The rate of compound interest at which a sum of Rs. 8000 amounts to Rs. 8820…

Concept: For compound interest compounded annually, the amount A after n years on principal P at rate r% per annum follows the identity A = P(1 + r/100)n. To find an unknown rate, substitute the known amount, principal and time into this identity and solve for r.

Applying it here:

1. Write the compound interest identity for n = 2 years: A = P(1 + r/100)2.

2. Substitute the given values P = 8000 and A = 8820: 8820 = 8000 × (1 + r/100)2.

3. Divide both sides by 8000: (1 + r/100)2 = 8820/8000 = 1.1025.

4. Take the square root of both sides: 1 + r/100 = √1.1025 = 1.05.

5. Solve for r: r/100 = 0.05, so r = 5.

Cross-check: Substituting r = 5 back into the identity: 8000 × (1.05)2 = 8000 × 1.1025 = Rs. 8820, exactly matching the amount stated in the question, confirming the rate.

So the rate of compound interest is 5% yearly.