Find the difference between the simple interest and the compound interest on Rs. 1200 for 1 year at 10% per annum, when interest is reckoned half-yearly.

Problem restatement
Compare CI (compounded half-yearly) and SI for 1 year at the same nominal rate (10%) on Rs. 1200; report CI − SI.

Given data

• P = Rs. 1200
• Nominal rate = 10% p.a.; half-yearly compounding ⇒ 5% per half-year
• Time = 1 year = 2 half-years

Concept/Approach
Compute CI via amount factor (1 + r÷m)^m for m = 2. Compute SI via P × r × t. Take the difference.

Step-by-step calculation
Amount (CI) = 1200 × (1 + 0.05)² = 1200 × 1.1025 = 1323.00CI = 1323.00 − 1200 = Rs. 123.00SI = P × r × t = 1200 × 0.10 × 1 = Rs. 120.00Difference = 123.00 − 120.00 = Rs. 3

Common pitfalls
Using 0.4 hour–type conversions here is irrelevant; the compounding frequency is semi-annual: use 5% twice.