The difference between the simple interest and the compound interest on a certain sum of money at 20% per annum for 2 years is Rs 56. What is the value of the sum (principal)?

Introduction:
This is a classic shortcut question involving the difference between compound interest and simple interest for 2 years. At a given annual rate, you can use a direct formula to relate this difference to the principal, making the calculation quick and efficient.

Given Data / Assumptions:

• Rate of interest (r) = 20% per annum.
• Time t = 2 years.
• Difference between SI and CI for 2 years = Rs 56 (CI − SI or SI − CI in magnitude).
• Interest is compounded annually for the compound interest case.
• We must find the principal P.

Concept / Approach:
For 2 years with annual compounding, the difference between compound interest and simple interest is given by Difference = P * (r/100)^2. This comes from the fact that compound interest earns extra interest in the second year on the first year’s interest, while simple interest does not.

Step-by-Step Solution:
Use the formula: Difference = P * (r/100)^2Here r = 20%, so r/100 = 0.20Thus Difference = P * (0.20)^2 = P * 0.04We are given: P * 0.04 = 56So P = 56 / 0.04P = 56 * 25 = Rs 1400

Verification / Alternative Check:
If P = Rs 1400 and r = 20%, simple interest for 2 years is SI2 = 1400 * 20 * 2 / 100 = 1400 * 0.40 = Rs 560. Compound amount A = 1400 * (1.20)^2 = 1400 * 1.44 = Rs 2016. CI2 = 2016 − 1400 = Rs 616. Difference CI2 − SI2 = 616 − 560 = Rs 56, matching the given difference.

Why Other Options Are Wrong:
Rs 3680, Rs 2650 and Rs 1170: Each of these values, when used as P, leads to a difference of P * 0.04 that is not equal to Rs 56.Rs 2800: Gives a difference of 2800 * 0.04 = Rs 112, which is double the required value.

Common Pitfalls:
Some candidates mistakenly use the simple interest formula instead of the dedicated difference formula, or they forget to square the rate fraction. Others misinterpret which difference is given, but since only the magnitude matters here, the formula still applies correctly.

Final Answer:
The required sum of money (principal) is Rs 1400.