Hire-Purchase with Flat Simple Interest: A car is purchased on hire-purchase. The cash price is $21,000. The terms require a deposit of 10% of the cash price and the remaining balance to be paid over 60 equal monthly instalments. If interest is charged at 12% per annum simple interest on the outstanding balance for the full 60 months, what is the total cost of the car (in $)?

Introduction / Context:
This question deals with a hire purchase agreement where the buyer pays a deposit and repays the balance with interest in equal monthly instalments. The interest is computed at a flat simple interest rate on the outstanding balance for the full term. You are asked to find the total cost of the car, including both the deposit and all interest charges.

Given Data / Assumptions:

• Cash price of the car = $21,000.
• Deposit = 10% of cash price.
• Remaining balance is repaid over 60 months.
• Annual flat simple interest rate = 12% per annum on the outstanding balance.
• Term = 60 months = 5 years.

Concept / Approach:
First compute the deposit and outstanding balance. Then, because interest is flat and simple, it is calculated on the initial outstanding balance for the entire term, even though instalments gradually reduce the amount owed. The total cost of the car equals the deposit plus principal repaid plus total interest. We use I = (P * r * t) / 100 with P as the outstanding balance after the deposit and t = 5 years.

Step-by-Step Solution:
Step 1: Compute the deposit: 10% of 21,000 = 0.10 * 21,000 = $2,100. Step 2: Outstanding balance to be financed = 21,000 − 2,100 = $18,900. Step 3: Term of repayment = 60 months = 5 years. Step 4: Annual flat simple interest rate r = 12%. Step 5: Use the SI formula on the outstanding balance: I = (P * r * t) / 100. Step 6: I = (18,900 * 12 * 5) / 100. Step 7: First compute 12 * 5 = 60, so I = (18,900 * 60) / 100 = 18,900 * 0.6 = $11,340. Step 8: Total paid through instalments = principal financed + interest = 18,900 + 11,340 = $30,240. Step 9: Add the initial deposit to get the total cost: 30,240 + 2,100 = $32,340. Step 10: Therefore, the total cost of the car is $32,340.

Verification / Alternative check:
Check the logic: The buyer pays the full cash price (21,000) plus additional interest on the financed portion. Interest of $11,340 on an outstanding balance of $18,900 over 5 years at 12% flat is consistent with I = 18,900 * 0.12 * 5. Summing the deposit and all repayments gives a figure significantly above the cash price, which is typical of hire purchase deals.

Why Other Options Are Wrong:

• $31,240 and $30,240: These omit part of the cost and are less than deposit + full flat interest.
• $33,600: Higher than the computed total and does not match the flat interest calculation.
• $29,240: Too low, not even equal to the sum of cash price and a modest interest.

Common Pitfalls:
Some learners only calculate interest on the cash price instead of the financed balance, while others wrongly apply reducing balance interest instead of flat simple interest. Another common error is forgetting to add back the initial deposit when computing the total cost. Always separate the steps: calculate deposit, financed balance, interest on that balance, then sum everything.

Final Answer:
The total cost of the car under this hire-purchase plan is $32,340.