Restructuring a due payment under simple interest: A must pay B Rs. 220 after 1 year. Instead, B asks A to pay Rs. 110 in cash now and defer Rs. 110 for 2 years. Assuming 10% per annum simple interest, what is the effect of this new mode of payment on A (gain or loss)?

Introduction / Context:
When a due payment is split into an immediate payment and a postponed balance, we evaluate both arrangements at a common “now” using simple-interest present worth. Comparing present worths shows whether the payer gains or loses under the new arrangement.

Given Data / Assumptions:

• Original obligation: 220 due after 1 year, r = 10% p.a. simple.
• New plan: pay 110 now and 110 after 2 years.
• All comparisons are done using present worth PW = A / (1 + r * t).

Concept / Approach:
Compute PW of the original single payment and PW of the split payments; then compare. If PW(new) > PW(original), the payer loses (pays more in present terms); if PW(new) < PW(original), the payer gains.

Step-by-Step Solution:
PW(original) = 220 / (1 + 0.10 * 1) = 220 / 1.10 = 200.PW(new) = 110 (now) + 110 / (1 + 0.10 * 2) = 110 + 110 / 1.20.Compute 110 / 1.20 = 91.6667 ⇒ PW(new) = 110 + 91.6667 = 201.6667.Difference = 201.6667 − 200 = 1.6667 (≈ Rs. 1.66). Since it is higher, A loses Rs. 1.66.

Verification / Alternative check:
Using the true-discount identity TD = A * r * t / (1 + r * t), you can confirm each present-worth conversion yields the same result as above for simple interest, reinforcing the difference of about Rs. 1.66.

Why Other Options Are Wrong:

• “No gain/loss” ignores the extra present burden created by the 2-year deferred portion.
• “A gains Rs. 7.34” or “A loses Rs. 7.34” are far from the precise computation under simple interest.

Common Pitfalls:

• Discounting the 110 now (it has no deferral time).
• Accidentally using compound interest or misusing time periods.

Final Answer:
A loses Rs. 1.66