Explain hire-purchase and calculate the cash price, deposit, interest, and total hire-purchase cost.

3.2.1
Hire-purchase is a system where a buyer takes possession of goods immediately and pays for them in regular installments, with ownership transferring only after the final payment has been made.

3.2.2

Step 1: Determine the cash price of the food processor.
The deposit of R974,85 represents 15% of the cash price.
Let $P$ be the cash price.

$$0.15 \times P = \text{R}974.85$$ $$P = \frac{\text{R}974.85}{0.15}$$ $$P = \text{R}6499.00$$

Step 2: Show how the deposit was calculated.

$$\text{Deposit} = 15\% \text{ of } \text{R}6499.00$$ $$\text{Deposit} = 0.15 \times \text{R}6499.00$$ $$\text{Deposit} = \boxed{\text{R}974.85}$$

3.2.3

Step 1: Calculate the amount financed after the deposit.

$$\text{Amount financed} = \text{Cash Price} - \text{Deposit}$$ $$\text{Amount financed} = \text{R}6499.00 - \text{R}974.85 = \text{R}5524.15$$

Step 2: Calculate the simple interest on the amount financed.
The interest rate is 18.5% p.a. simple interest for 3 years.

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$ $$\text{Interest} = \text{R}5524.15 \times 0.185 \times 3$$ $$\text{Interest} = \text{R}3067.99325$$

Step 3: Calculate the total hire-purchase cost.

$$\text{Total Hire-Purchase Cost} = \text{Deposit} + \text{Amount financed} + \text{Interest}$$ $$\text{Total Hire-Purchase Cost} = \text{R}974.85 + \text{R}5524.15 + \text{R}3067.99325$$ $$\text{Total Hire-Purchase Cost} = \text{R}9566.99325$$

Step 4: Calculate the discount (savings) if buying cash instead of hire-purchase.

$$\text{Discount} = \text{Total Hire-Purchase Cost} - \text{Cash Price}$$ $$\text{Discount} = \text{R}9566.99325 - \text{R}6499.00 = \text{R}3067.99325$$

Step 5: Calculate the discount percentage offered (relative to the total hire-purchase cost).

$$\text{Discount Percentage} = \frac{\text{Discount}}{\text{Total Hire-Purchase Cost}} \times 100\%$$ $$\text{Discount Percentage} = \frac{\text{R}3067.99325}{\text{R}9566.99325} \times 100\%$$ $$\text{Discount Percentage} \approx 0.32069 \times 100\%$$ $$\text{Discount Percentage} = \boxed{32.07\%}$$

3.2.4

Step 1: Calculate the amount financed after the deposit.

$$\text{Amount financed} = \text{Cash Price} - \text{Deposit}$$ $$\text{Amount financed} = \text{R}6499.00 - \text{R}974.85 = \text{R}5524.15$$

Step 2: Calculate the simple interest on the amount financed.

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$ $$\text{Interest} = \text{R}5524.15 \times 0.185 \times 3$$ $$\text{Interest} = \text{R}3067.99325$$

Step 3: Calculate the total amount payable after three years, excluding the deposit.

$$\text{Amount Payable} = \text{Amount financed} + \text{Interest}$$ $$\text{Amount Payable} = \text{R}5524.15 + \text{R}3067.99325$$ $$\text{Amount Payable} = \boxed{\text{R}8592.14}$$

3.2.5

Step 1: Calculate the total hire-purchase cost.

$$\text{Total Hire-Purchase Cost} = \text{Deposit} + \text{Amount Payable (from 3.2.4)}$$ $$$$