterly, for 3 years. How much will you have after 3 years?

Solution: A = 5000(1 + 0.08/4)^(43) = 5000(1 + 0.02)^(12) = 5000 (1.02)^12 = 5000 1.26824 = R6341.21 (approximately) 2.3 Ratios and Rates Ratio: A ratio compares two quantities of the same units.

It can be written as a:b, a/b, or "a to b." Ratios must have the same units before being compared.

Example: The ratio of boys to girls in a class is 2:

3. If there are 12 boys, how many girls are there?

Solution: 2/3 = 12/x => 2x = 36 => x = 18 girls Rate: A rate compares two quantities of different units. Common examples include speed (km/h) and price per unit (R/kg).

Example: A car travels 300 km in 4 hours. What is the average speed?

Solution: Speed = Distance / Time = 300 km / 4 hours = 75 km/h 2.4 Financial Documents (Bank Statements & Payslips)

Bank Statement: A summary of your bank account activity over a period of time, including deposits, withdrawals, interest earned, and fees charged.

Key elements: Account number, statement period, opening balance, closing balance, transaction details (date, description, amount).

Payslip: A document detailing your earnings and deductions for a specific pay period.

Key elements: Employee details, pay period, gross salary, deductions (PAYE, UIF, medical aid, pension fund), net salary (take-home pay). PAYE (Pay As You Earn) is income tax deducted from your salary. UIF (Unemployment Insurance Fund) provides financial assistance to workers who become unemployed. 2.5 Rounding and Estimation Rounding: Approximating a number to a nearby value.

Rule: If the digit to the right of the rounding place is 5 or greater, round up. If it is less than 5, round down.

Example: Round 123.456 to two decimal places: 123.46 Round 123.456 to the nearest whole number: 123 Estimation: Finding an approximate answer to a problem. Estimation is useful for checking the reasonableness of calculations.

Example: Estimate the total cost of 3 items costing R49.99, R25.50, and R19.

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5. Estimate: R50 + R26 + R20 = R96 Guided Practice (With Solutions)

Question 1: A store is offering a 20% discount on a pair of jeans that originally costs R

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0. How much will the jeans cost after the discount?

Solution: Calculate the discount amount: 20% of R450 = (20/100) * R450 = R90 Subtract the discount from the original price: R450 - R90 = R360 Answer: The jeans will cost R360 after the discount.

Commentary: This question directly applies the percentage concept. Note the importance of understanding that a discount reduces the original price.

Question 2: Sipho invests R8000 in a fixed deposit account that pays simple interest at a rate of 7.5% per year. How much interest will he earn after 4 years? What will be the total value of his investment after 4 years?