If the compound interest on a sum of Rs.5000 at the rate of 10% per annum is…

For interest compounded yearly, the amount after t years is given by A = P(1 + r/100)t, where P is the principal, r is the annual rate of interest (in %), and t is the time in years. The compound interest is CI = A − P.

1. Here, P = Rs. 5000, r = 10% per annum, and CI = Rs. 1050. Since the interest is compounded yearly, the number of compounding periods per year, n = 1.

2. The total amount after t years is A = P + CI = 5000 + 1050 = Rs. 6050.

3. Substituting into the compound interest formula: A = P(1 + r/100)t gives 6050 = 5000 × (1.1)t.

4. Dividing both sides by 5000: (1.1)t = 6050/5000 = 1.21.

5. Since 1.12 = 1.21, comparing powers gives t = 2 years.

Verification: substituting t = 2 back into the formula gives A = 5000 × 1.12 = 5000 × 1.21 = Rs. 6050, and the compound interest is 6050 − 5000 = Rs. 1050 — exactly matching the value given in the question, confirming the time period is 2 years.