The difference between the compound interest and the simple interest on the same principal at the rate of 12% per annum for 3 years is Rs 112.32, when interest is compounded annually. Using this information about the excess of compound interest over simple interest, what is the principal amount?

Introduction / Context:
This question compares compound interest with simple interest on the same principal, time, and rate. For a given principal, compound interest over multiple years is always higher than simple interest because interest is earned on both principal and accumulated interest. The problem tells us that this excess of compound interest over simple interest is Rs 112.32 when the rate is 12% per annum for 3 years. The candidate must use the standard formulas for simple and compound interest and set up an equation to determine the principal. This is a typical higher level interest problem in many aptitude exams.

Given Data / Assumptions:

• Rate of interest R = 12% per annum.
• Time period T = 3 years.
• Principal amount P rupees (unknown).
• Interest is compounded annually in the compound interest case.
• Difference (CI − SI) over 3 years = Rs 112.32.

Concept / Approach:
Simple interest for 3 years is:
SI = (P * R * T) / 100 = (P * 12 * 3) / 100 = 0.36P For compound interest compounded annually, amount is:
Amount A = P * (1 + R / 100) ^ T With R = 12% and T = 3 years:
A = P * (1.12) ^ 3 Then compound interest is:
CI = A − P = P * ((1.12) ^ 3 − 1) The problem gives:
CI − SI = P * ((1.12) ^ 3 − 1) − 0.36P = 112.32 Factoring P allows us to compute P from this equation once we evaluate (1.12) ^ 3 accurately.

Step-by-Step Solution:
Compute (1.12) ^ 3. (1.12) ^ 2 = 1.2544. (1.12) ^ 3 = 1.2544 * 1.12 = 1.404928. Thus CI = P * (1.404928 − 1) = P * 0.404928. Simple interest for 3 years at 12%: SI = 0.36P. Difference CI − SI = 0.404928P − 0.36P = 0.044928P. Given CI − SI = Rs 112.32. So 0.044928P = 112.32. P = 112.32 / 0.044928. P = 2500. Therefore, the principal is Rs 2500.

Verification / Alternative check:
Check simple interest on Rs 2500 for 3 years at 12%. SI = (2500 * 12 * 3) / 100 = 900. For compound interest, amount A = 2500 * (1.12) ^ 3 = 2500 * 1.404928 = 3512.32. Compound interest CI = A − P = 3512.32 − 2500 = 1012.32. The difference CI − SI = 1012.32 − 900 = 112.32, which matches the given value. This confirms that P = Rs 2500 is correct.

Why Other Options Are Wrong:
If P were Rs 25000 or Rs 50000, the difference CI − SI would be ten or twenty times larger than 112.32, which is clearly inconsistent.
If P were Rs 5000 or Rs 3000, recalculating CI and SI would give differences that do not equal 112.32. Only P = Rs 2500 produces exactly the given difference between compound interest and simple interest over 3 years at 12% per annum.

Common Pitfalls:
Many students miscalculate the power (1.12) ^ 3 or mistakenly use 3 * 12% for compound interest as if it were simple interest. Another error is to subtract incorrectly when finding CI − SI, or to round intermediate steps too aggressively, losing precision. Keeping a few decimal places until the end and systematically applying the formulas helps prevent these mistakes. It is also important to remember that the difference increases with time and rate, so unrealistic principal guesses can be ruled out by estimation.

Final Answer:
The principal amount for which the difference between compound interest and simple interest is Rs 112.32 is Rs 2500.