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?
Aptitude
Simple Interest
Difficulty: Medium
Choose an option
Answer
Correct Answer: Rs 100
Explanation
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:
Accumulation factors to end of year 5: 1.32 (4 yrs), 1.24 (3 yrs), 1.16 (2 yrs), 1.08 (1 yr), 1.00 (0 yr)Sum of factors = 1.32 + 1.24 + 1.16 + 1.08 + 1.00 = 5.80Let annual payment = X. Then X * 5.80 = 580 ⇒ X = Rs 100Verification / Alternative check:
Backward check confirms total accumulated value equals Rs 580 at year 5.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.