What is the difference (in rupees) between: (1) the compound interest earned in 1 year on ₹10,000 at 40% per annum when interest is compounded quarterly, and (2) the compound interest earned in 1 year when it is compounded annually at the same 40% per annum?

Introduction:
This question tests comparing compound interest under different compounding frequencies for the same annual rate and time. More frequent compounding produces a higher amount because interest is added sooner and then earns interest again within the year. Here we compare quarterly compounding versus annual compounding for 1 year at a high rate of 40%, which makes the difference noticeable.

Given Data / Assumptions:

• Principal P = ₹10,000
• Annual rate r = 40% per annum
• Time = 1 year
• Case 1: Compounded quarterly (4 times/year)
• Case 2: Compounded annually (1 time/year)

Concept / Approach:
Compute CI in each case and subtract. For annual compounding over 1 year: amount = P * (1 + 40/100). CI = amount - P. For quarterly compounding: quarterly rate = 40%/4 = 10%, number of quarters = 4, amount = P * (1 + 10/100)^4 = P * (1.1)^4. CI is again amount minus principal. Difference is CI_quarterly - CI_annual.

Step-by-Step Solution:
Annual compounding amount = 10000 * 1.40 = 14000 CI (annual) = 14000 - 10000 = 4000 Quarterly rate = 10% Quarterly compounding factor = (1.1)^4 (1.1)^2 = 1.21, so (1.1)^4 = 1.21^2 = 1.4641 Quarterly amount = 10000 * 1.4641 = 14641 CI (quarterly) = 14641 - 10000 = 4641 Difference = 4641 - 4000 = 641

Verification / Alternative check:
Since quarterly compounding is more frequent, the difference must be positive. The computed difference ₹641 is consistent and matches the gap between 1.4641P and 1.40P for P=10000.

Why Other Options Are Wrong:
461, 463, and 346 are too small compared to the correct compounding gap at 40% annual. 400 matches neither CI difference nor any correct intermediate step.

Common Pitfalls:
Using 40% as quarterly rate, using only one quarter instead of four, or subtracting annual amount from quarterly interest without consistently converting to CI first.

Final Answer:
The required difference is ₹641.