CI vs SI for 1 year at 10% when reckoned half-yearly: Find the difference between compound interest and simple interest on ₹ 600 for 1 year at 10% per annum when compounding (for CI) is half-yearly.

Introduction / Context:For one year, simple interest at 10% is straightforward. For CI with half-yearly crediting, apply 5% twice. The CI will be slightly higher, and the small difference demonstrates frequency effects within a single year.

Given Data / Assumptions:

• P = ₹ 600
• Nominal r = 10% p.a.
• Compounding frequency = half-yearly (i = 5% per half-year, n = 2)

Concept / Approach:SI(1 year) = P * 0.10. CI amount with half-yearly = P * (1.05)^2. The difference is CI − SI.

Step-by-Step Solution:SI = 600 * 0.10 = ₹ 60.00A_CI = 600 * (1.05)^2 = 600 * 1.1025 = ₹ 661.50 → CI = ₹ 61.50Difference = 61.50 − 60.00 = ₹ 1.50

Verification / Alternative check:Effective annual rate under half-yearly compounding at 10% nominal is 1.05^2 − 1 = 10.25%; 10.25% of 600 is ₹ 61.50 (CI).

Why Other Options Are Wrong:₹ 6.60 and ₹ 4.40 are far too large; zero would only occur with no compounding or zero rate; ₹ 3.00 is not exact.

Common Pitfalls:Using 10% twice (giving 20%) or treating half-yearly as still 10% flat with no compounding.

Final Answer:₹ 1.50