Compound vs Simple Interest – Extra ₹ 10 after 2 years at 5%: At 5% per annum, the amount at compound interest exceeds that at simple interest by ₹ 10 after 2 years. Find the principal.

Introduction / Context:
The 2-year CI–SI shortcut gives a direct route to the principal when the excess is known.

Given Data / Assumptions:

• CI − SI = ₹ 10
• r = 5% per annum
• t = 2 years

Concept / Approach:
CI − SI over 2 years = P * r^2 / 10000. Solve for P.

Step-by-Step Solution:
10 = P * 25 / 10000 → P = 10 / 0.0025P = ₹ 4,000

Verification / Alternative check:
SI = 4000 * 5% * 2 = 400; CI = 4000[(1.05)^2 − 1] = 400 + 10 = 410; difference = 10.

Why Other Options Are Wrong:
₹ 4050/₹ 5000/₹ 5500 yield excesses different from ₹ 10 at 5% for 2 years.

Common Pitfalls:
Forgetting the square on r in the 2-year CI–SI formula.

Final Answer:
₹ 4000