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Mapotio plans to purchase a bakkie (motor vehicle) - NSC Mathematical Literacy - Question 1 - 2018 - Paper 2
Question 1
Mapotio plans to purchase a bakkie (motor vehicle). She received the following quotation from a car dealer on 28 February 2018: Extract of a quotation for a bakkie ... show full transcript
Worked Solution & Example Answer:Mapotio plans to purchase a bakkie (motor vehicle) - NSC Mathematical Literacy - Question 1 - 2018 - Paper 2
Step 1
Calculate (rounded off to ONE decimal place) the percentage discount given on the bakkie’s selling price, excluding VAT.
Answer
To calculate the percentage discount, use the formula:
[ \text{Percentage Discount} = \left(\frac{\text{Discount}}{\text{Selling Price (excluding VAT)}}\right) \times 100 ]
Substituting the values:
[ \text{Percentage Discount} = \left(\frac{6140}{160087.72}\right) \times 100 \approx 3.8% ]
Step 2
Show how the amount of R166 561,76 was calculated.
Answer
To find the subtotal amount of R166 561,76, add the costs together:
- Selling Price Excluding VAT: R160 087,72
- Accessories: R3 500,00 (Smash-and-grab film) + R3 500,00 (Door protector)
- Other Charges: R4 298,25 (On-road charges) + R1 315,79 (Transaction fee)
Calculating:
[ \text{Subtotal} = \text{Selling Price} + \text{Accessories} + \text{Other Charges} ]
[ \text{Subtotal} = 160087.72 + 3500 + 3500 + 4298.25 + 1315.79 = R166 561.76 ]
Step 3
Give ONE reason why customers would prefer to install the accessories (extras), as shown in the quotation.
Answer
Customers may prefer to install accessories for safety features, such as the smash-and-grab film that enhances vehicle security, or for aesthetic reasons, enhancing the bakkie’s appearance.
Step 4
Show whether the interest earned on this investment is sufficient to cover the total purchase price of R189 880,41.
Answer
To determine if the interest is sufficient, we first calculate the interest earned on the investment of R1,25 million for a period of 27 months at 6% per annum, compounded annually.
- Total amount invested: R1,250,000
- Interest Rate: 6% per annum
- Time: 27 months = 2.25 years
Using the compound interest formula:
[ A = P(1 + r/n)^{nt} ]
Where:
- ( A ) = the amount of money accumulated after n years, including interest
- ( P ) = the principal amount (the initial amount)
- ( r ) = annual interest rate (decimal)
- ( t ) = the number of years
Substituting the values:
[ A = 1250000 \left(1 + \frac{0.06}{1}\right)^{1 \times 2.25} ]
Calculating: [ A \approx 1250000 \times (1.06)^{2.25} \approx 1250000 \times 1.1384 \approx 1424050.00 ]
Thus, interest earned: [ \text{Interest} = A - P = 1424050 - 1250000 = R174050.00 ]
Since R174050.00 is greater than R189 880,41, the investment is sufficient to cover the total purchase price.