Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate percentages in various contexts (discounts, VAT).
• Apply simple and compound interest formulas.
• Analyze hire purchase agreements.
• Solve practical problems using these skills.

Lesson summary

This week, we will delve deeper into numbers and calculations, focusing on percentages, simple and compound interest, and hire purchase agreements. These skills are fundamental for managing your finances effectively, understanding deals and discounts, and making informed decisions about loans and investments – all crucial for navigating the South African economy. Understanding these concepts will empower you to be a responsible consumer, a savvy investor (even on a small scale!), and generally more financially literate.

Lesson notes

Percentages A percentage is a way of expressing a number as a fraction of

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0. The word "percent" comes from the Latin "per centum," meaning "out of one hundred." Percentages are used extensively in financial calculations, statistics, and everyday life.

Calculating a Percentage of a Number: To find x% of a number N, multiply N by x/

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0. Example: Find 15% of 800 Rand.

Solution: (15/100) 800 = 0.15 800 = R120 Percentage Increase: To calculate the percentage increase from an original value to a new value: ((New Value - Original Value) / Original Value) * 100%

Example: A loaf of bread increased in price from R12 to R

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5. What is the percentage increase?

Solution: ((15-12)/12) 100% = (3/12) 100% = 25% Percentage Decrease: To calculate the percentage decrease from an original value to a new value: ((Original Value - New Value) / Original Value) * 100%

Example: A shop is offering a 20% discount on a R500 pair of shoes. What is the new price?

Solution: Discount = (20/100) * R500 = R

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0. New price = R500 - R100 = R

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0. Alternatively, calculate 80% of R500, which also gives R

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0. Simple Interest Simple interest is calculated only on the principal amount. It's often used for short-term loans or investments.

Formula: A = P(1 + rt)* A = Future Value (Total amount including principal and interest) P = Principal Amount (Initial amount) r = Interest Rate (as a decimal, e.g., 10% = 0.10) t = Time (in years)

Example: You invest R2000 in a savings account that pays 8% simple interest per year. How much will you have after 3 years?

Solution: A = 2000(1 + 0.08 3) = 2000(1 + 0.24) = 2000 1.24 = R2480 Compound Interest Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. This means you earn interest on your interest, leading to faster growth.

Formula: A = P(1 + r/n)^(nt)* A = Future Value P = Principal Amount r = Interest Rate (as a decimal) n = Number of times interest is compounded per year (e.g., annually = 1, semi-annually = 2, quarterly = 4, monthly = 12) t = Time (in years)

Example: You invest R5000 in an account that pays 10% interest compounded annually. How much will you have after 5 years?

Solution: A = 5000(1 + 0.10/1)^(15) = 5000(1.10)^5 = 5000 1.61051 = R8052.55

Example: You invest R5000 in an account that pays 10% interest compounded monthly. How much will you have after 5 years?

Solution: A = 5000(1 + 0.10/12)^(125) = 5000(1.008333)^60 = 5000 1.6453 = R8226.50 (Notice the difference between annual and monthly compounding - you earn more with monthly compounding!) Hire Purchase Hire purchase (HP) is a method of buying goods where you pay for them in installments over a period of time. The total cost of the item is usually higher than the cash price because it includes interest and other charges.

Calculating Total Repayment: Total Repayment = Deposit + (Monthly Payment Number of Months)

Calculating Total Interest Paid: Total Interest Paid = Total Repayment - Cash Price

Example: A TV costs R8000 cash. You can buy it on hire purchase by paying a 10% deposit and then R400 per month for 24 months. Calculate the total cost and the total interest paid.

Solution: Deposit = 10% of R8000 = 0.10 R8000 = R800 Total Monthly Payments = R400 24 = R9600 Total Repayment = R800 + R9600 = R10400 Total Interest Paid = R10400 - R8000 = R2400 Understanding APR (Annual Percentage Rate) in South Africa The APR represents the actual yearly cost of a loan, including interest, fees, and other charges, expressed as a percentage. It's crucial in South Africa because it allows you to compare different loan offers fairly. Banks and micro-lenders are required to disclose the AP

R. A lower APR is always better. Guided Practice (With Solutions)

Question 1: A shop offers a 25% discount on all clothing. If a shirt originally costs R280, what is the discounted price?

Solution: Discount amount = 25% of R280 = (25/100) R280 = R70 Discounted price = R280 - R70 = R210

Commentary:* This question tests your understanding of calculating a percentage and applying it as a discount.

Question 2: You invest R3000 in a fixed deposit account that pays 7% simple interest per year. How much interest will you earn after 4 years?

Solution: A = P(1 + rt) => A = 3000(1 + 0.07 4) = 3000(1 + 0.28) = 3000 * 1.28 = R3840 Interest Earned = A - P = R3840 - R3000 = R840

Commentary:* This question applies the simple interest formula. Remember to find the total amount first, then subtract the principal to find the interest earned.

Question 3: A car costs R150,000 cash. You can buy it on hire purchase by paying a 15% deposit and then R5500 per month for 36 months. Calculate the total cost and the total interest paid.