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Write down the ratio of the deposit amount : the total amount for the course in the form 1 : ... rounded off to TWO decimal places.

Mathematics

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2.2.1

  1. Identify the deposit amount and the total course amount.

    The deposit amount is R45 000.
    The total amount for the course is R208 300.

  2. Write the ratio and simplify it to the form 1:…1 : \dots.

    The ratio of the deposit amount to the total amount is 45000208300\frac{45000}{208300}.
    To express this in the form 1:x1 : x, we divide the total amount by the deposit amount:

    x=20830045000=4.6288…x = \frac{208300}{45000} = 4.6288\dots
  3. Round the value to two decimal places.

    x≈4.63x \approx 4.63

    The ratio is 1:4.631 : \mathbf{4.63}.

    2.2.2

  4. Identify the total course amount, deposit, and food-preparation module cost from Option A.

    Total amount for the course = R208 300
    Deposit amount = R45 000
    Food-preparation module cost = R99 650

  5. Calculate the balance owing for the patisserie module.

    The balance for the patisserie module is the total amount minus the deposit and the food-preparation module cost.

    Balance=R208 300−R45 000−R99 650\text{Balance} = \text{R}208\,300 - \text{R}45\,000 - \text{R}99\,650 Balance=R163 300−R99 650\text{Balance} = \text{R}163\,300 - \text{R}99\,650 Balance=R63 650\text{Balance} = \text{R}63\,650

    The balance owing for the patisserie module is R63 650\mathbf{R63\,650}.

    2.2.3

  6. Calculate the total cost for the food-preparation module under Payment Plan 1.

    Payment Plan 1: 12 months at R9 000 per month.

    Cost1=12×R9 000=R108 000\text{Cost}_1 = 12 \times \text{R}9\,000 = \text{R}108\,000
  7. Calculate the total cost for the food-preparation module under Payment Plan 2.

    Payment Plan 2: R51 825 per semester. The food-preparation module is one year, which is 2 semesters (since 1 semester = 6 months).

    Cost2=2×R51 825=R103 650\text{Cost}_2 = 2 \times \text{R}51\,825 = \text{R}103\,650
  8. Determine the difference between the two payment plans.

    Difference=Cost1−Cost2\text{Difference} = \text{Cost}_1 - \text{Cost}_2 Difference=R108 000−R103 650\text{Difference} = \text{R}108\,000 - \text{R}103\,650 Difference=R4 350\text{Difference} = \text{R}4\,350

    The difference between payment plan 1 and payment plan 2 for the food-preparation module is R4 350\mathbf{R4\,350}.

    2.2.4

  9. Calculate the amount after the first year.

    Initial investment (P) = R39 500
    Interest rate for the first year (i1i_1) = 7.15% = 0.0715
    Amount after 1st year (A1A_1) = P(1+i1)P(1 + i_1)

    A1=R39 500(1+0.0715)A_1 = \text{R}39\,500(1 + 0.0715) A1=R39 500(1.0715)A_1 = \text{R}39\,500(1.0715) A1=R42 324.25A_1 = \text{R}42\,324.25
  10. Calculate the amount after the second year.

    The amount from the first year becomes the new principal for the second year.
    Interest rate for the second year (i2i_2) = 7.85% = 0.0785
    Amount after 2nd year (A2A_2) = A1(1+i2)A_1(1 + i_2)

    A2=R42 324.25(1+0.0785)A_2 = \text{R}42\,324.25(1 + 0.0785) A2=R42 324.25(1.0785)A_2 = \text{R}42\,324.25(1.0785) A2=R45 640.408125A_2 = \text{R}45\,640.408125
  11. Round the final amount to two decimal places.

    A2≈R45 640.41A_2 \approx \text{R}45\,640.41

    The total amount that she will receive at the end of the two years is R45 640.41\mathbf{R45\,640.41}.

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