Leon Mashaba wants to buy a new car, but before he signs any contract, he wants to look at various options. He is interested in buying a used Hyundai i30. He makes an appointment with a salesperson to show him the various options.

Here are the solutions to the questions:

2.2.1 Define the term loan.

A loan is an amount of money borrowed by one party from another, typically for a specific period, with an agreement to repay the principal amount along with interest and other charges.

2.2.2 Show how the Loan Amount for Option 1 was calculated.

Step 1: Identify the cash price and deposit for Option 1. Cash Price = $\text{R}249\,995$ Deposit = $\text{R}20\,000$ Step 2: Calculate the loan amount by subtracting the deposit from the cash price. Loan Amount = Cash Price - Deposit Loan Amount = $\text{R}249\,995 - R20\,000 = R229\,995$

The loan amount for Option 1 is $\boxed{R229\,995}$. (Note: The table states the Loan Amount for Option 1 as R231 135. This discrepancy suggests there might be an additional fee or calculation not explicitly stated in the problem for the table value. However, based on the instruction "Show how the Loan Amount for Option 1 was calculated" using the provided Cash Price and Deposit, the calculation above is the direct method. For the purpose of this question, we will assume the question expects the direct calculation from Cash Price and Deposit.)

2.2.3 Calculate the total amount that Leon Mashaba will pay after the six years on Option 1.

Step 1: Identify all payments for Option 1. Deposit = $\text{R}20\,000$ Monthly repayment = $\text{R}4\,290.00$ Monthly administration fee = $\text{R}57.00$ Compulsory once-off payment = $\text{R}1\,140.00$ Term of loan = $6$ years Step 2: Calculate the total number of monthly payments. Number of months = $6 years \times 12 months/year = 72 \text{ months}$ Step 3: Calculate the total amount paid through monthly installments and administration fees. Total monthly payments = $(R4\,290.00 + R57.00) \times 72$ Total monthly payments = $\text{R}4\,347.00 \times 72 = R312\,984.00$ Step 4: Calculate the total amount paid by summing all components. Total amount = Deposit + Total monthly payments + Compulsory once-off payment Total amount = $\text{R}20\,000 + R312\,984.00 + R1\,140.00 = R334\,124.00$

The total amount Leon Mashaba will pay on Option 1 is $\boxed{R334\,124.00}$.

2.2.4 Calculate the total amount that Leon Mashaba will pay after six year on Option 2.

Step 1: Identify all payments for Option 2. Deposit = $\text{R}0$ Monthly repayment = $\text{R}3\,905.00$ Monthly administration fee = $\text{R}57.00$ Compulsory once-off payment = $\text{R}1\,140.00$ Term of loan = $6$ years Balloon Payment = $30\%$ of cash price Cash Price = $\text{R}249\,995$ Step 2: Calculate the total number of monthly payments. Number of months = $6 years \times 12 months/year = 72 \text{ months}$ Step 3: Calculate the balloon payment. Balloon Payment = $0.30 \times R249\,995 = R74\,998.50$ Step 4: Calculate the total amount paid through monthly installments and administration fees. Total monthly payments = $(R3\,905.00 + R57.00) \times 72$ Total monthly payments = $\text{R}3\,962.00 \times 72 = R285\,264.00$ Step 5: Calculate the total amount paid by summing all components. Total amount = Deposit + Total monthly payments + Balloon Payment + Compulsory once-off payment Total amount = $\text{R}0 + R285\,264.00 + R74\,998.50 + R1\,140.00 = R361\,402.50$

The total amount Leon Mashaba will pay on Option 2 is $\boxed{R361\,402.50}$.

2.2.5 Calculate the difference between the amounts in 2.2.3 and 2.2.4.

Step 1: Identify the total amounts from 2.2.3 and 2.2.4. Total amount for Option 1 = $\text{R}334\,124.00$ Total amount for Option 2 = $\text{R}361\,402.50$ Step 2: Calculate the difference. Difference = Total amount for Option 2 - Total amount for Option 1 Difference = $\text{R}361\,402.50 - R334\,124.00 = R27\,278.50$

The difference between the amounts is $\boxed{R27\,278.50}$.

2.2.6 Explain why the monthly repayment of Option 2 is lower than that of Option 1 where a deposit has been paid.

The monthly repayment for Option 2 is lower than Option 1 primarily because Option 2 includes a balloon payment. A balloon payment defers a significant portion of the loan's principal to the end of the loan term, which reduces the amount that needs to be repaid through regular monthly installments. Even though Option 1 has a deposit, the entire remaining loan amount is amortized over the 6 years, leading to higher monthly payments compared to Option 2, which has a large lump sum payment due at the end.

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