The difference between the compound interest and simple interest for 3 years at 5% per annum on Rs 8,000 will be

Work it year by year. Simple interest is Rs 400 each year, so for 3 years it is Rs 1,200. Compound interest earns interest on accumulated interest. Year 1 gives Rs 400, taking the amount to Rs 8,400. Year 2 earns 5% of 8,400 = Rs 420, so the extra over SI is Rs 20. Year 3 earns 5% of 8,820 = Rs 441, so the extra over SI is Rs 41. Total CI is 400 + 420 + 441 = Rs 1,261, and the difference is 1,261 minus 1,200 = Rs 61.

Check with the formula: amount = 8000 x (1.05)^3 = Rs 9,261, so CI = Rs 1,261. The shortcut for 3 years is P x (R/100)^2 x (300+R)/100 = 8000 x 0.0025 x 3.05 = Rs 61.

Why the others fail: Rs 55, Rs 69 and Rs 75 do not come out of this data. Stopping after the year-2 extra gives only Rs 20, and missing the year-3 interest on interest gives a wrong figure.

Concept: the gap between compound and simple interest comes entirely from interest earned on interest. For Mains, the same logic explains why long-tenure loans and savings behave so differently.

Trap: stopping at the year-2 extra or using the wrong power of 1.05. Always write the year-by-year principal before comparing.