The difference between simple interest and compound interest, compounded annually, on a certain sum of money for 2 years at 12 percent per annum is Rs 72. What is the value of the sum in rupees?

Introduction / Context:
This problem is another application of the standard formula for the difference between compound interest and simple interest over 2 years at the same annual rate. Here, the rate is 12 percent per annum, and the difference between CI and SI is given as Rs 72. The task is to find the principal. This type of question strengthens the understanding of how compound interest adds an extra component over simple interest in the second year.

Given Data / Assumptions:
- Time period T = 2 years.
- Rate of interest R = 12 percent per annum.
- Interest is compounded annually for the compound interest calculation.
- Difference between CI and SI over 2 years is D = Rs 72.
- We must find the principal P.

Concept / Approach:
For 2 years, the difference between compound and simple interest on a principal P at annual rate R is:
D = CI − SI = P * (R/100)^2This formula comes from the extra interest in the second year on the first year's interest. Knowing D and R, we can solve directly for P without first computing CI and SI separately.

Step-by-Step Solution:
Given R = 12 %, so R/100 = 0.12.Compute (R/100)^2 = (0.12)^2 = 0.0144.Difference D is 72, so D = P * 0.0144.Thus, 72 = P * 0.0144.Solve for P: P = 72 / 0.0144.Compute P: 72 / 0.0144 = 5000.Therefore, the required sum is Rs 5000.

Verification / Alternative check:
Let P = 5000 and R = 12 %. Simple interest for 2 years is SI = (5000 * 12 * 2) / 100 = 5000 * 0.24 = 1200. For compound interest, amount A = 5000 * (1.12)^2. (1.12)^2 = 1.2544, so A = 5000 * 1.2544 = 6272. Compound interest CI = A − P = 6272 − 5000 = 1272. The difference CI − SI = 1272 − 1200 = 72, which matches the given value and confirms that P = 5000 is correct.

Why Other Options Are Wrong:
If P were Rs 10000, the difference D would be 10000 * 0.0144 = 144, not 72. For Rs 20000 it would be 288, and for Rs 15000 it would be 216. A principal of Rs 2500 would yield a difference of 36. Only Rs 5000 gives the exact difference of Rs 72 at 12 percent per annum for 2 years.

Common Pitfalls:
Students sometimes mistakenly use 12 instead of 0.12 when squaring the rate, which produces huge errors. Another mistake is to try to compute CI and SI step by step without recognizing the shortcut formula D = P * (R/100)^2. Keeping track of rate as a decimal and using the direct formula makes the problem simple and reduces chances of miscalculation.

Final Answer:
The value of the sum is Rs 5000.