CAPS Grade 12 Mathematical Literacy: Finance and Entrepreneurship Revision Notes

Introduction

Finance and entrepreneurship concepts are crucial for understanding how businesses operate and manage their financial resources. These topics are essential for real-world applications and are frequently tested in exams. The key learning objectives for this section include understanding budgeting, bond repayments, the National Credit Act, business finance, appreciation and depreciation, inflation, investments, and loans.

Key Points

Budgeting

1. Definition: A budget is a summary of monthly income and expenses.
2. Categories:
3. Fixed expenses: Consistent monthly costs, like rent.
4. Variable expenses: Costs that fluctuate monthly, like utility bills.
5. Emergency expenses: Funds set aside for unexpected costs, like car repairs .

Income Tax

1. Definition: A portion of earnings deducted by the government to run the country.
2. Calculation: Depends on total annual earnings after deductions .

Bond Repayments

1. Definition: Monthly payments made to repay a bank loan used to purchase a house.
2. Formula:
   [
   PV = PMT \left(\frac{1 – (1 + i)^{-n}}{i}\right)
   ]
   Where:
3. ( PV ) = Present Value of the loan amount
4. ( PMT ) = Periodic payment required
5. ( i ) = Periodic interest rate
6. ( n ) = Number of compounding periods .

National Credit Act

1. Purpose: Protect consumers and regulate the cost of credit.
2. Provisions:
3. Initiation fees and service fees are applicable.
4. Interest rates and transactions are regulated to protect consumers .

Business Finance

1. Appreciation and Depreciation:
2. Depreciation: Decrease in value over time.
3. Appreciation: Increase in value over time.

4. Formulas:
   [
   \text{Simple Depreciation/Appreciation: } A = P(1 \pm ni)
   ]
   [
   \text{Compound Depreciation/Appreciation: } A = P(1 \pm i)^n
   ]
   Where:

   • ( A ) = Adjusted value
   • ( P ) = Principal or initial value
   • ( n ) = Time in years
   • ( i ) = Rate as a percentage .

5. Inflation:
   [
   \text{Rate of Inflation (%) = } \frac{\text{End cost – Original cost}}{\text{Original cost}} \times 100
   ] .

6. Consumer Price Index (CPI): Measures changes in prices for a ‘basket’ of goods and services, reflecting urban consumer expenses .

7. Unemployment Insurance Fund (UIF): Both employer and employee contribute 1% each of the worker’s salary towards the fund, which assists workers during unemployment .

Entrepreneurship

1. Terminology:
2. Capital: Money or assets for investment.
3. Cost Price: Cost to produce/buy a product.
4. Gross/Net Income: Income before/after deductions.
5. Gross/Net Profit: Profit before/after expenses .

Investments and Loans

1. Interest Calculation:
2. Simple Interest:
   [
   A = P(1 + in)
   ]
3. Compound Interest:
   [
   A = P(1 + i)^n
   ]
4. ( A ) = Total amount
5. ( P ) = Principal
6. ( i ) = Interest rate
7. ( n ) = Number of years .

Real-World Applications

Budgeting Example

Scenario: Monthly income is R20,000. Fixed expenses (rent): R8,000, Variable expenses (food): R4,000, Emergency fund: R2,000.
Solution:
Total Budget = Fixed + Variable + Emergency
= R8,000 + R4,000 + R2,000
= R14,000
Remaining = Monthly income – Total Budget
= R20,000 – R14,000
= R6,000.

Bond Repayment Example

Scenario: Loan of R500,000 at an annual interest rate of 8% over 20 years.
Solution:
[
PMT = \frac{500,000 \times 0.08}{1 – (1 + 0.08)^{-20}}
= R50,000
]

Entrepreneurship Example

Scenario: Selling handmade crafts. Cost to produce: R20, Selling Price: R30.
Solution:
Profit per item = Selling Price – Cost Price
= R30 – R20
= R10 .

Common Misconceptions and Errors

1. Confusing gross profit with net profit: Remember, gross is before expenses are deducted, net is after.
2. Misinterpreting the compound interest period: Ensure the calculation matches the defined period (e.g., monthly, annually).
3. Overlooking variable expenses in budgets: Always include estimates for non-fixed costs to avoid budget shortfalls.

Practice and Review

Practice Questions

1. Budgeting:
2. Calculate the remaining amount after budgeting fixed, variable, and emergency expenses from a monthly income of R25,000.
3. Bond Repayments:
4. Calculate the monthly repayment for a loan of R300,000 at an interest rate of 7% over 25 years using the bond repayment formula.
5. National Credit Act:
6. If a loan of R5,000 incurs an initiation fee, service fee, and 20% interest rate, calculate the total repayment amount.

Examination Tips

1. Keywords: Look for terms like “income,” “expenditure,” “gross,” “net,” “interest,” and “appreciation.”
2. Manage Time: Allocate time to each question. If stuck, move to the next question and return if time permits.

Connections and Extensions

• Economics Link: Understanding finance and entrepreneurship concepts is crucial for broader economic studies.
• Practical Projects: Create a simple budget for a hypothetical business to understand real-world applications.

Summary and Quick Review

1. Budgeting: Categorize into fixed, variable, and emergency expenses.
2. Bond Repayments: Use the provided formula to calculate monthly payments.
3. National Credit Act: Recognize the protection it offers to consumers.
4. Entrepreneurship: Learn key terms and their applications in business scenarios.
5. Investments: Differentiate between simple and compound interest calculations.

Additional Resources

• SARS Website: For detailed information on income tax.
• National Credit Regulator (NCR): For detailed information on the National Credit Act.
• South African Reserve Bank: For updates on inflation and interest rates.

With these notes and resources, you should be well-equipped to understand and apply the key concepts in finance and entrepreneurship for Grade 12 Mathematical Literacy.