Simple Interest — Equal annual payments of ₹ 160 are made at the end of each year for 5 years. At 5% per annum simple interest, these payments together will discharge a debt of how much (amount due at the end of year 5)?

Introduction / Context:With simple interest, the future value at a common focal date (here, end of year 5) of each payment is found by adding linear interest for the remaining years to the focal date. The sum of these accumulated values equals the debt amount due at that focal date.

Given Data / Assumptions:

• Payment each year (end): ₹ 160.
• Number of payments: 5 (at ends of years 1 to 5).
• Rate: 5% per annum, simple interest.
• Focal date: end of year 5.

Concept / Approach:Accumulate each installment to end of year 5 using simple interest: FV_k = 160 * (1 + r * (5 - k)), for k = 1…5. Sum all five future values to get the total amount these payments can discharge at the focal date.

Step-by-Step Solution:Accumulation factors to end year 5: for k=1: (1+0.05*4)=1.20; k=2: 1.15; k=3: 1.10; k=4: 1.05; k=5: 1.00.Sum of factors = 1.20 + 1.15 + 1.10 + 1.05 + 1.00 = 5.50.Total future value = 160 * 5.50 = ₹ 880.

Verification / Alternative check:Each payment grows linearly by 5% per year for the remaining years; arithmetic series of factors ensures a neat sum.

Why Other Options Are Wrong:₹ 980 and ₹ 1,100 overstate the accumulation; ₹ 440 and ₹ 220 undercount or ignore time value.

Common Pitfalls:Discounting (present value) instead of accumulating to a future date, or incorrectly compounding under SI.

Final Answer:₹ 880