Second-year interest at 8% CI given first-year interest: At 8% per annum compound interest, the interest in the first year on a principal is ₹ 48. What will be the interest for the second year?

Introduction / Context:
Under compound interest, second-year interest accrues on the first-year amount, not just the principal. Hence I2 = (P * (1 + r)) * r. If we know I1 = P * r, we can compute I2 quickly from I1 without finding P explicitly.

Given Data / Assumptions:

• I1 = ₹ 48 at r = 8% = 0.08
• Annual compounding

Concept / Approach:
I2 = I1 * (1 + r) because I2 = (P * (1 + r)) * r = (P * r) * (1 + r) = I1 * (1 + r).

Step-by-Step Solution:
I2 = 48 * (1 + 0.08) = 48 * 1.08 = ₹ 51.84

Verification / Alternative check:
We can recover P: P = I1 / r = 48 / 0.08 = ₹ 600. Amount after Year-1 = 600 * 1.08 = 648. I2 = 648 * 0.08 = 51.84 (same).

Why Other Options Are Wrong:
₹ 52.55 and ₹ 53.04 assume higher r; ₹ 58.60 is too large; ₹ 50 flatly ignores the compounding uplift.

Common Pitfalls:
Reusing I1 as I2 (SI logic) or forgetting to multiply by (1 + r) for the second year under compounding.

Final Answer:
₹ 51.84