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Calculate the total value of monthly instalments for Option 1, and the monthly interest rate for Option 1.

Business/Management

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Step-by-step solution

18 steps

2.2.1

  1. Identify the term agreement for bond payment option one from Table 4.

    The term agreement for Option 1 is 10 years.

  2. Convert the term agreement from years to months.

    Term in months=10 years×12 months/year\text{Term in months} = 10 \text{ years} \times 12 \text{ months/year} Term in months=120 months\text{Term in months} = 120 \text{ months}

    The term agreement in months for bond payment option one is 120 months\boxed{\text{120 months}}.

    2.2.2

  3. Identify the annual interest rate from Table 4.

    The annual interest rate is 10.75%10.75\%.

  4. Convert the annual interest rate to a monthly rate.

    Monthly interest rate=10.75%12\text{Monthly interest rate} = \frac{10.75\%}{12} Monthly interest rate=0.107512\text{Monthly interest rate} = \frac{0.1075}{12} Monthly interest rate≈0.00895833...\text{Monthly interest rate} \approx 0.00895833...
  5. Convert to a percentage and round to one decimal place.

    Monthly interest rate≈0.00895833...×100%\text{Monthly interest rate} \approx 0.00895833... \times 100\% Monthly interest rate≈0.895833...%\text{Monthly interest rate} \approx 0.895833...\% Monthly interest rate≈0.9%\text{Monthly interest rate} \approx 0.9\%

    The interest rate per month, rounded to one decimal place, is 0.9%\boxed{0.9\%}.

    2.2.3

  6. Identify the monthly instalment and once-off costs for Option 1 from Table 4.

    Monthly instalment (Option 1) = R68 033
    Once-off costs (Option 1) = R1 600 015

  7. Calculate the total value of monthly instalments for Option 1.

    The term in months for Option 1 is 120 months (from 2.2.1).

    Total value of monthly instalments=Monthly instalment×Number of months\text{Total value of monthly instalments} = \text{Monthly instalment} \times \text{Number of months} Total value of monthly instalments=R68 033×120\text{Total value of monthly instalments} = \text{R}68\,033 \times 120 Total value of monthly instalments=R8 163 960\text{Total value of monthly instalments} = \text{R}8\,163\,960
  8. Calculate the total cost of the house using the given formula.

    Total cost=Total value of monthly instalments+Once-off costs\text{Total cost} = \text{Total value of monthly instalments} + \text{Once-off costs} Total cost=R8 163 960+R1 600 015\text{Total cost} = \text{R}8\,163\,960 + \text{R}1\,600\,015 Total cost=R9 763 975\text{Total cost} = \text{R}9\,763\,975

    The total cost of the house if Mpho uses bond payment option one is R9 763 975\boxed{\text{R}9\,763\,975}.

    2.2.4

  9. Identify the purchase price from Table 4.

    Purchase Price = R5 990 000

  10. Calculate the difference between the total cost (from 2.2.3) and the purchase price.

    Difference=Total cost−Purchase Price\text{Difference} = \text{Total cost} - \text{Purchase Price} Difference=R9 763 975−R5 990 000\text{Difference} = \text{R}9\,763\,975 - \text{R}5\,990\,000 Difference=R3 773 975\text{Difference} = \text{R}3\,773\,975
  11. Calculate the percentage more than the purchase price.

    Percentage more=DifferencePurchase Price×100%\text{Percentage more} = \frac{\text{Difference}}{\text{Purchase Price}} \times 100\% Percentage more=R3 773 975R5 990 000×100%\text{Percentage more} = \frac{\text{R}3\,773\,975}{\text{R}5\,990\,000} \times 100\% Percentage more≈0.6300459...×100%\text{Percentage more} \approx 0.6300459... \times 100\% Percentage more≈63.00%\text{Percentage more} \approx 63.00\%

    Mpho will be paying approximately 63.00%\boxed{63.00\%} more than the purchase price.

    2.2.5 & 2.2.6

  12. Identify the principal amount, interest rate, and time for the loan.

    Principal (PP) = R350 000
    Interest rate (rr) = 17% = 0.17
    Time (tt) = 3 years

  13. Calculate the total amount Mpho pays back using the simple interest formula A=P(1+rt)A = P(1 + rt).

    A=R350 000(1+0.17×3)A = \text{R}350\,000 (1 + 0.17 \times 3) A=R350 000(1+0.51)A = \text{R}350\,000 (1 + 0.51) A=R350 000(1.51)A = \text{R}350\,000 (1.51) A=R528 500A = \text{R}528\,500
  14. Round the amount to the nearest one hundred rand.

    The amount R528 500 is already rounded to the nearest one hundred rand.
    The amount Mpho pays back, rounded to the nearest one hundred rand, is R528 500\boxed{\text{R}528\,500}.

    2.2.7

  15. Calculate the total monthly instalments for Option 2.

    Term agreement (Option 2) = 15 years = 15×12=18015 \times 12 = 180 months.
    Monthly instalment (Option 2) = R55 935.

    Total instalments (Option 2)=R55 935×180\text{Total instalments (Option 2)} = \text{R}55\,935 \times 180 Total instalments (Option 2)=R10 068 300\text{Total instalments (Option 2)} = \text{R}10\,068\,300
  16. Calculate the total monthly instalments for Option 3.

    Term agreement (Option 3) = 20 years = 20×12=24020 \times 12 = 240 months.
    Monthly instalment (Option 3) = R50 659.

    Total instalments (Option 3)=R50 659×240\text{Total instalments (Option 3)} = \text{R}50\,659 \times 240 Total instalments (Option 3)=R12 158 160\text{Total instalments (Option 3)} = \text{R}12\,158\,160
  17. Calculate the difference between the total monthly instalments of Option 2 and Option 3.

    Difference=∣Total instalments (Option 2)−Total instalments (Option 3)∣\text{Difference} = |\text{Total instalments (Option 2)} - \text{Total instalments (Option 3)}| Difference=∣R10 068 300−R12 158 160∣\text{Difference} = |\text{R}10\,068\,300 - \text{R}12\,158\,160| Difference=∣−R2 089 860∣\text{Difference} = |-\text{R}2\,089\,860| Difference=R2 089 860\text{Difference} = \text{R}2\,089\,860
  18. Verify Mpho's statement.

    Mpho stated that the difference is less than R2 000 000.
    Our calculated difference is R2 089 860.
    Since R2 089 860 is not less than R2 000 000 (it is greater), Mpho's statement is invalid.
    Mpho's statement is invalid\boxed{\text{invalid}}.

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