Maths Literacy Matric Revision: Bond repayments

CAPS Mathematical Literacy Grade 12: Finance – Bond Repayments

Introduction

Understanding bond repayments is crucial for making informed financial decisions, especially when purchasing a house. Bonds allow individuals to buy homes and pay them off over time, which involves paying the principal amount plus interest to the bank.

Key Points

  1. Bond Definition:
  2. A bond is a loan from the bank to the borrower for purchasing property.

  3. Monthly Repayments:

  4. Include both the principal amount and the interest.
  5. Calculated using a formula to ensure the loan is paid off over the specified period.

  6. Formula:

  7. The formula to calculate bond repayments is:

    [
    PV = PMT \left(\frac{1 – (1 + i)^{-n}}{i}\right)
    ]
    where:
    – ( PV ) = Present Value (loan amount)
    – ( PMT ) = Monthly Payment
    – ( i ) = Monthly Interest Rate
    – ( n ) = Number of Payments

Real-World Applications

Example Calculation of Monthly Bond Repayment:
Step 1: Identify the values:
– Loan Amount (( PV )): R1,200,000
– Annual Interest Rate: 8%
– Loan Period: 20 years

  • Step 2: Convert annual interest rate to monthly:
  • Monthly Interest Rate (( i )): ( \frac{8}{12 \times 100} = 0.0067 )

  • Step 3: Calculate the number of monthly payments:

  • Number of Payments (( n )): ( 20 \times 12 = 240 )

  • Step 4: Use the formula to find PMT:

[
PMT = \frac{PV \cdot i}{1 – (1 + i)^{-n}}
]

[
PMT = \frac{1,200,000 \times 0.0067}{1 – (1 + 0.0067)^{-240}}
]

[
PMT ≈ R10,034.92
]

So, the monthly repayment would be approximately R10,034.92.

Common Misconceptions and Errors

  1. Ignoring Compounding Interest:
  2. Mistake: Assuming interest is calculated on the initial amount only.
  3. Correction: Interest is compounded, meaning it is calculated on the current loan balance, which includes previously added interest.

  4. Wrong Interest Rate Conversion:

  5. Mistake: Using the annual rate for monthly calculations without dividing by 12.
  6. Correction: Always convert annual rates to monthly by dividing by 12.

Practice and Review

Practice Questions:
1. Calculate the monthly bond repayment for a loan of R950,000 at an interest rate of 7% over 15 years.
2. If the loan period is reduced to 10 years with a loan amount of R1,500,000 and an interest rate of 9%, what would be the new monthly repayment?

Examination Tips:
1. Always convert annual interest rates to monthly.
2. Make sure your calculator is set correctly to handle the exponentiation for compounding interest.
3. Answer questions methodically to avoid missing steps.

Connections and Extensions

  • Interest Rates and Economic Factors: Understand how changing interest rates affect bond repayments and overall housing affordability.
  • Comparison with Other Loans: Compare bond repayments with other types of loans like personal loans, to grasp different financial products.

Summary and Quick Review

  • Formula: Use the bond repayment formula to calculate monthly repayments.
  • Interest: Always convert annual rates to monthly.
  • Practice: Regularly practice different scenarios to become proficient.

Additional Resources

  • Online Calculators: Use reliable online bond repayment calculators.
  • Financial Literacy Websites: Websites like SARS provide additional financial information and resources.
  • Educational Videos: Look for videos on bond repayments and interest calculations on YouTube and other educational platforms.

By mastering these concepts and practicing regularly, you can better understand and manage bond repayments effectively, thus making smarter financial decisions in real life .

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