Compound vs Simple Interest – Difference given to find principal: At 8% per annum, compounded annually, the compound interest exceeds the simple interest by ₹ 6.40 over 2 years. Find the principal.

Introduction / Context:
For 2 years, CI − SI = P * r^2 / 10000. Knowing r and the difference, we can solve directly for P and then sanity-check.

Given Data / Assumptions:

• CI − SI = ₹ 6.40
• r = 8% per annum
• t = 2 years

Concept / Approach:
6.40 = P * (8^2) / 10000 = P * 64 / 10000 = 0.0064 P → P = 6.40 / 0.0064.

Step-by-Step Solution:
P = 1000(Optional) SI = 1000 * 8% * 2 = ₹ 160; CI = 160 + 6.40 = ₹ 166.40

Verification / Alternative check:
Compute CI via A = 1000(1.08)^2 − 1000 = 1000(1.1664 − 1) = 166.40; difference with SI = 6.40.

Why Other Options Are Wrong:
₹ 800 and ₹ 1800 give differences 5.12 and 11.52, not ₹ 6.40; ₹ 10,000 is off by a factor of 10.

Common Pitfalls:
Using 2 * 8% = 16% of P as the difference (that is SI, not the CI-SI gap).

Final Answer:
₹ 1000