The difference between the compound interest and the simple interest on a certain sum of money for 2 years at 5% per annum is Rs 41. What is the principal amount (sum of money)?

Introduction:
This problem asks you to find the principal when you are given the difference between compound interest and simple interest for 2 years at the same rate. This is a standard shortcut type question where a known formula for the difference between CI and SI over 2 years can be used.

Given Data / Assumptions:

• Difference between CI and SI for 2 years = Rs 41
• Annual rate of interest r = 5% per annum
• Time t = 2 years
• We need to find the principal P

Concept / Approach:
For 2 years at rate r per annum, the difference between compound interest and simple interest on principal P is given by:
Difference = P * (r/100)^2This comes from the extra interest earned in compound interest due to interest on interest in the second year. Using this direct formula allows quick calculation of the principal.

Step-by-Step Solution:
Step 1: Write the formula for difference.Difference = P * (r/100)^2Here, Difference = 41, r = 5%Step 2: Substitute the values.41 = P * (5/100)^2(5/100)^2 = 25 / 10,000 = 1 / 400So 41 = P * (1 / 400)Step 3: Solve for P.P = 41 * 400P = Rs 16,400

Verification / Alternative check:
We can check quickly by recomputing the difference. With P = Rs 16,400 and r = 5%,
Difference = 16,400 * (5/100)^2Difference = 16,400 * 1/400 = Rs 41This exactly matches the given difference, confirming that the principal is correct.

Why Other Options Are Wrong:

• Rs 7,200, Rs 9,600, Rs 8,400, Rs 12,300: For each of these values, P * (5/100)^2 would not equal Rs 41. They are distractors that reflect typical calculation mistakes or wrong use of the formula.

Common Pitfalls:
Some students try to compute SI and CI separately using long methods instead of using the direct formula. Others misremember the formula, sometimes writing P * r^2 / 200 instead of P * (r^2 / 10,000). Always remember that (r/100)^2 is used for 2 years when comparing CI and SI.

Final Answer:
The principal amount (sum of money) is Rs 16,400.