A certain sum of money invested at compound interest at a rate of 15% per annum (compounded annually) earns Rs. 3225 as compound interest in 2 years. What is the original sum (principal) in rupees?

Introduction / Context: This is a reverse compound interest problem where the interest amount over a given period is known, and the original principal must be determined. The interest is compounded annually at a rate of 15% per annum for 2 years, and the total compound interest earned over those 2 years is Rs. 3225.

Given Data / Assumptions:

Compound interest CI for 2 years = Rs. 3225 Rate of interest r = 15% per annum Time t = 2 years Compounding is annual Principal P is unknown

Concept / Approach: For annual compounding, the amount after 2 years is: A = P * (1 + r/100)^2. The compound interest is: CI = A − P = P * [(1 + r/100)^2 − 1]. Thus: CI = P * [(1.15)^2 − 1]. We compute (1.15)^2, subtract 1 to get the interest factor, and then use CI = P * factor to solve for P.

Step-by-Step Solution: Step 1: Compute the 2-year growth factor. (1.15)^2 = 1.15 * 1.15 = 1.3225. Step 2: Find the interest factor. (1.15)^2 − 1 = 1.3225 − 1 = 0.3225. Step 3: Relate CI to P. CI = P * 0.3225. 3225 = 0.3225 * P. Step 4: Solve for P. P = 3225 / 0.3225 = 10,000.

Verification / Alternative check: Verify by calculating CI from P = 10,000. Amount after 2 years at 15% compounded annually: A = 10,000 * 1.3225 = 13,225. CI = 13,225 − 10,000 = 3,225 rupees. This matches the given compound interest, confirming that the principal must be Rs. 10,000.

Why Other Options Are Wrong: If P were 15,000, CI would be 15,000 * 0.3225 = 4,837.50. For 20,000, CI would be 6,450. For 32,250, CI would be even larger. None of these equal 3,225, so those options cannot be correct.

Common Pitfalls: A common mistake is to use simple interest formulas or to treat 15% as a flat rate per year without squaring the factor for 2 years. Others may try to solve using yearly interest step-by-step without recognizing the compact formula, which can introduce arithmetic errors. Recognizing the clean factor 1.3225 in this problem simplifies the solution significantly.

Final Answer: The original sum (principal) was Rs. 10,000.