The difference between simple interest and compound interest, compounded annually, on a certain sum of money for 2 years at the rate of 4% per annum is Rs 1. What is the principal (sum of money in rupees)?

Introduction:
This is another short question where the difference between compound interest and simple interest over 2 years is used to back calculate the principal. The rate is small (4%), and a standard formula makes this calculation very quick in competitive exams.

Given Data / Assumptions:

• Rate of interest (r) = 4% per annum.
• Time period (t) = 2 years.
• Difference between simple interest and compound interest for 2 years is Rs 1 (in magnitude).
• Compounding is annual in the CI case.
• We need to determine the principal P.

Concept / Approach:
For 2 years and annual compounding, the difference between CI and SI is given by Difference = P * (r/100)^2. This formula captures the interest on interest that simple interest does not include. By substituting the given values, we can immediately find P.

Step-by-Step Solution:
Difference = P * (r/100)^2Here r = 4%, so r/100 = 0.04Thus Difference = P * (0.04)^2 = P * 0.0016Given that the difference is Rs 1, we have P * 0.0016 = 1So P = 1 / 0.0016P = 625

Verification / Alternative Check:
If P = Rs 625, compute SI and CI for 2 years. Simple interest: SI2 = 625 * 4 * 2 / 100 = 625 * 0.08 = Rs 50. Compound amount: A = 625 * (1.04)^2 = 625 * 1.0816 = Rs 676.0. CI2 = 676 − 625 = Rs 51. Difference CI2 − SI2 = 51 − 50 = Rs 1, matching the statement.

Why Other Options Are Wrong:
Rs 620, Rs 630, Rs 640 and Rs 600: For each of these principals, P * 0.0016 gives differences not equal to 1. For example, 600 * 0.0016 = 0.96, and 640 * 0.0016 = 1.024.

Common Pitfalls:
Students sometimes forget to square the rate fraction and instead multiply only by r/100, which leads to a wrong principal. Others may attempt to calculate SI and CI separately without realizing the availability of the shortcut formula, making the computation longer and more error prone.

Final Answer:
The principal (sum of money) is Rs 625.