What is the difference in the total interest obtained on Rs. 10000 at the rate…

For a principal P compounding at an effective rate of r% per compounding cycle over T cycles, the amount is A = P(1 + r/100)T, and the compound interest is CI = A − P. When a nominal annual rate is quoted but interest is added only once every few years, the rate for that longer cycle scales with the number of years it spans, and the number of cycles T changes accordingly.

1. Semi-annual compounding: interest is added every 6 months, so over 2 years there are 2 × 2 = 4 compounding cycles, and the rate per cycle is 10/2 = 5%. Amount = 10000(1 + 5/100)4 = Rs 12155.06, so the compound interest = Rs 2155.06.

2. Bi-annual compounding (once every two years): the entire 2-year span is treated as a single compounding cycle, so T = 1, and the rate for that cycle is 10 × 2 = 20% (the nominal annual rate scaled to the 2-year cycle). Amount = 10000(1 + 20/100)1 = Rs 12000, so the compound interest = Rs 2000.

As a check, compounding more often (every 6 months) must yield at least as much interest as compounding less often (once every 2 years) for the same nominal rate — Rs 2155.06 is greater than Rs 2000, which is consistent.

Difference = 2155.06 − 2000 = Rs 155.06, which rounds to Rs 155.