Compound vs Simple Interest — Use 2-year difference to recover principal: For a certain principal, the difference between the 2-year compound interest and the 2-year simple interest at 8% per annum is ₹ 32. Find the principal.

Introduction / Context:
The difference between compound interest (CI) and simple interest (SI) over exactly two years at the same annual rate is a classic identity. It isolates the “extra” interest-on-interest that CI accumulates. This lets us back-solve the principal without separately knowing the amount.

Given Data / Assumptions:

• Annual rate r = 8% = 0.08
• Time t = 2 years
• CI − SI over 2 years = ₹ 32
• Principal P unknown

Concept / Approach:
For two years at rate r (decimal), CI − SI = P * r^2. This follows from CI for 2 years = P[(1 + r)^2 − 1] = P(2r + r^2), SI for 2 years = P(2r), hence the difference is P r^2.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 5250, ₹ 5550, ₹ 6000, ₹ 4800 do not satisfy 32 = P * 0.0064.

Common Pitfalls:

• Using r as “8” instead of 0.08 in the formula.
• Applying the identity to durations other than 2 years; it is specific to 2 years in this neat form.

Final Answer:
₹ 5000.