Mr. Duggal invested Rs. 20000 with rate of interest @ 20 p.c.p.a. The interest…

Concept: When the compounding frequency changes partway through an investment, compute the amount separately for each stretch using that stretch's own rate-per-period and number of compounding periods, then chain the amounts together -- the closing amount of one stretch becomes the principal for the next.

1. Year 1 compounds half-yearly, so the 20% annual rate splits into a half-yearly rate of 10%, applied over 2 half-year periods.

2. Amount at the end of year 1: A1 = 20,000 × (1.10)2 = 20,000 × 1.21 = Rs. 24,200.

3. Year 2 compounds yearly, so the 20% yearly rate is applied once on the year-1 amount: A2 = 24,200 × 1.20 = Rs. 29,040.

4. Total compound interest = A2 − P = 29,040 − 20,000 = Rs. 9,040.

Cross-check: Building the half-yearly growth step by step gives the same figure -- 20,000 → 22,000 (first half-year at 10%) → 24,200 (second half-year at 10%) → 29,040 (year 2 at 20%) -- confirming the total interest of Rs. 9,040.