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Calculate the amount that Tumi will be able to Invest in the bank, if he is going to invest the total amount he has set aside.

Mathematics

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Question 1

1.1 Calculate the amount that Tumi will be able to invest in the bank, if he is going to invest the total amount he has set aside.

  1. Calculate the total number of months Tumi saved.

    Number of months=2 years×12 months/year=24 months\text{Number of months} = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}
  2. Calculate the total amount Tumi saved.

    Total saved=R800/month×24 months=R19 200\text{Total saved} = \text{R}800/\text{month} \times 24 \text{ months} = \text{R}19\,200

    The amount Tumi will be able to invest is R19 200\boxed{\text{R}19\,200}.

    1.2 Determine the Interest he will earn from the bank.

  3. Identify the principal amount, interest rate, and time.

    Principal (PP) = R19 200 (from 1.1)
    Interest rate (ii) = 12.5% p.a. = 0.125
    Time (nn) = 36 months = 3612\frac{36}{12} years = 3 years

  4. Calculate the simple interest using the formula I=P×i×nI = P \times i \times n.

    I=R19 200×0.125×3=R7 200I = \text{R}19\,200 \times 0.125 \times 3 = \text{R}7\,200

    The interest Tumi will earn is R7 200\boxed{\text{R}7\,200}.

    1.3 What is the total amount that he will receive at the end of the investment period?

  5. Calculate the total amount by adding the principal and the interest.

    Total amount=Principal+Interest\text{Total amount} = \text{Principal} + \text{Interest} Total amount=R19 200+R7 200=R26 400\text{Total amount} = \text{R}19\,200 + \text{R}7\,200 = \text{R}26\,400

    The total amount Tumi will receive is R26 400\boxed{\text{R}26\,400}.

    Question 2

    2.1 Calculate how much Tumi had to put down as a deposit for the house.

  6. Calculate the deposit amount, which is 11.5% of the house price.

    Deposit=11.5%×R549 000\text{Deposit} = 11.5\% \times \text{R}549\,000 Deposit=0.115×R549 000=R63 135\text{Deposit} = 0.115 \times \text{R}549\,000 = \text{R}63\,135

    The deposit for the house is R63 135\boxed{\text{R}63\,135}.

    2.2 If Tumi uses the money he received from the bank at the end of his investment term, will he have enough to pay for the deposit? Show by means of calculations.

  7. Compare the amount received from the bank (from 1.3) with the deposit amount (from 2.1).

    Amount received from bank = R26 400
    Deposit required = R63 135

  8. Determine if the amount received is enough.

    Since R26 400<R63 135\text{R}26\,400 < \text{R}63\,135, Tumi will not have enough money to pay for the deposit using only the investment.
    Tumi will need an additional amount of:

    R63 135−R26 400=R36 735\text{R}63\,135 - \text{R}26\,400 = \text{R}36\,735

    No, Tumi will not have enough money\boxed{\text{not have enough money}} for the deposit.

    2.3 Tumi learns that he will have to pay a monthly instalment of R5 380 over a period of 20 years.

    2.3.1 If the interest rate does not change, Show with calculations that the total amount paid, including the deposit will be R1 354 335.

  9. Calculate the total number of months for the instalments.

    Number of months=20 years×12 months/year=240 months\text{Number of months} = 20 \text{ years} \times 12 \text{ months/year} = 240 \text{ months}
  10. Calculate the total amount paid in instalments.

    Total instalments=R5 380/month×240 months=R1 291 200\text{Total instalments} = \text{R}5\,380/\text{month} \times 240 \text{ months} = \text{R}1\,291\,200
  11. Calculate the total amount paid, including the deposit.

    Total amount paid=Total instalments+Deposit\text{Total amount paid} = \text{Total instalments} + \text{Deposit} Total amount paid=R1 291 200+R63 135=R1 354 335\text{Total amount paid} = \text{R}1\,291\,200 + \text{R}63\,135 = \text{R}1\,354\,335

    The total amount paid, including the deposit, is indeed R1 354 335\boxed{\text{R}1\,354\,335}.

    2.3.2 How much more money would Tumi have paid by the end of the 20 years?

  12. Calculate the difference between the total amount paid and the original house price.

    More money paid=Total amount paid−House price\text{More money paid} = \text{Total amount paid} - \text{House price} More money paid=R1 354 335−R549 000=R805 335\text{More money paid} = \text{R}1\,354\,335 - \text{R}549\,000 = \text{R}805\,335

    Tumi would have paid R805 335\boxed{\text{R}805\,335} more.

    2.3.3 Calculate the percentage interest that Tumi would have paid by the end of 20 years if the monthly instalment did not change. Round your answer off to one decimal place.

  13. Determine the actual loan amount.

    Loan amount=House price−Deposit\text{Loan amount} = \text{House price} - \text{Deposit} Loan amount=R549 000−R63 135=R485 865\text{Loan amount} = \text{R}549\,000 - \text{R}63\,135 = \text{R}485\,865
  14. Calculate the total interest paid on the loan.

    Total interest on loan=Total instalments−Loan amount\text{Total interest on loan} = \text{Total instalments} - \text{Loan amount} Total interest on loan=R1 291 200−R485 865=R805 335\text{Total interest on loan} = \text{R}1\,291\,200 - \text{R}485\,865 = \text{R}805\,335
  15. Calculate the percentage interest relative to the loan amount.

    Percentage interest=Total interest on loanLoan amount×100%\text{Percentage interest} = \frac{\text{Total interest on loan}}{\text{Loan amount}} \times 100\% Percentage interest=R805 335R485 865×100%\text{Percentage interest} = \frac{\text{R}805\,335}{\text{R}485\,865} \times 100\% Percentage interest≈1.6574×100%≈165.74%\text{Percentage interest} \approx 1.6574 \times 100\% \approx 165.74\%
  16. Round the answer to one decimal place.

    Percentage interest≈165.7%\text{Percentage interest} \approx 165.7\%

    The percentage interest Tumi would have paid is approximately 165.7%\boxed{165.7\%}.

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