Find the difference between the compound interests on Rs. 5000 for 1½ years at 4% p.a. when interest is compounded (i) yearly and (ii) half-yearly.

Problem restatement
Compute CI for 1½ years at 4% p.a. under two regimes: annual compounding vs half-yearly compounding. Report the difference (half-yearly minus yearly).

Given data

• P = Rs. 5000
• r = 4% p.a.
• Time = 1.5 years

Concept/Approach
(i) Compounded yearly: 1 full year compounded, then simple interest for the remaining half-year on the amount after 1 year.
(ii) Compounded half-yearly: 3 half-year periods at 2% each.

Step-by-step calculation
(i) Yearly: Amount = P × 1.04 × (1 + 0.04 × 0.5) = P × 1.04 × 1.02 = P × 1.0608(ii) Half-yearly: Amount = P × (1.02)³ = P × 1.061208Difference in amount = P(1.061208 − 1.0608) = P × 0.000408With P = 5000: Difference = 5000 × 0.000408 = Rs. 2.04

Verification/Alternative
Compute each amount numerically: Yearly = 5000 × 1.0608 = 5304.00; Half-yearly = 5000 × 1.061208 = 5306.04; Difference = 2.04.

Common pitfalls
Applying annual compounding for 1.5 years as 1.04^1.5 (not standard in yearly compounding) or ignoring the half-year SI treatment.