What would be the interest accrued in two years on Rs.300 if the sum is…

Concept: Compound interest is calculated on the accumulated amount from previous periods, not just the original principal. For principal P, rate r% per annum, and time n years compounded annually, the amount is A = P(1 + r/100)n, and the compound interest is CI = A − P.

Application:

1. Identify the values: Principal P = Rs. 300, Rate r = 10% per annum, Time n = 2 years.

2. Compute the yearly growth factor: 1 + r/100 = 1 + 10/100 = 1.1.

3. Raise the growth factor to the power of n: (1.1)2 = 1.21.

4. Compute the amount after 2 years: A = P × 1.21 = 300 × 1.21 = Rs. 363.

5. Compute the compound interest: CI = A − P = 363 − 300 = Rs. 63.

Cross-check: for 2 years, CI = SI + P(r/100)2. The simple interest is SI = (P × r × n)/100 = (300 × 10 × 2)/100 = Rs. 60, and the interest-on-interest term is P(r/100)2 = 300 × (10/100)2 = Rs. 3, so CI = 60 + 3 = Rs. 63 — the two methods agree.

Therefore, the interest accrued in two years is Rs. 63.