Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate simple and compound interest.
• Understand and calculate hire purchase agreements.
• Explain inflation and its impact.
• Convert amounts between different currencies.
• Solve real-world financial problems.

Lesson summary

This week, we delve into the fascinating and crucial world of Finance and Growth. Understanding financial concepts is not just about passing exams; it's about empowering yourselves to make informed decisions about your money, savings, and investments throughout your lives. In a country like South Africa, where socio-economic challenges are prevalent, financial literacy is essential for building a secure future, avoiding debt traps, and contributing to the economy. This week's focus will be on understanding simple and compound interest, hire purchase agreements, inflation, and exchange rates, all crucial for making informed financial decisions.

Lesson notes

2.1 Simple Interest Simple interest is calculated only on the principal amount (the initial amount borrowed or invested). The interest earned remains constant throughout the investment period.

Formula: I = P r * t Where: I = Simple Interest P = Principal amount r = Interest rate (expressed as a decimal) t = Time (in years)

Future Value (A): A = P + I or A = P(1 + rt)

Example 1: Sipho invests R5000 in a fixed deposit account that pays simple interest at a rate of 8% per annum. How much interest will he earn after 3 years? What is the total value of his investment after 3 years? P = R5000 r = 8% = 0.08 t = 3 years I = P r t = R5000 0.08 3 = R1200 The interest earned is R

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0. A = P + I = R5000 + R1200 = R6200 Alternatively, A = P(1 + rt) = R5000(1 + (0.08 3)) = R5000(1 + 0.24) = R5000 1.24 = R6200 The total value of his investment 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 that you earn interest on your interest, resulting in faster growth compared to simple interest.

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

Where: A = Future Value P = Principal amount r = Interest rate (expressed as a decimal) n = Number of times that interest is compounded per year (e.g., annually: n=1, semi-annually: n=2, quarterly: n=4, monthly: n=12) t = Time (in years)

Example 2: Thandi invests R8000 in a savings account that pays compound interest at a rate of 10% per annum, compounded annually. How much will she have after 5 years? P = R8000 r = 10% = 0.10 n = 1 (compounded annually) t = 5 years A = P(1 + r/n)^(nt) = R8000(1 + 0.10/1)^(15) = R8000(1.10)^5 = R8000 1.61051 = R12884.08 Thandi will have R12884.08 after 5 years.

Example 3: What if Thandi's interest was compounded monthly instead of annually? P = R8000 r = 10% = 0.10 n = 12 (compounded monthly) t = 5 years A = P(1 + r/n)^(nt) = R8000(1 + 0.10/12)^(125) = R8000(1 + 0.008333)^(60) = R8000(1.008333)^60 = R8000 1.64531 = R13162.48 Thandi will have R13162.48 after 5 years. Notice that compounding monthly results in a slightly higher return. 2.3 Hire Purchase Hire purchase (HP) is a method of buying goods where you pay a deposit and then pay the remaining amount in installments over a specified period. The total cost of the item is usually higher than the cash price due to interest and other charges. It's a way for people to afford items they can't pay for upfront, but it's important to understand the total cost involved.

Calculations: Amount Financed: Cash Price - Deposit Total Repayment Amount: Monthly Installment Number of Months Total Cost: Deposit + Total Repayment Amount Interest Paid: Total Cost – Cash Price Example 4: Zola wants to buy a fridge with a cash price of R

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0. He enters into a hire purchase agreement that requires a 15% deposit and monthly installments of R250 for 24 months.

Calculate: a) The deposit amount b) The amount financed c) The total repayment amount d) The total cost of the fridge e) The interest paid a) Deposit = 15% of R6000 = 0.15 * R6000 = R900 b) Amount Financed = Cash Price - Deposit = R6000 - R900 = R5100 c) Total Repayment Amount = Monthly Installment Number of Months = R250 24 = R6000 d) Total Cost = Deposit + Total Repayment Amount = R900 + R6000 = R6900 e) Interest Paid = Total Cost - Cash Price = R6900 - R6000 = R900 2.4 Inflation Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. It erodes the value of money over time. In South Africa, the Reserve Bank targets an inflation rate between 3% and 6%.

Calculating Price Increase: New Price = Original Price * (1 + Inflation Rate)

Example 5: A loaf of bread currently costs R

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5. If the inflation rate is 6% per annum, what will be the price of the bread in one year? New Price = R15 (1 + 0.06) = R15 1.06 = R15.90 The bread will cost R15.90 in one year. 2.5 Exchange Rates An exchange rate is the value of one currency in relation to another. For example, the ZAR/USD exchange rate tells you how many South African Rand you need to buy one US Dollar. Exchange rates fluctuate constantly due to various economic factors.

Conversion: To convert ZAR to another currency: Divide the ZAR amount by the exchange rate.

To convert another currency to ZAR: Multiply the foreign currency amount by the exchange rate.

Example 6: The current exchange rate is 1 USD = 18 ZAR. a) How many Rand will you get for 50 USD? b) How many USD will you get for 900 ZAR? a) ZAR = USD Exchange Rate = 50 18 = 900 ZAR b) USD = ZAR / Exchange Rate = 900 / 18 = 50 USD Guided Practice (With Solutions)

Question 1: John invests R10 000 in a savings account that pays simple interest at 7% per annum. Calculate the amount of interest he will earn after 4 years and the total value of his investment.