A sapphire ring has a marked cash price of $1,800. It is offered on hire purchase terms with a $200 deposit and the remaining balance to be paid over 24 equal monthly instalments. Interest is charged at a flat rate of 11.5% per annum on the outstanding balance (cash price minus deposit). What is the amount of each monthly repayment?

Introduction / Context:
This problem is based on a common consumer finance arrangement called hire purchase. The buyer pays a deposit and then repays the remaining balance with interest through equal monthly instalments. The key concept is the calculation of flat rate simple interest on the financed balance, not on the full cash price. Understanding such calculations helps in comparing the true cost of credit when buying goods like jewellery, appliances, or vehicles on instalment plans.

Given Data / Assumptions:

Cash price of the sapphire ring = $1,800
Deposit paid immediately = $200
Balance financed on hire purchase = cash price minus deposit
Flat rate simple interest = 11.5 percent per annum on the financed balance
Repayment term = 24 months = 2 years
Monthly instalments are equal throughout the term

Concept / Approach:
First, compute the financed balance by subtracting the deposit from the cash price. Next, calculate simple interest on this balance using the formula I = P * R * T, where P is the financed amount, R is the annual rate in decimal, and T is the time in years. Then add the interest to the financed balance to obtain the total amount to be repaid in instalments. Finally, divide the total payable by the number of monthly payments to obtain the monthly instalment amount.

Step-by-Step Solution:
Step 1: Compute the financed balance. Financed balance P = 1,800 - 200 = 1,600 dollars. Step 2: Convert the annual flat rate from percent to decimal. R = 11.5 percent = 11.5 / 100 = 0.115. Step 3: Express the term T in years: 24 months = 2 years. Step 4: Compute simple interest on the financed balance. I = P * R * T = 1,600 * 0.115 * 2. Step 5: Calculate the interest: 1,600 * 0.115 = 184 per year. Step 6: For 2 years, I = 184 * 2 = 368 dollars. Step 7: Compute total amount to be repaid in instalments. Total instalment amount = financed balance + interest = 1,600 + 368 = 1,968 dollars. Step 8: Number of monthly instalments = 24. Step 9: Monthly instalment = 1,968 / 24 = 82 dollars.

Verification / Alternative check:
To verify, multiply the monthly instalment back by the number of months. That is 82 * 24 = 1,968 dollars. Subtract the financed balance of 1,600 dollars from this total to obtain the interest component: 1,968 - 1,600 = 368 dollars. Now check whether this interest equals simple interest at 11.5 percent per annum over 2 years on 1,600 dollars. Indeed, 1,600 * 0.115 * 2 = 368. This confirms that the monthly instalment of 82 dollars is correct.

Why Other Options Are Wrong:
Option $53 and option $42 produce far too little total repayment over 24 months and would not cover both principal and the flat rate interest. Option $62 is closer but still results in a total repayment of only 62 * 24 = 1,488 dollars, which is even less than the financed balance of 1,600 dollars. Only 82 dollars per month correctly repays both the financed balance and the charged interest.

Common Pitfalls:
One common mistake is to apply the interest to the entire cash price instead of the balance after the deposit, which inflates the interest excessively. Another error is to treat 24 months as 24 years in the formula, or to treat 11.5 percent as a monthly rate instead of an annual rate. Always convert the term into years for the simple interest formula and ensure that the deposit is subtracted before calculating the financed amount.

Final Answer:
Each monthly repayment on the hire purchase plan is $82.