Maths Literacy Matric Revision: Hire purchase agreements

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Revision Notes: Hire Purchase Agreements in Mathematical Literacy (Grade 12, CAPS)

Introduction

Hire Purchase Agreements are crucial in understanding personal and business finance. This term relates to the buying of goods or assets where the buyer agrees to pay in installments while using the goods. This concept is particularly important when examining consumer credit and managing financial obligations over time.

Essential Learning Objectives:
– Understanding the mechanics of hire purchase agreements.
– Calculating total costs, including interest and installment payments.
– Recognizing the implications of hire purchase agreements on personal finances.

1. Key Points

  1. Definition:

    • A hire purchase (HP) agreement is a contract where one pays for goods in parts or a percentage at a time. The goods are used by the purchaser while they are being paid for.

  2. Cost Components:

    • Principal Amount: Initial price of the item.
    • Interest Rate: Percentage charged on the principal amount annually.
    • Installments: Regular payments made over time.

  3. Formulas:

    • To calculate the total cost with interest: ( \text{Total Cost} = \text{Principal} + (\text{Principal} \times \text{Interest Rate} \times \text{Time}) )
    • To find monthly installment: ( \text{Installment} = \frac{\text{Total Cost}}{\text{Number of Months}} )

  4. Terms:

    • Principal (P): The initial amount of the goods.
    • Interest Rate (i): The percentage rate applied per year.
    • Time (t): The duration over which the payments are made, usually in years.

  5. Calculation Example:

    • If a laptop costs R10,000 and the interest rate is 12% per year, over 2 years, the interest is calculated as:
      ( \text{Interest} = R10,000 \times 0.12 \times 2 = R2,400 ).
      Thus, the total cost is ( R10,000 + R2,400 = R12,400 ).
      Monthly installment over 24 months would be ( \frac{R12,400}{24} = R516.67 ).

2. Real-World Applications

Scenario: Buying a Car
– Initial Price: R150,000
– Interest Rate: 10% per year
– Payment Period: 5 years

Calculation:
– Total Interest ( = R150,000 \times 0.10 \times 5 = R75,000 )
– Total Cost ( = R150,000 + R75,000 = R225,000 )
– Monthly Installment ( = \frac{R225,000}{(5 \times 12)} = R3,750 )

Steps:
1. Calculate annual interest.
2. Multiply annual interest by the number of years.
3. Add this to the principal to get the total cost.
4. Divide by the total number of monthly installments.

3. Common Misconceptions and Errors

  1. Interest Misunderstanding:

    • Believing interest is deducted only once rather than each year.
    • Solution: Always calculate interest annually and multiply by the number of years.

  2. Ignoring Total Cost:

    • Overlooking that the installment cost includes both principal and interest.
    • Solution: Always add total interest to the principal before calculating installments.

  3. Calculation Errors:

    • Mistakes in arithmetic leading to incorrect total costs or installments.
    • Solution: Double-check calculations or use financial calculators.

4. Practice and Review

Basic Questions:
1. If a TV costs R8,000 with an interest rate of 10% per year for 3 years, what is the total cost?
2. Calculate monthly installments for the same TV over 36 months.

Challenging Question:
1. A bike is bought for R5,000 with a 15% annual interest rate over 4 years. Calculate the total interest paid and the monthly installments.

Examination Tips:
– Look for keywords like “interest rate annually,” “total cost,” and “installments.”
– Pay attention to the number of years and monthly division in the questions.
– Time management: Allocate specific time per question to ensure completion.

5. Connections and Extensions

  • Connections: This topic connects to real-world financial management, budgeting, and loans.
  • Extensions: Explore more complex financial instruments and their impact on long-term financial health, such as mortgages and annuities.

6. Summary and Quick Review

  • Key Concept: Hire purchase involves buying goods through installments with added interest over time.
  • Formulas:
  • Total Cost = Principal + (Principal * Interest Rate * Time)
  • Monthly Installment = Total Cost / Number of Months
  • Tips: Always ensure accurate calculation of interest and total cost before dividing into installments.

7. Additional Resources

These notes provide a comprehensive yet accessible guide on hire purchase agreements, incorporating essential calculations and real-life applications.