Explain hire purchase and calculate the original price of a stove and the VAT amount from its selling price.

Question

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2.2.1

Hire purchase is a method of buying goods where a consumer pays a deposit and then pays the remaining balance in regular installments over an agreed period. The buyer does not legally own the goods until the final installment has been paid.

2.2.2

Identify the new selling price and the saving amount.
New selling price (including VAT) $= \text{R}10\,999.00$
Saving $= \text{R}2\,000.00$
Calculate the original price by adding the saving to the new selling price.
$\text{Original Price} = \text{New Selling Price} + \text{Saving}$ $\text{Original Price} = \text{R}10\,999.00 + \text{R}2\,000.00$ $\text{Original Price} = \text{R}12\,999.00$
The original price of the stove is $\boxed{\text{R}12\,999.00}$ .

2.2.3
Identify the new selling price and the VAT rate.
New selling price (including VAT) $= \text{R}10\,999.00$
Assume VAT rate $= 15\%$ (standard rate in South Africa).
Calculate the VAT amount included in the selling price.
The selling price includes VAT, meaning it represents $100\% + 15\% = 115\%$ of the price before VAT.
To find the VAT amount, use the formula:
$\text{VAT Amount} = \frac{\text{VAT Rate}}{1 + \text{VAT Rate}} \times \text{Price Including VAT}$ $\text{VAT Amount} = \frac{0.15}{1 + 0.15} \times \text{R}10\,999.00$ $\text{VAT Amount} = \frac{0.15}{1.15} \times \text{R}10\,999.00$ $\text{VAT Amount} \approx 0.13043478 \times \text{R}10\,999.00$ $\text{VAT Amount} \approx \text{R}1\,434.6956$ $\text{VAT Amount} \approx \text{R}1\,434.70$
The VAT amount included in the new selling price is $\boxed{\text{R}1\,434.70}$ .

2.2.4

The stove in the advertisement is shown to be gas/electric because the text in the advertisement explicitly states "5 Burner Gas/Electric Stove with oven". This indicates it has both gas burners and an electric oven, or a combination of both for the burners and oven.

2.2.5
Calculate the total hire purchase price excluding the deposit.
Monthly payment $= \text{R}609.00$
Number of months $= 36$
$\text{Total Hire Purchase Price (excluding deposit)} = \text{R}609.00 \times 36$ $\text{Total Hire Purchase Price (excluding deposit)} = \text{R}21\,924.00$
Calculate one third of the total hire purchase price (excluding deposit).
$\frac{1}{3} \times \text{R}21\,924.00 = \text{R}7\,308.00$
Calculate the saving if buying with the cash option compared to the hire purchase option (excluding deposit).
Cash Option Price $= \text{R}10\,999.00$
$\text{Saving} = \text{Total Hire Purchase Price (excluding deposit)} - \text{Cash Option Price}$ $\text{Saving} = \text{R}21\,924.00 - \text{R}10\,999.00$ $\text{Saving} = \text{R}10\,925.00$
Compare the saving with one third of the hire purchase price (excluding deposit).
Is $\text{R}10\,925.00 > \text{R}7\,308.00$ ?
Yes, $\text{R}10\,925.00$ is greater than $\text{R}7\,308.00$ .

The statement is $\boxed{\text{valid}}$ . She will save more than one third of the total hire price (excluding deposit) if she buys with the cash option.

Explain hire purchase and calculate the original price of a stove and the VAT amount from its selling price.

Step-by-step solution

2.2.1

2.2.2

Identify the new selling price and the saving amount.

Calculate the original price by adding the saving to the new selling price.

2.2.3

Identify the new selling price and the VAT rate.

Calculate the VAT amount included in the selling price.

2.2.4

2.2.5

Calculate the total hire purchase price excluding the deposit.

Calculate one third of the total hire purchase price (excluding deposit).

Calculate the saving if buying with the cash option compared to the hire purchase option (excluding deposit).

Compare the saving with one third of the hire purchase price (excluding deposit).

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