Compound Interest – Interest earned in the second year: What principal will generate ₹ 208 as compound interest in the second year at 4% per annum (annual compounding)?

Introduction / Context:
Under annual compounding, the interest in the second year equals the first-year amount times r, i.e., P * (1 + r) * r. This lets us back-solve for P from the known second-year interest.

Given Data / Assumptions:

• Second-year interest = ₹ 208
• r = 4% = 0.04
• Compounded annually

Concept / Approach:
Second-year CI = P * (1 + r) * r = P * 1.04 * 0.04 = 0.0416 P.

Step-by-Step Solution:
0.0416 P = 208 → P = 208 / 0.0416 = ₹ 5,000

Verification / Alternative check:
Year 1 interest = 5000 * 4% = 200 → amount = 5200. Year 2 interest = 5200 * 4% = 208 (matches).

Why Other Options Are Wrong:
₹ 6,500 or ₹ 10,000 produce second-year interest larger than ₹ 208; ₹ 1,30,000 is far off.

Common Pitfalls:
Using P * r (first-year interest) instead of P * (1 + r) * r for the second year.

Final Answer:
₹ 5000