A has to pay Rs. 220 to B after 1 year. B suggests that A should instead pay Rs. 110 in cash now and defer payment of the remaining Rs. 110 for 2 years. A agrees. If the rate of interest is 10% per annum, what is the net gain or loss for A under this new mode of payment?

Introduction / Context:
This question compares two different repayment schedules using the concept of time value of money at 10 percent simple interest per annum. We must determine if changing from a single payment after 1 year to a split payment, with part paid now and part after 2 years, results in any net gain or loss for A. Standard exam convention is to compare the total obligations at a common future date using simple interest.

Given Data / Assumptions:

• Original obligation: pay Rs. 220 after 1 year.
• New plan: pay Rs. 110 now and Rs. 110 after 2 years.
• Simple interest rate r = 10 percent per annum.
• We compare both arrangements by equating values at the end of 2 years.
• Money can earn or cost 10 percent per year in the market.

Concept / Approach:
The idea is to transform each payment schedule into an equivalent amount at a common comparison date, namely 2 years from now. Under simple interest, a payment made earlier grows to a larger amount at a later date. A payment made between now and the comparison date can be accumulated, and a payment made later can be taken as it is at the comparison date. If both schemes result in the same total amount at the comparison date, then there is no net gain or loss.

Step-by-Step Solution:
Step 1: Treat the end of year 2 as the comparison date. Step 2: Under the original scheme, A pays Rs. 220 at the end of year 1. Step 3: If this payment is considered at the end of year 2, it would earn one more year of interest at 10 percent. Amount at end of year 2 = 220 * (1 + 0.10 * 1) = 220 * 1.10 = 242. Step 4: Under the new scheme, A pays Rs. 110 now and Rs. 110 at the end of year 2. Step 5: The Rs. 110 paid now, if hypothetically invested at 10 percent for 2 years, would amount to 110 * (1 + 0.10 * 2) = 110 * 1.20 = 132 at the end of year 2. Step 6: The second payment at the end of year 2 is Rs. 110, so the total equivalent amount at the end of year 2 is 132 + 110 = 242. Step 7: The total amount at the comparison date is the same, 242, under both schemes.

Verification / Alternative check:
Since both arrangements translate to the same obligation of Rs. 242 at the end of year 2, the creditor and debtor are in equivalent positions when the market rate is 10 percent simple interest. This implies that, under this comparison method, there is no financial advantage to either party. Therefore, A neither gains nor loses.

Why Other Options Are Wrong:
Options suggesting that A gains or loses Rs. 7.34, Rs. 7.43, or Rs. 11 arise when inconsistent reference dates or incorrect discounting methods are used. If a single comparison date and the same simple interest rate are correctly applied to all cash flows, both arrangements give the same equivalent amount, so such gains or losses should not appear.

Common Pitfalls:
The main difficulty is choosing and sticking to a single comparison date. Some learners compare cash flows partly at the present and partly at future dates without adjusting using the interest rate, which leads to incorrect differences. Others mix simple interest and true discount formulas incorrectly. Always select a common date, accumulate earlier payments to that date, and then compare totals.

Final Answer:
There is no net gain or loss for A under the new mode of payment.