A car is purchased on hire purchase. The cash price is $21 000. The buyer pays a deposit of 10% of the price and agrees to pay the balance over 60 equal monthly instalments. Simple interest is charged at 12% per annum on the balance. What is the monthly instalment?

Introduction / Context:
This question applies the concept of simple interest to a hire purchase transaction. A deposit is paid first, and the remaining balance is financed at simple interest over a fixed number of monthly instalments. You must find the equal monthly instalment amount.

Given Data / Assumptions:

• Cash price of the car = $21 000.
• Deposit = 10% of $21 000.
• Balance is repaid over 60 months (which is 5 years).
• Rate of interest (R) = 12% per annum (simple interest on the balance).
• Interest is calculated on the financed balance for the full period.

Concept / Approach:
First, compute the deposit and the remaining balance. Then calculate the total simple interest on this balance over the full period using SI = (P * R * T) / 100. Add this interest to the balance to get the total amount that must be repaid through instalments. Finally, divide this total by the number of monthly instalments to get the monthly payment.

Step-by-Step Solution:
Step 1: Deposit = 10% of $21 000 = (10 / 100) * 21000 = $2100. Step 2: Balance financed = 21000 - 2100 = $18 900. Step 3: Time T = 60 months = 5 years. Step 4: Simple interest on the balance: SI = (P * R * T) / 100 = (18900 * 12 * 5) / 100. Step 5: Compute 18900 * 12 = 226800; then 226800 * 5 = 1134000. Step 6: Divide by 100: SI = 1134000 / 100 = $11 340. Step 7: Total amount to be repaid via instalments = balance + interest = 18 900 + 11 340 = $30 240. Step 8: Monthly instalment = 30240 / 60 = $504.

Verification / Alternative check:
Multiply the monthly instalment of $504 by 60 months to confirm the total repaid via instalments: 504 * 60 = 30 240, which matches the computed total of principal plus interest. The deposit is separate and does not affect the calculation of each monthly instalment on the financed balance.

Why Other Options Are Wrong:
$503 and $505 are close to the correct amount but do not exactly match the total repayable when multiplied by 60 months. $506 would give a larger total repayment than required, overpaying the sum of principal and interest.

Common Pitfalls:
Some students mistakenly compute interest on the full cash price instead of the financed balance, or they incorrectly convert the number of months into years. Another common error is to use compound interest instead of simple interest, which is not what the question specifies. Always be careful about whether the deposit is included or excluded from the interest calculation.

Final Answer:
The required monthly instalment on the hire purchase is $504.