Simple Interest – Equal annual payments to discharge a debt: What equal annual payment will exactly discharge a debt of Rs 580 due in 5 years at 8% per annum simple interest, assuming payments are made at the end of each year?

Introduction / Context:When equal annual payments are made under simple interest and the target is to clear a debt at the end of a fixed period, earlier payments accrue simple interest up to the final date. The sum of accumulated values of all payments equals the debt due at maturity.

Given Data / Assumptions:

• Debt due at end of year 5: Rs 580
• Rate r = 8% per annum
• Five equal payments X at ends of years 1, 2, 3, 4, 5

Concept / Approach:Accumulate each payment to the end of year 5 using SI factors: (1 + r * n), where n is the number of years remaining to year 5. Sum of accumulated payments = 580.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Rs 166.40 / 120 / 90 / 65.60: do not satisfy X * 5.80 = 580.

Common Pitfalls:

• Compounding instead of using simple accumulation factors.
• Using discounting to present instead of accumulation to year 5.

Final Answer:Rs 100 per year.